id	sid	tid	token	lemma	pos
ejpam-2044	1	1	european	european	PROPN
ejpam-2044	1	2	journal	journal	PROPN
ejpam-2044	1	3	of	of	ADP
ejpam-2044	1	4	pure	pure	ADJ
ejpam-2044	1	5	and	and	CCONJ
ejpam-2044	1	6	applied	apply	VERB
ejpam-2044	1	7	mathematics	mathematic	NOUN
ejpam-2044	1	8	vol	vol	NOUN
ejpam-2044	1	9	.	.	PUNCT
ejpam-2044	2	1	7	7	NUM
ejpam-2044	2	2	,	,	PUNCT
ejpam-2044	2	3	no	no	INTJ
ejpam-2044	2	4	.	.	NOUN
ejpam-2044	2	5	3	3	NUM
ejpam-2044	2	6	,	,	PUNCT
ejpam-2044	2	7	2014	2014	NUM
ejpam-2044	2	8	,	,	PUNCT
ejpam-2044	2	9	267	267	NUM
ejpam-2044	2	10	-	-	SYM
ejpam-2044	2	11	288	288	NUM
ejpam-2044	2	12	issn	issn	PROPN
ejpam-2044	2	13	1307	1307	NUM
ejpam-2044	2	14	-	-	SYM
ejpam-2044	2	15	5543	5543	NUM
ejpam-2044	2	16	–	–	PUNCT
ejpam-2044	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2044	2	18	characterization	characterization	NOUN
ejpam-2044	2	19	theorems	theorem	VERB
ejpam-2044	2	20	for	for	ADP
ejpam-2044	2	21	scale	scale	NOUN
ejpam-2044	2	22	invariance	invariance	NOUN
ejpam-2044	2	23	property	property	NOUN
ejpam-2044	2	24	of	of	ADP
ejpam-2044	2	25	insurance	insurance	NOUN
ejpam-2044	2	26	premium	premium	NOUN
ejpam-2044	2	27	calculation	calculation	NOUN
ejpam-2044	2	28	principles	principle	NOUN
ejpam-2044	2	29	mykola	mykola	PROPN
ejpam-2044	2	30	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	2	31	,	,	PUNCT
ejpam-2044	2	32	vitaliy	vitaliy	ADV
ejpam-2044	2	33	drozdenko∗	drozdenko∗	VERB
ejpam-2044	2	34	dragomanov	dragomanov	NOUN
ejpam-2044	2	35	national	national	ADJ
ejpam-2044	2	36	pedagogical	pedagogical	ADJ
ejpam-2044	2	37	university	university	NOUN
ejpam-2044	2	38	,	,	PUNCT
ejpam-2044	2	39	department	department	NOUN
ejpam-2044	2	40	of	of	ADP
ejpam-2044	2	41	higher	high	ADJ
ejpam-2044	2	42	mathematics	mathematic	NOUN
ejpam-2044	2	43	,	,	PUNCT
ejpam-2044	2	44	institute	institute	NOUN
ejpam-2044	2	45	of	of	ADP
ejpam-2044	2	46	mathematics	mathematics	PROPN
ejpam-2044	2	47	and	and	CCONJ
ejpam-2044	2	48	physics	physics	NOUN
ejpam-2044	2	49	,	,	PUNCT
ejpam-2044	2	50	9	9	NUM
ejpam-2044	2	51	pyrogov	pyrogov	NOUN
ejpam-2044	2	52	str	str	NOUN
ejpam-2044	2	53	.	.	PUNCT
ejpam-2044	2	54	,	,	PUNCT
ejpam-2044	2	55	room	room	NOUN
ejpam-2044	2	56	460	460	NUM
ejpam-2044	2	57	,	,	PUNCT
ejpam-2044	2	58	kyiv	kyiv	ADJ
ejpam-2044	2	59	,	,	PUNCT
ejpam-2044	2	60	ua-01601	ua-01601	NOUN
ejpam-2044	2	61	,	,	PUNCT
ejpam-2044	2	62	ukraine	ukraine	NOUN
ejpam-2044	2	63	.	.	PUNCT
ejpam-2044	3	1	abstract	abstract	ADJ
ejpam-2044	3	2	.	.	PUNCT
ejpam-2044	4	1	characterization	characterization	NOUN
ejpam-2044	4	2	theorems	theorem	NOUN
ejpam-2044	4	3	for	for	ADP
ejpam-2044	4	4	the	the	DET
ejpam-2044	4	5	scale	scale	NOUN
ejpam-2044	4	6	invariance	invariance	NOUN
ejpam-2044	4	7	property	property	NOUN
ejpam-2044	4	8	of	of	ADP
ejpam-2044	4	9	the	the	DET
ejpam-2044	4	10	insurance	insurance	NOUN
ejpam-2044	4	11	premium	premium	NOUN
ejpam-2044	4	12	calculation	calculation	NOUN
ejpam-2044	4	13	principles	principle	NOUN
ejpam-2044	4	14	are	be	AUX
ejpam-2044	4	15	presented	present	VERB
ejpam-2044	4	16	.	.	PUNCT
ejpam-2044	5	1	theorems	theorem	NOUN
ejpam-2044	5	2	formulated	formulate	VERB
ejpam-2044	5	3	in	in	ADP
ejpam-2044	5	4	a	a	DET
ejpam-2044	5	5	form	form	NOUN
ejpam-2044	5	6	of	of	ADP
ejpam-2044	5	7	necessary	necessary	ADJ
ejpam-2044	5	8	and	and	CCONJ
ejpam-2044	5	9	sufficient	sufficient	ADJ
ejpam-2044	5	10	conditions	condition	NOUN
ejpam-2044	5	11	for	for	ADP
ejpam-2044	5	12	the	the	DET
ejpam-2044	5	13	mentioned	mention	VERB
ejpam-2044	5	14	property	property	NOUN
ejpam-2044	5	15	to	to	PART
ejpam-2044	5	16	be	be	AUX
ejpam-2044	5	17	hold	hold	NOUN
ejpam-2044	5	18	.	.	PUNCT
ejpam-2044	6	1	conditions	condition	NOUN
ejpam-2044	6	2	are	be	AUX
ejpam-2044	6	3	imposed	impose	VERB
ejpam-2044	6	4	on	on	ADP
ejpam-2044	6	5	the	the	DET
ejpam-2044	6	6	auxiliary	auxiliary	ADJ
ejpam-2044	6	7	functions	function	NOUN
ejpam-2044	6	8	with	with	ADP
ejpam-2044	6	9	the	the	DET
ejpam-2044	6	10	help	help	NOUN
ejpam-2044	6	11	of	of	ADP
ejpam-2044	6	12	which	which	PRON
ejpam-2044	6	13	several	several	ADJ
ejpam-2044	6	14	methods	method	NOUN
ejpam-2044	6	15	of	of	ADP
ejpam-2044	6	16	pricing	pricing	NOUN
ejpam-2044	6	17	of	of	ADP
ejpam-2044	6	18	insurance	insurance	NOUN
ejpam-2044	6	19	contracts	contract	NOUN
ejpam-2044	6	20	are	be	AUX
ejpam-2044	6	21	defined	define	VERB
ejpam-2044	6	22	.	.	PUNCT
ejpam-2044	7	1	presented	present	VERB
ejpam-2044	7	2	theorems	theorem	NOUN
ejpam-2044	7	3	cover	cover	VERB
ejpam-2044	7	4	cases	case	NOUN
ejpam-2044	7	5	of	of	ADP
ejpam-2044	7	6	mean	mean	ADJ
ejpam-2044	7	7	value	value	NOUN
ejpam-2044	7	8	,	,	PUNCT
ejpam-2044	7	9	insurer	insurer	NOUN
ejpam-2044	7	10	equivalent	equivalent	ADJ
ejpam-2044	7	11	/	/	SYM
ejpam-2044	7	12	zero	zero	NUM
ejpam-2044	7	13	utility	utility	NOUN
ejpam-2044	7	14	,	,	PUNCT
ejpam-2044	7	15	customer	customer	NOUN
ejpam-2044	7	16	equivalent	equivalent	ADJ
ejpam-2044	7	17	/	/	SYM
ejpam-2044	7	18	zero	zero	NUM
ejpam-2044	7	19	utility	utility	NOUN
ejpam-2044	7	20	,	,	PUNCT
ejpam-2044	7	21	and	and	CCONJ
ejpam-2044	7	22	swiss	swiss	ADJ
ejpam-2044	7	23	premium	premium	NOUN
ejpam-2044	7	24	calculation	calculation	NOUN
ejpam-2044	7	25	principles	principle	NOUN
ejpam-2044	7	26	.	.	PUNCT
ejpam-2044	8	1	2010	2010	NUM
ejpam-2044	8	2	mathematics	mathematic	NOUN
ejpam-2044	8	3	subject	subject	NOUN
ejpam-2044	8	4	classifications	classification	NOUN
ejpam-2044	8	5	:	:	PUNCT
ejpam-2044	8	6	91b30	91b30	NUM
ejpam-2044	8	7	,	,	PUNCT
ejpam-2044	8	8	62p20	62p20	NOUN
ejpam-2044	8	9	,	,	PUNCT
ejpam-2044	8	10	62p05	62p05	DET
ejpam-2044	8	11	key	key	ADJ
ejpam-2044	8	12	words	word	NOUN
ejpam-2044	8	13	and	and	CCONJ
ejpam-2044	8	14	phrases	phrase	NOUN
ejpam-2044	8	15	:	:	PUNCT
ejpam-2044	8	16	characterization	characterization	NOUN
ejpam-2044	8	17	theorem	theorem	NOUN
ejpam-2044	8	18	,	,	PUNCT
ejpam-2044	8	19	insurance	insurance	NOUN
ejpam-2044	8	20	premium	premium	NOUN
ejpam-2044	8	21	,	,	PUNCT
ejpam-2044	8	22	scale	scale	NOUN
ejpam-2044	8	23	invariance	invariance	NOUN
ejpam-2044	8	24	property	property	NOUN
ejpam-2044	8	25	,	,	PUNCT
ejpam-2044	8	26	mean	mean	VERB
ejpam-2044	8	27	value	value	NOUN
ejpam-2044	8	28	principle	principle	NOUN
ejpam-2044	8	29	,	,	PUNCT
ejpam-2044	8	30	insurer	insurer	NOUN
ejpam-2044	8	31	/	/	SYM
ejpam-2044	8	32	customer	customer	NOUN
ejpam-2044	8	33	equivalent	equivalent	ADJ
ejpam-2044	8	34	/	/	SYM
ejpam-2044	8	35	zero	zero	NUM
ejpam-2044	8	36	utility	utility	NOUN
ejpam-2044	8	37	principle	principle	NOUN
ejpam-2044	8	38	,	,	PUNCT
ejpam-2044	8	39	swiss	swiss	ADJ
ejpam-2044	8	40	principle	principle	NOUN
ejpam-2044	8	41	1	1	NUM
ejpam-2044	8	42	.	.	PUNCT
ejpam-2044	9	1	introduction	introduction	NOUN
ejpam-2044	9	2	let	let	VERB
ejpam-2044	9	3	us	we	PRON
ejpam-2044	9	4	consider	consider	VERB
ejpam-2044	9	5	a	a	DET
ejpam-2044	9	6	random	random	ADJ
ejpam-2044	9	7	variable	variable	NOUN
ejpam-2044	9	8	x	x	PUNCT
ejpam-2044	9	9	representing	represent	VERB
ejpam-2044	9	10	size	size	NOUN
ejpam-2044	9	11	of	of	ADP
ejpam-2044	9	12	the	the	DET
ejpam-2044	9	13	insurance	insurance	NOUN
ejpam-2044	9	14	compensation	compensation	NOUN
ejpam-2044	9	15	related	relate	VERB
ejpam-2044	9	16	to	to	ADP
ejpam-2044	9	17	a	a	DET
ejpam-2044	9	18	particular	particular	ADJ
ejpam-2044	9	19	insurance	insurance	NOUN
ejpam-2044	9	20	pact	pact	NOUN
ejpam-2044	9	21	.	.	PUNCT
ejpam-2044	10	1	premium	premium	NOUN
ejpam-2044	10	2	to	to	PART
ejpam-2044	10	3	be	be	AUX
ejpam-2044	10	4	paid	pay	VERB
ejpam-2044	10	5	for	for	ADP
ejpam-2044	10	6	the	the	DET
ejpam-2044	10	7	risk	risk	NOUN
ejpam-2044	10	8	x	x	X
ejpam-2044	10	9	will	will	AUX
ejpam-2044	10	10	be	be	AUX
ejpam-2044	10	11	denoted	denote	VERB
ejpam-2044	10	12	as	as	ADP
ejpam-2044	10	13	π[x	π[x	NOUN
ejpam-2044	10	14	]	]	PUNCT
ejpam-2044	10	15	.	.	PUNCT
ejpam-2044	11	1	in	in	ADP
ejpam-2044	11	2	majority	majority	NOUN
ejpam-2044	11	3	of	of	ADP
ejpam-2044	11	4	the	the	DET
ejpam-2044	11	5	cases	case	NOUN
ejpam-2044	11	6	the	the	DET
ejpam-2044	11	7	random	random	ADJ
ejpam-2044	11	8	variable	variable	NOUN
ejpam-2044	11	9	x	x	PUNCT
ejpam-2044	11	10	is	be	AUX
ejpam-2044	11	11	assumed	assume	VERB
ejpam-2044	11	12	to	to	PART
ejpam-2044	11	13	be	be	AUX
ejpam-2044	11	14	a	a	DET
ejpam-2044	11	15	non	non	ADJ
ejpam-2044	11	16	-	-	ADJ
ejpam-2044	11	17	negative	negative	ADJ
ejpam-2044	11	18	one	one	NUM
ejpam-2044	11	19	,	,	PUNCT
ejpam-2044	11	20	i.e.	i.e.	X
ejpam-2044	11	21	,	,	PUNCT
ejpam-2044	11	22	it	it	PRON
ejpam-2044	11	23	takes	take	VERB
ejpam-2044	11	24	vale	vale	ADJ
ejpam-2044	11	25	zero	zero	NUM
ejpam-2044	11	26	if	if	SCONJ
ejpam-2044	11	27	the	the	DET
ejpam-2044	11	28	contract	contract	NOUN
ejpam-2044	11	29	will	will	AUX
ejpam-2044	11	30	not	not	PART
ejpam-2044	11	31	produce	produce	VERB
ejpam-2044	11	32	a	a	DET
ejpam-2044	11	33	claim	claim	NOUN
ejpam-2044	11	34	and	and	CCONJ
ejpam-2044	11	35	will	will	AUX
ejpam-2044	11	36	be	be	AUX
ejpam-2044	11	37	equal	equal	ADJ
ejpam-2044	11	38	to	to	ADP
ejpam-2044	11	39	the	the	DET
ejpam-2044	11	40	claim	claim	NOUN
ejpam-2044	11	41	size	size	NOUN
ejpam-2044	11	42	if	if	SCONJ
ejpam-2044	11	43	there	there	PRON
ejpam-2044	11	44	will	will	AUX
ejpam-2044	11	45	be	be	AUX
ejpam-2044	11	46	a	a	DET
ejpam-2044	11	47	claim	claim	NOUN
ejpam-2044	11	48	.	.	PUNCT
ejpam-2044	12	1	in	in	ADP
ejpam-2044	12	2	some	some	DET
ejpam-2044	12	3	case	case	NOUN
ejpam-2044	12	4	,	,	PUNCT
ejpam-2044	12	5	however	however	ADV
ejpam-2044	12	6	,	,	PUNCT
ejpam-2044	12	7	negative	negative	ADJ
ejpam-2044	12	8	values	value	NOUN
ejpam-2044	12	9	of	of	ADP
ejpam-2044	12	10	variable	variable	NOUN
ejpam-2044	12	11	x	x	PRON
ejpam-2044	12	12	are	be	AUX
ejpam-2044	12	13	also	also	ADV
ejpam-2044	12	14	allowed	allow	VERB
ejpam-2044	12	15	;	;	PUNCT
ejpam-2044	12	16	such	such	ADJ
ejpam-2044	12	17	negative	negative	ADJ
ejpam-2044	12	18	values	value	NOUN
ejpam-2044	12	19	are	be	AUX
ejpam-2044	12	20	often	often	ADV
ejpam-2044	12	21	interpreted	interpret	VERB
ejpam-2044	12	22	as	as	ADP
ejpam-2044	12	23	compensations	compensation	NOUN
ejpam-2044	12	24	which	which	PRON
ejpam-2044	12	25	have	have	VERB
ejpam-2044	12	26	to	to	PART
ejpam-2044	12	27	be	be	AUX
ejpam-2044	12	28	paid	pay	VERB
ejpam-2044	12	29	by	by	ADP
ejpam-2044	12	30	the	the	DET
ejpam-2044	12	31	customer	customer	NOUN
ejpam-2044	12	32	to	to	ADP
ejpam-2044	12	33	the	the	DET
ejpam-2044	12	34	insurance	insurance	NOUN
ejpam-2044	12	35	company	company	NOUN
ejpam-2044	12	36	.	.	PUNCT
ejpam-2044	13	1	let	let	VERB
ejpam-2044	13	2	us	we	PRON
ejpam-2044	13	3	now	now	ADV
ejpam-2044	13	4	define	define	VERB
ejpam-2044	13	5	several	several	ADJ
ejpam-2044	13	6	insurance	insurance	NOUN
ejpam-2044	13	7	premium	premium	NOUN
ejpam-2044	13	8	calculation	calculation	NOUN
ejpam-2044	13	9	principles	principle	NOUN
ejpam-2044	13	10	which	which	PRON
ejpam-2044	13	11	we	we	PRON
ejpam-2044	13	12	would	would	AUX
ejpam-2044	13	13	like	like	VERB
ejpam-2044	13	14	to	to	PART
ejpam-2044	13	15	investigate	investigate	VERB
ejpam-2044	13	16	.	.	PUNCT
ejpam-2044	14	1	net	net	ADJ
ejpam-2044	14	2	premium	premium	NOUN
ejpam-2044	14	3	is	be	AUX
ejpam-2044	14	4	defined	define	VERB
ejpam-2044	14	5	as	as	ADP
ejpam-2044	14	6	expected	expect	VERB
ejpam-2044	14	7	value	value	NOUN
ejpam-2044	14	8	of	of	ADP
ejpam-2044	14	9	the	the	DET
ejpam-2044	14	10	losses	loss	NOUN
ejpam-2044	14	11	associated	associate	VERB
ejpam-2044	14	12	with	with	ADP
ejpam-2044	14	13	the	the	DET
ejpam-2044	14	14	risk	risk	NOUN
ejpam-2044	14	15	x	x	X
ejpam-2044	14	16	,	,	PUNCT
ejpam-2044	14	17	i.e.	i.e.	X
ejpam-2044	14	18	,	,	PUNCT
ejpam-2044	14	19	πnet[x	πnet[x	NOUN
ejpam-2044	14	20	]	]	X
ejpam-2044	14	21	=	=	SYM
ejpam-2044	14	22	e[x	e[x	NOUN
ejpam-2044	14	23	]	]	PUNCT
ejpam-2044	14	24	.	.	PUNCT
ejpam-2044	15	1	∗corresponding	∗corresponde	VERB
ejpam-2044	15	2	author	author	NOUN
ejpam-2044	15	3	.	.	PUNCT
ejpam-2044	16	1	email	email	NOUN
ejpam-2044	16	2	addresses	address	NOUN
ejpam-2044	16	3	:	:	PUNCT
ejpam-2044	16	4	prats4@yandex.ru	prats4@yandex.ru	NUM
ejpam-2044	16	5	(	(	PUNCT
ejpam-2044	16	6	m.	m.	NOUN
ejpam-2044	16	7	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	16	8	)	)	PUNCT
ejpam-2044	16	9	,	,	PUNCT
ejpam-2044	16	10	drozdenko@yandex.ru	drozdenko@yandex.ru	NOUN
ejpam-2044	16	11	(	(	PUNCT
ejpam-2044	16	12	v.	v.	ADP
ejpam-2044	16	13	drozdenko	drozdenko	NOUN
ejpam-2044	16	14	)	)	PUNCT
ejpam-2044	16	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2044	17	1	267	267	NUM
ejpam-2044	18	1	c	c	X
ejpam-2044	18	2	©	©	PROPN
ejpam-2044	18	3	2014	2014	NUM
ejpam-2044	18	4	ejpam	ejpam	NOUN
ejpam-2044	18	5	all	all	DET
ejpam-2044	18	6	rights	right	NOUN
ejpam-2044	18	7	reserved	reserve	VERB
ejpam-2044	18	8	.	.	PUNCT
ejpam-2044	19	1	m.	m.	NOUN
ejpam-2044	19	2	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	19	3	,	,	PUNCT
ejpam-2044	19	4	v.	v.	ADP
ejpam-2044	19	5	drozdenko	drozdenko	PROPN
ejpam-2044	19	6	/	/	SYM
ejpam-2044	19	7	eur	eur	PROPN
ejpam-2044	19	8	.	.	PUNCT
ejpam-2044	20	1	j.	j.	PROPN
ejpam-2044	20	2	pure	pure	PROPN
ejpam-2044	20	3	appl	appl	PROPN
ejpam-2044	20	4	.	.	PROPN
ejpam-2044	20	5	math	math	PROPN
ejpam-2044	20	6	,	,	PUNCT
ejpam-2044	20	7	7	7	NUM
ejpam-2044	20	8	(	(	PUNCT
ejpam-2044	20	9	2014	2014	NUM
ejpam-2044	20	10	)	)	PUNCT
ejpam-2044	20	11	,	,	PUNCT
ejpam-2044	20	12	267	267	X
ejpam-2044	20	13	-	-	SYM
ejpam-2044	20	14	288	288	NUM
ejpam-2044	20	15	268	268	NUM
ejpam-2044	20	16	mean	mean	NOUN
ejpam-2044	20	17	value	value	NOUN
ejpam-2044	20	18	premium	premium	NOUN
ejpam-2044	20	19	for	for	ADP
ejpam-2044	20	20	the	the	DET
ejpam-2044	20	21	risk	risk	NOUN
ejpam-2044	20	22	x	x	PUNCT
ejpam-2044	20	23	,	,	PUNCT
ejpam-2044	20	24	which	which	PRON
ejpam-2044	20	25	in	in	ADP
ejpam-2044	20	26	the	the	DET
ejpam-2044	20	27	article	article	NOUN
ejpam-2044	20	28	will	will	AUX
ejpam-2044	20	29	be	be	AUX
ejpam-2044	20	30	denoted	denote	VERB
ejpam-2044	20	31	as	as	ADP
ejpam-2044	20	32	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	20	33	]	]	PUNCT
ejpam-2044	20	34	,	,	PUNCT
ejpam-2044	20	35	based	base	VERB
ejpam-2044	20	36	on	on	ADP
ejpam-2044	20	37	a	a	DET
ejpam-2044	20	38	function	function	NOUN
ejpam-2044	20	39	v(x	v(x	NOUN
ejpam-2044	20	40	)	)	PUNCT
ejpam-2044	20	41	∈	∈	PROPN
ejpam-2044	20	42	c2(r	c2(r	NOUN
ejpam-2044	20	43	)	)	PUNCT
ejpam-2044	20	44	such	such	ADJ
ejpam-2044	20	45	that	that	SCONJ
ejpam-2044	20	46	v′(x	v′(x	NOUN
ejpam-2044	20	47	)	)	PUNCT
ejpam-2044	20	48	>	>	X
ejpam-2044	20	49	0	0	PUNCT
ejpam-2044	20	50	and	and	CCONJ
ejpam-2044	20	51	v′′(x	v′′(x	NOUN
ejpam-2044	20	52	)	)	PUNCT
ejpam-2044	20	53	≥	≥	NOUN
ejpam-2044	20	54	0	0	NUM
ejpam-2044	20	55	for	for	ADP
ejpam-2044	20	56	x	x	PROPN
ejpam-2044	20	57	∈	∈	PROPN
ejpam-2044	20	58	r	r	NOUN
ejpam-2044	20	59	,	,	PUNCT
ejpam-2044	20	60	is	be	AUX
ejpam-2044	20	61	defined	define	VERB
ejpam-2044	20	62	as	as	ADP
ejpam-2044	20	63	a	a	DET
ejpam-2044	20	64	solution	solution	NOUN
ejpam-2044	20	65	to	to	ADP
ejpam-2044	20	66	the	the	DET
ejpam-2044	20	67	equation	equation	NOUN
ejpam-2044	20	68	v(πm.v.[x	v(πm.v.[x	VERB
ejpam-2044	20	69	]	]	PUNCT
ejpam-2044	20	70	)	)	PUNCT
ejpam-2044	21	1	=	=	PRON
ejpam-2044	21	2	e[v(x	e[v(x	PROPN
ejpam-2044	21	3	)	)	PUNCT
ejpam-2044	21	4	]	]	PUNCT
ejpam-2044	21	5	.	.	PUNCT
ejpam-2044	22	1	(	(	PUNCT
ejpam-2044	22	2	1	1	X
ejpam-2044	22	3	)	)	PUNCT
ejpam-2044	22	4	insurer	insurer	NOUN
ejpam-2044	22	5	equivalent	equivalent	ADJ
ejpam-2044	22	6	utility	utility	NOUN
ejpam-2044	22	7	premium	premium	NOUN
ejpam-2044	22	8	for	for	ADP
ejpam-2044	22	9	the	the	DET
ejpam-2044	22	10	risk	risk	NOUN
ejpam-2044	22	11	x	x	PUNCT
ejpam-2044	22	12	,	,	PUNCT
ejpam-2044	22	13	which	which	PRON
ejpam-2044	22	14	we	we	PRON
ejpam-2044	22	15	denote	denote	VERB
ejpam-2044	22	16	as	as	ADP
ejpam-2044	22	17	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	22	18	]	]	PUNCT
ejpam-2044	22	19	,	,	PUNCT
ejpam-2044	22	20	is	be	AUX
ejpam-2044	22	21	defined	define	VERB
ejpam-2044	22	22	as	as	ADP
ejpam-2044	22	23	a	a	DET
ejpam-2044	22	24	solution	solution	NOUN
ejpam-2044	22	25	to	to	ADP
ejpam-2044	22	26	the	the	DET
ejpam-2044	22	27	equation	equation	NOUN
ejpam-2044	22	28	u(w	u(w	PROPN
ejpam-2044	22	29	)	)	PUNCT
ejpam-2044	23	1	=	=	SYM
ejpam-2044	23	2	e[u(w	e[u(w	PROPN
ejpam-2044	24	1	+	+	NOUN
ejpam-2044	24	2	πi.e.u.[x	πi.e.u.[x	NOUN
ejpam-2044	24	3	]	]	X
ejpam-2044	24	4	−	−	NOUN
ejpam-2044	24	5	x	x	SYM
ejpam-2044	24	6	)	)	PUNCT
ejpam-2044	24	7	]	]	PUNCT
ejpam-2044	24	8	,	,	PUNCT
ejpam-2044	24	9	(	(	PUNCT
ejpam-2044	24	10	2	2	X
ejpam-2044	24	11	)	)	PUNCT
ejpam-2044	24	12	where	where	SCONJ
ejpam-2044	24	13	w	w	NOUN
ejpam-2044	24	14	is	be	AUX
ejpam-2044	24	15	insurer	insurer	NOUN
ejpam-2044	24	16	’s	’s	PART
ejpam-2044	24	17	capital	capital	NOUN
ejpam-2044	24	18	at	at	ADP
ejpam-2044	24	19	the	the	DET
ejpam-2044	24	20	moment	moment	NOUN
ejpam-2044	24	21	when	when	SCONJ
ejpam-2044	24	22	the	the	DET
ejpam-2044	24	23	contract	contract	NOUN
ejpam-2044	24	24	is	be	AUX
ejpam-2044	24	25	initiated	initiate	VERB
ejpam-2044	24	26	,	,	PUNCT
ejpam-2044	24	27	and	and	CCONJ
ejpam-2044	24	28	the	the	DET
ejpam-2044	24	29	function	function	NOUN
ejpam-2044	24	30	u(x	u(x	VERB
ejpam-2044	24	31	)	)	PUNCT
ejpam-2044	24	32	∈	∈	PROPN
ejpam-2044	24	33	c2(r	c2(r	NOUN
ejpam-2044	24	34	)	)	PUNCT
ejpam-2044	24	35	is	be	AUX
ejpam-2044	24	36	insurer	insurer	NOUN
ejpam-2044	24	37	’s	’s	PART
ejpam-2044	24	38	utility	utility	NOUN
ejpam-2044	24	39	function	function	NOUN
ejpam-2044	24	40	satisfying	satisfy	VERB
ejpam-2044	24	41	conditions	condition	NOUN
ejpam-2044	24	42	u	u	NOUN
ejpam-2044	24	43	′(x	′(x	NOUN
ejpam-2044	24	44	)	)	PUNCT
ejpam-2044	24	45	>	>	X
ejpam-2044	24	46	0	0	PUNCT
ejpam-2044	24	47	and	and	CCONJ
ejpam-2044	24	48	u	u	PROPN
ejpam-2044	24	49	′′(x	′′(x	NOUN
ejpam-2044	24	50	)	)	PUNCT
ejpam-2044	24	51	≤	≤	NOUN
ejpam-2044	24	52	0	0	NUM
ejpam-2044	25	1	for	for	ADP
ejpam-2044	25	2	x	x	PROPN
ejpam-2044	25	3	∈	∈	PROPN
ejpam-2044	25	4	r.	r.	PROPN
ejpam-2044	25	5	in	in	ADP
ejpam-2044	25	6	some	some	DET
ejpam-2044	25	7	cases	case	NOUN
ejpam-2044	25	8	insurer	insurer	NOUN
ejpam-2044	25	9	’s	’s	PART
ejpam-2044	25	10	utility	utility	NOUN
ejpam-2044	25	11	function	function	NOUN
ejpam-2044	25	12	is	be	AUX
ejpam-2044	25	13	selected	select	VERB
ejpam-2044	25	14	in	in	ADP
ejpam-2044	25	15	such	such	DET
ejpam-2044	25	16	a	a	DET
ejpam-2044	25	17	way	way	NOUN
ejpam-2044	25	18	that	that	PRON
ejpam-2044	25	19	the	the	DET
ejpam-2044	25	20	value	value	NOUN
ejpam-2044	25	21	u(0	u(0	NOUN
ejpam-2044	25	22	)	)	PUNCT
ejpam-2044	25	23	represents	represent	VERB
ejpam-2044	25	24	insurer	insurer	NOUN
ejpam-2044	25	25	’s	’s	PART
ejpam-2044	25	26	utility	utility	NOUN
ejpam-2044	25	27	at	at	ADP
ejpam-2044	25	28	the	the	DET
ejpam-2044	25	29	moment	moment	NOUN
ejpam-2044	25	30	when	when	SCONJ
ejpam-2044	25	31	the	the	DET
ejpam-2044	25	32	contract	contract	NOUN
ejpam-2044	25	33	is	be	AUX
ejpam-2044	25	34	initiated	initiate	VERB
ejpam-2044	25	35	.	.	PUNCT
ejpam-2044	26	1	in	in	ADP
ejpam-2044	26	2	such	such	ADJ
ejpam-2044	26	3	cases	case	NOUN
ejpam-2044	26	4	equation	equation	NOUN
ejpam-2044	26	5	(	(	PUNCT
ejpam-2044	26	6	2	2	NUM
ejpam-2044	26	7	)	)	PUNCT
ejpam-2044	26	8	for	for	ADP
ejpam-2044	26	9	the	the	DET
ejpam-2044	26	10	risk	risk	NOUN
ejpam-2044	26	11	x	x	VERB
ejpam-2044	26	12	is	be	AUX
ejpam-2044	26	13	replaced	replace	VERB
ejpam-2044	26	14	by	by	ADP
ejpam-2044	26	15	the	the	DET
ejpam-2044	26	16	equation	equation	NOUN
ejpam-2044	26	17	u(0	u(0	NOUN
ejpam-2044	26	18	)	)	PUNCT
ejpam-2044	26	19	=	=	PUNCT
ejpam-2044	26	20	e[u(πi.z.u.[x	e[u(πi.z.u.[x	NOUN
ejpam-2044	26	21	]	]	PUNCT
ejpam-2044	26	22	−	−	NOUN
ejpam-2044	26	23	x	x	SYM
ejpam-2044	26	24	)	)	PUNCT
ejpam-2044	26	25	]	]	PUNCT
ejpam-2044	26	26	(	(	PUNCT
ejpam-2044	26	27	3	3	X
ejpam-2044	26	28	)	)	PUNCT
ejpam-2044	26	29	and	and	CCONJ
ejpam-2044	26	30	corresponding	correspond	VERB
ejpam-2044	26	31	method	method	NOUN
ejpam-2044	26	32	of	of	ADP
ejpam-2044	26	33	pricing	pricing	NOUN
ejpam-2044	26	34	of	of	ADP
ejpam-2044	26	35	the	the	DET
ejpam-2044	26	36	insurance	insurance	NOUN
ejpam-2044	26	37	contracts	contract	NOUN
ejpam-2044	26	38	is	be	AUX
ejpam-2044	26	39	called	call	VERB
ejpam-2044	26	40	insurer	insurer	NOUN
ejpam-2044	26	41	zero	zero	NUM
ejpam-2044	26	42	utility	utility	NOUN
ejpam-2044	26	43	premium	premium	NOUN
ejpam-2044	26	44	calculation	calculation	NOUN
ejpam-2044	26	45	principle	principle	NOUN
ejpam-2044	26	46	;	;	PUNCT
ejpam-2044	26	47	here	here	ADV
ejpam-2044	26	48	the	the	DET
ejpam-2044	26	49	premium	premium	NOUN
ejpam-2044	26	50	is	be	AUX
ejpam-2044	26	51	denoted	denote	VERB
ejpam-2044	26	52	as	as	ADP
ejpam-2044	26	53	πi.z.u.[x	πi.z.u.[x	ADV
ejpam-2044	26	54	]	]	PUNCT
ejpam-2044	26	55	.	.	PUNCT
ejpam-2044	27	1	customer	customer	NOUN
ejpam-2044	27	2	equivalent	equivalent	ADJ
ejpam-2044	27	3	utility	utility	NOUN
ejpam-2044	27	4	premium	premium	NOUN
ejpam-2044	27	5	for	for	ADP
ejpam-2044	27	6	the	the	DET
ejpam-2044	27	7	risk	risk	NOUN
ejpam-2044	27	8	x	x	PUNCT
ejpam-2044	27	9	,	,	PUNCT
ejpam-2044	27	10	which	which	PRON
ejpam-2044	27	11	we	we	PRON
ejpam-2044	27	12	denote	denote	VERB
ejpam-2044	27	13	as	as	ADP
ejpam-2044	27	14	πc.e.u.[x	πc.e.u.[x	NUM
ejpam-2044	27	15	]	]	PUNCT
ejpam-2044	27	16	,	,	PUNCT
ejpam-2044	27	17	is	be	AUX
ejpam-2044	27	18	defined	define	VERB
ejpam-2044	27	19	as	as	ADP
ejpam-2044	27	20	a	a	DET
ejpam-2044	27	21	solution	solution	NOUN
ejpam-2044	27	22	to	to	ADP
ejpam-2044	27	23	the	the	DET
ejpam-2044	27	24	equation	equation	NOUN
ejpam-2044	27	25	u(ω−πc.e.u.[x	u(ω−πc.e.u.[x	PROPN
ejpam-2044	27	26	]	]	X
ejpam-2044	27	27	)	)	PUNCT
ejpam-2044	28	1	=	=	SYM
ejpam-2044	28	2	e[u(ω−	e[u(ω−	ADJ
ejpam-2044	28	3	x	x	X
ejpam-2044	28	4	)	)	PUNCT
ejpam-2044	28	5	]	]	PUNCT
ejpam-2044	28	6	,	,	PUNCT
ejpam-2044	28	7	(	(	PUNCT
ejpam-2044	28	8	4	4	X
ejpam-2044	28	9	)	)	PUNCT
ejpam-2044	28	10	where	where	SCONJ
ejpam-2044	28	11	ω	ω	PROPN
ejpam-2044	28	12	is	be	AUX
ejpam-2044	28	13	customer	customer	NOUN
ejpam-2044	28	14	’s	’s	PART
ejpam-2044	28	15	capital	capital	NOUN
ejpam-2044	28	16	at	at	ADP
ejpam-2044	28	17	the	the	DET
ejpam-2044	28	18	moment	moment	NOUN
ejpam-2044	28	19	when	when	SCONJ
ejpam-2044	28	20	the	the	DET
ejpam-2044	28	21	contract	contract	NOUN
ejpam-2044	28	22	is	be	AUX
ejpam-2044	28	23	initiated	initiate	VERB
ejpam-2044	28	24	,	,	PUNCT
ejpam-2044	28	25	and	and	CCONJ
ejpam-2044	28	26	the	the	DET
ejpam-2044	28	27	function	function	NOUN
ejpam-2044	28	28	u(x	u(x	VERB
ejpam-2044	28	29	)	)	PUNCT
ejpam-2044	28	30	∈	∈	PROPN
ejpam-2044	28	31	c2(r	c2(r	NOUN
ejpam-2044	28	32	)	)	PUNCT
ejpam-2044	28	33	is	be	AUX
ejpam-2044	28	34	customer	customer	NOUN
ejpam-2044	28	35	’s	’s	PART
ejpam-2044	28	36	utility	utility	NOUN
ejpam-2044	28	37	function	function	NOUN
ejpam-2044	28	38	satisfying	satisfy	VERB
ejpam-2044	28	39	conditions	condition	NOUN
ejpam-2044	28	40	u′(x	u′(x	NOUN
ejpam-2044	28	41	)	)	PUNCT
ejpam-2044	28	42	>	>	X
ejpam-2044	28	43	0	0	PUNCT
ejpam-2044	28	44	and	and	CCONJ
ejpam-2044	28	45	u′′(x	u′′(x	NOUN
ejpam-2044	28	46	)	)	PUNCT
ejpam-2044	28	47	≤	≤	NOUN
ejpam-2044	28	48	0	0	NUM
ejpam-2044	29	1	for	for	ADP
ejpam-2044	29	2	x	x	PROPN
ejpam-2044	29	3	∈	∈	PROPN
ejpam-2044	29	4	r.	r.	PROPN
ejpam-2044	29	5	in	in	ADP
ejpam-2044	29	6	the	the	DET
ejpam-2044	29	7	cases	case	NOUN
ejpam-2044	29	8	when	when	SCONJ
ejpam-2044	29	9	customer	customer	NOUN
ejpam-2044	29	10	’s	’s	PART
ejpam-2044	29	11	utility	utility	NOUN
ejpam-2044	29	12	function	function	NOUN
ejpam-2044	29	13	is	be	AUX
ejpam-2044	29	14	selected	select	VERB
ejpam-2044	29	15	in	in	ADP
ejpam-2044	29	16	such	such	DET
ejpam-2044	29	17	a	a	DET
ejpam-2044	29	18	way	way	NOUN
ejpam-2044	29	19	that	that	PRON
ejpam-2044	29	20	the	the	DET
ejpam-2044	29	21	value	value	NOUN
ejpam-2044	29	22	u(0	u(0	NOUN
ejpam-2044	29	23	)	)	PUNCT
ejpam-2044	29	24	represents	represent	VERB
ejpam-2044	29	25	customer	customer	NOUN
ejpam-2044	29	26	’s	’s	PART
ejpam-2044	29	27	utility	utility	NOUN
ejpam-2044	29	28	at	at	ADP
ejpam-2044	29	29	the	the	DET
ejpam-2044	29	30	moment	moment	NOUN
ejpam-2044	29	31	when	when	SCONJ
ejpam-2044	29	32	the	the	DET
ejpam-2044	29	33	contract	contract	NOUN
ejpam-2044	29	34	is	be	AUX
ejpam-2044	29	35	initiated	initiate	VERB
ejpam-2044	29	36	,	,	PUNCT
ejpam-2044	29	37	equation	equation	NOUN
ejpam-2044	29	38	(	(	PUNCT
ejpam-2044	29	39	4	4	NUM
ejpam-2044	29	40	)	)	PUNCT
ejpam-2044	29	41	for	for	ADP
ejpam-2044	29	42	the	the	DET
ejpam-2044	29	43	risk	risk	NOUN
ejpam-2044	29	44	x	x	VERB
ejpam-2044	29	45	is	be	AUX
ejpam-2044	29	46	replaced	replace	VERB
ejpam-2044	29	47	by	by	ADP
ejpam-2044	29	48	the	the	DET
ejpam-2044	29	49	equation	equation	NOUN
ejpam-2044	29	50	u(−πc.z.u.[x	u(−πc.z.u.[x	PROPN
ejpam-2044	29	51	]	]	PUNCT
ejpam-2044	29	52	)	)	PUNCT
ejpam-2044	30	1	=	=	SYM
ejpam-2044	30	2	e[u(−x	e[u(−x	NOUN
ejpam-2044	30	3	)	)	PUNCT
ejpam-2044	30	4	]	]	PUNCT
ejpam-2044	30	5	(	(	PUNCT
ejpam-2044	30	6	5	5	NUM
ejpam-2044	30	7	)	)	PUNCT
ejpam-2044	30	8	and	and	CCONJ
ejpam-2044	30	9	corresponding	correspond	VERB
ejpam-2044	30	10	method	method	NOUN
ejpam-2044	30	11	of	of	ADP
ejpam-2044	30	12	pricing	pricing	NOUN
ejpam-2044	30	13	of	of	ADP
ejpam-2044	30	14	the	the	DET
ejpam-2044	30	15	insurance	insurance	NOUN
ejpam-2044	30	16	contracts	contract	NOUN
ejpam-2044	30	17	is	be	AUX
ejpam-2044	30	18	called	call	VERB
ejpam-2044	30	19	customer	customer	NOUN
ejpam-2044	30	20	zero	zero	NUM
ejpam-2044	30	21	utility	utility	NOUN
ejpam-2044	30	22	premium	premium	NOUN
ejpam-2044	30	23	calculation	calculation	NOUN
ejpam-2044	30	24	principle	principle	NOUN
ejpam-2044	30	25	;	;	PUNCT
ejpam-2044	30	26	here	here	ADV
ejpam-2044	30	27	the	the	DET
ejpam-2044	30	28	premium	premium	NOUN
ejpam-2044	30	29	is	be	AUX
ejpam-2044	30	30	denoted	denote	VERB
ejpam-2044	30	31	as	as	ADP
ejpam-2044	30	32	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	30	33	]	]	PUNCT
ejpam-2044	30	34	.	.	PUNCT
ejpam-2044	31	1	swiss	swiss	ADJ
ejpam-2044	31	2	premium	premium	NOUN
ejpam-2044	31	3	for	for	ADP
ejpam-2044	31	4	the	the	DET
ejpam-2044	31	5	risk	risk	NOUN
ejpam-2044	31	6	x	x	PUNCT
ejpam-2044	31	7	,	,	PUNCT
ejpam-2044	31	8	which	which	PRON
ejpam-2044	31	9	in	in	ADP
ejpam-2044	31	10	the	the	DET
ejpam-2044	31	11	article	article	NOUN
ejpam-2044	31	12	will	will	AUX
ejpam-2044	31	13	be	be	AUX
ejpam-2044	31	14	denoted	denote	VERB
ejpam-2044	31	15	as	as	ADP
ejpam-2044	31	16	πswiss[x	πswiss[x	PROPN
ejpam-2044	31	17	]	]	X
ejpam-2044	31	18	,	,	PUNCT
ejpam-2044	31	19	based	base	VERB
ejpam-2044	31	20	on	on	ADP
ejpam-2044	31	21	a	a	DET
ejpam-2044	31	22	parameter	parameter	NOUN
ejpam-2044	31	23	∆	∆	X
ejpam-2044	31	24	∈	∈	PROPN
ejpam-2044	32	1	[	[	X
ejpam-2044	32	2	0	0	NUM
ejpam-2044	32	3	,	,	PUNCT
ejpam-2044	32	4	1	1	NUM
ejpam-2044	32	5	]	]	PUNCT
ejpam-2044	32	6	and	and	CCONJ
ejpam-2044	32	7	a	a	DET
ejpam-2044	32	8	function	function	NOUN
ejpam-2044	32	9	v	v	NOUN
ejpam-2044	32	10	(	(	PUNCT
ejpam-2044	32	11	x	x	NOUN
ejpam-2044	32	12	)	)	PUNCT
ejpam-2044	32	13	∈	∈	PROPN
ejpam-2044	32	14	c2(r	c2(r	NOUN
ejpam-2044	32	15	)	)	PUNCT
ejpam-2044	32	16	such	such	ADJ
ejpam-2044	32	17	that	that	DET
ejpam-2044	32	18	v	v	ADP
ejpam-2044	32	19	′(x	′(x	NOUN
ejpam-2044	32	20	)	)	PUNCT
ejpam-2044	32	21	>	>	X
ejpam-2044	32	22	0	0	PUNCT
ejpam-2044	32	23	and	and	CCONJ
ejpam-2044	32	24	v	v	ADP
ejpam-2044	32	25	′′(x	′′(x	NOUN
ejpam-2044	32	26	)	)	PUNCT
ejpam-2044	32	27	≥	≥	NOUN
ejpam-2044	32	28	0	0	NUM
ejpam-2044	32	29	for	for	ADP
ejpam-2044	32	30	x	x	PROPN
ejpam-2044	32	31	∈	∈	PROPN
ejpam-2044	32	32	r	r	NOUN
ejpam-2044	32	33	,	,	PUNCT
ejpam-2044	32	34	is	be	AUX
ejpam-2044	32	35	defined	define	VERB
ejpam-2044	32	36	as	as	ADP
ejpam-2044	32	37	a	a	DET
ejpam-2044	32	38	solution	solution	NOUN
ejpam-2044	32	39	to	to	ADP
ejpam-2044	32	40	the	the	DET
ejpam-2044	32	41	equation	equation	NOUN
ejpam-2044	32	42	v	v	NOUN
ejpam-2044	32	43	(	(	PUNCT
ejpam-2044	32	44	(	(	PUNCT
ejpam-2044	32	45	1−∆)πswiss[x	1−∆)πswiss[x	NUM
ejpam-2044	32	46	]	]	X
ejpam-2044	32	47	)	)	PUNCT
ejpam-2044	32	48	=	=	SYM
ejpam-2044	32	49	e[v	e[v	X
ejpam-2044	32	50	(	(	PUNCT
ejpam-2044	32	51	x	x	X
ejpam-2044	32	52	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	32	53	]	]	PUNCT
ejpam-2044	32	54	)	)	PUNCT
ejpam-2044	32	55	]	]	PUNCT
ejpam-2044	32	56	.	.	PUNCT
ejpam-2044	33	1	(	(	PUNCT
ejpam-2044	33	2	6	6	X
ejpam-2044	33	3	)	)	PUNCT
ejpam-2044	33	4	observe	observe	VERB
ejpam-2044	33	5	that	that	SCONJ
ejpam-2044	33	6	,	,	PUNCT
ejpam-2044	33	7	in	in	ADP
ejpam-2044	33	8	the	the	DET
ejpam-2044	33	9	case	case	NOUN
ejpam-2044	33	10	of	of	ADP
ejpam-2044	33	11	∆	∆	PROPN
ejpam-2044	33	12	=	=	SYM
ejpam-2044	33	13	0	0	NUM
ejpam-2044	33	14	,	,	PUNCT
ejpam-2044	33	15	swiss	swiss	ADJ
ejpam-2044	33	16	premium	premium	NOUN
ejpam-2044	33	17	principle	principle	NOUN
ejpam-2044	33	18	is	be	AUX
ejpam-2044	33	19	equivalent	equivalent	ADJ
ejpam-2044	33	20	to	to	PART
ejpam-2044	33	21	mean	mean	VERB
ejpam-2044	33	22	value	value	NOUN
ejpam-2044	33	23	premium	premium	NOUN
ejpam-2044	33	24	principle	principle	NOUN
ejpam-2044	33	25	with	with	ADP
ejpam-2044	33	26	v(x	v(x	PROPN
ejpam-2044	33	27	)	)	PUNCT
ejpam-2044	33	28	:	:	PUNCT
ejpam-2044	34	1	=	=	SYM
ejpam-2044	34	2	v	v	X
ejpam-2044	34	3	(	(	PUNCT
ejpam-2044	34	4	x	x	NOUN
ejpam-2044	34	5	)	)	PUNCT
ejpam-2044	34	6	.	.	PUNCT
ejpam-2044	35	1	m.	m.	NOUN
ejpam-2044	35	2	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	35	3	,	,	PUNCT
ejpam-2044	35	4	v.	v.	ADP
ejpam-2044	35	5	drozdenko	drozdenko	PROPN
ejpam-2044	35	6	/	/	SYM
ejpam-2044	35	7	eur	eur	PROPN
ejpam-2044	35	8	.	.	PUNCT
ejpam-2044	36	1	j.	j.	PROPN
ejpam-2044	36	2	pure	pure	PROPN
ejpam-2044	36	3	appl	appl	PROPN
ejpam-2044	36	4	.	.	PROPN
ejpam-2044	36	5	math	math	PROPN
ejpam-2044	36	6	,	,	PUNCT
ejpam-2044	36	7	7	7	NUM
ejpam-2044	36	8	(	(	PUNCT
ejpam-2044	36	9	2014	2014	NUM
ejpam-2044	36	10	)	)	PUNCT
ejpam-2044	36	11	,	,	PUNCT
ejpam-2044	36	12	267	267	X
ejpam-2044	36	13	-	-	SYM
ejpam-2044	36	14	288	288	NUM
ejpam-2044	36	15	269	269	NUM
ejpam-2044	36	16	observe	observe	VERB
ejpam-2044	36	17	also	also	ADV
ejpam-2044	36	18	that	that	SCONJ
ejpam-2044	36	19	,	,	PUNCT
ejpam-2044	36	20	in	in	ADP
ejpam-2044	36	21	the	the	DET
ejpam-2044	36	22	case	case	NOUN
ejpam-2044	36	23	of	of	ADP
ejpam-2044	36	24	∆=	∆=	NOUN
ejpam-2044	36	25	1	1	NUM
ejpam-2044	36	26	,	,	PUNCT
ejpam-2044	36	27	equation	equation	NOUN
ejpam-2044	36	28	(	(	PUNCT
ejpam-2044	36	29	6	6	NUM
ejpam-2044	36	30	)	)	PUNCT
ejpam-2044	36	31	can	can	AUX
ejpam-2044	36	32	be	be	AUX
ejpam-2044	36	33	rewritten	rewrite	VERB
ejpam-2044	36	34	as	as	ADP
ejpam-2044	36	35	−v	−v	NOUN
ejpam-2044	36	36	(	(	PUNCT
ejpam-2044	36	37	0	0	NUM
ejpam-2044	36	38	)	)	PUNCT
ejpam-2044	36	39	=	=	SYM
ejpam-2044	36	40	e[−v	e[−v	X
ejpam-2044	36	41	(	(	PUNCT
ejpam-2044	36	42	−(π[x	−(π[x	VERB
ejpam-2044	36	43	]	]	PUNCT
ejpam-2044	36	44	−	−	NOUN
ejpam-2044	36	45	x	x	SYM
ejpam-2044	36	46	)	)	PUNCT
ejpam-2044	36	47	)	)	PUNCT
ejpam-2044	36	48	]	]	PUNCT
ejpam-2044	36	49	.	.	PUNCT
ejpam-2044	37	1	therefore	therefore	ADV
ejpam-2044	37	2	,	,	PUNCT
ejpam-2044	37	3	in	in	ADP
ejpam-2044	37	4	the	the	DET
ejpam-2044	37	5	case	case	NOUN
ejpam-2044	37	6	of	of	ADP
ejpam-2044	37	7	∆	∆	PROPN
ejpam-2044	37	8	=	=	SYM
ejpam-2044	37	9	1	1	NUM
ejpam-2044	37	10	,	,	PUNCT
ejpam-2044	37	11	swiss	swiss	ADJ
ejpam-2044	37	12	premium	premium	NOUN
ejpam-2044	37	13	principle	principle	NOUN
ejpam-2044	37	14	is	be	AUX
ejpam-2044	37	15	equivalent	equivalent	ADJ
ejpam-2044	37	16	to	to	PART
ejpam-2044	37	17	insurer	insurer	VERB
ejpam-2044	37	18	zero	zero	NUM
ejpam-2044	37	19	utility	utility	NOUN
ejpam-2044	37	20	premium	premium	NOUN
ejpam-2044	37	21	principle	principle	NOUN
ejpam-2044	37	22	with	with	ADP
ejpam-2044	37	23	insurer	insurer	NOUN
ejpam-2044	37	24	’s	’s	PART
ejpam-2044	37	25	utility	utility	NOUN
ejpam-2044	37	26	function	function	NOUN
ejpam-2044	37	27	u(x	u(x	VERB
ejpam-2044	37	28	)	)	PUNCT
ejpam-2044	37	29	:	:	PUNCT
ejpam-2044	37	30	=	=	X
ejpam-2044	37	31	−v	−v	NOUN
ejpam-2044	37	32	(	(	PUNCT
ejpam-2044	37	33	−x	−x	NOUN
ejpam-2044	37	34	)	)	PUNCT
ejpam-2044	37	35	.	.	PUNCT
ejpam-2044	38	1	sometimes	sometimes	ADV
ejpam-2044	38	2	described	describe	VERB
ejpam-2044	38	3	methods	method	NOUN
ejpam-2044	38	4	of	of	ADP
ejpam-2044	38	5	pricing	pricing	NOUN
ejpam-2044	38	6	of	of	ADP
ejpam-2044	38	7	the	the	DET
ejpam-2044	38	8	insurance	insurance	NOUN
ejpam-2044	38	9	contracts	contract	NOUN
ejpam-2044	38	10	are	be	AUX
ejpam-2044	38	11	applied	apply	VERB
ejpam-2044	38	12	to	to	ADP
ejpam-2044	38	13	some	some	DET
ejpam-2044	38	14	special	special	ADJ
ejpam-2044	38	15	classes	class	NOUN
ejpam-2044	38	16	of	of	ADP
ejpam-2044	38	17	risks	risk	NOUN
ejpam-2044	38	18	:	:	PUNCT
ejpam-2044	38	19	as	as	ADP
ejpam-2044	38	20	an	an	DET
ejpam-2044	38	21	example	example	NOUN
ejpam-2044	38	22	of	of	ADP
ejpam-2044	38	23	such	such	DET
ejpam-2044	38	24	a	a	DET
ejpam-2044	38	25	class	class	NOUN
ejpam-2044	38	26	one	one	NOUN
ejpam-2044	38	27	can	can	AUX
ejpam-2044	38	28	mention	mention	VERB
ejpam-2044	38	29	the	the	DET
ejpam-2044	38	30	class	class	NOUN
ejpam-2044	38	31	of	of	ADP
ejpam-2044	38	32	all	all	DET
ejpam-2044	38	33	nonnegative	nonnegative	ADJ
ejpam-2044	38	34	risks	risk	NOUN
ejpam-2044	38	35	,	,	PUNCT
ejpam-2044	38	36	alternatively	alternatively	ADV
ejpam-2044	38	37	one	one	PRON
ejpam-2044	38	38	could	could	AUX
ejpam-2044	38	39	mention	mention	VERB
ejpam-2044	38	40	the	the	DET
ejpam-2044	38	41	class	class	NOUN
ejpam-2044	38	42	of	of	ADP
ejpam-2044	38	43	all	all	DET
ejpam-2044	38	44	non	non	ADJ
ejpam-2044	38	45	-	-	ADJ
ejpam-2044	38	46	negative	negative	ADJ
ejpam-2044	38	47	risks	risk	NOUN
ejpam-2044	38	48	bounded	bound	VERB
ejpam-2044	38	49	from	from	ADP
ejpam-2044	38	50	above	above	ADV
ejpam-2044	38	51	by	by	ADP
ejpam-2044	38	52	some	some	DET
ejpam-2044	38	53	fixed	fix	VERB
ejpam-2044	38	54	real	real	ADJ
ejpam-2044	38	55	value	value	NOUN
ejpam-2044	38	56	,	,	PUNCT
ejpam-2044	38	57	etc	etc	X
ejpam-2044	38	58	.	.	X
ejpam-2044	38	59	in	in	ADP
ejpam-2044	38	60	such	such	ADJ
ejpam-2044	38	61	cases	case	NOUN
ejpam-2044	38	62	domains	domain	NOUN
ejpam-2044	38	63	of	of	ADP
ejpam-2044	38	64	the	the	DET
ejpam-2044	38	65	functions	function	NOUN
ejpam-2044	38	66	v(x	v(x	PROPN
ejpam-2044	38	67	)	)	PUNCT
ejpam-2044	38	68	,	,	PUNCT
ejpam-2044	38	69	u(x	u(x	PROPN
ejpam-2044	38	70	)	)	PUNCT
ejpam-2044	38	71	,	,	PUNCT
ejpam-2044	38	72	u(x	u(x	PROPN
ejpam-2044	38	73	)	)	PUNCT
ejpam-2044	38	74	,	,	PUNCT
ejpam-2044	38	75	and	and	CCONJ
ejpam-2044	38	76	v	v	X
ejpam-2044	38	77	(	(	PUNCT
ejpam-2044	38	78	x	x	X
ejpam-2044	38	79	)	)	PUNCT
ejpam-2044	38	80	could	could	AUX
ejpam-2044	38	81	be	be	AUX
ejpam-2044	38	82	subsets	subset	NOUN
ejpam-2044	38	83	of	of	ADP
ejpam-2044	38	84	r	r	NOUN
ejpam-2044	38	85	such	such	ADJ
ejpam-2044	38	86	that	that	DET
ejpam-2044	38	87	equations	equation	NOUN
ejpam-2044	38	88	(	(	PUNCT
ejpam-2044	38	89	1	1	NUM
ejpam-2044	38	90	)	)	PUNCT
ejpam-2044	38	91	–	–	PUNCT
ejpam-2044	38	92	(	(	PUNCT
ejpam-2044	38	93	6	6	NUM
ejpam-2044	38	94	)	)	PUNCT
ejpam-2044	38	95	(	(	PUNCT
ejpam-2044	38	96	here	here	ADV
ejpam-2044	38	97	choice	choice	NOUN
ejpam-2044	38	98	of	of	ADP
ejpam-2044	38	99	the	the	DET
ejpam-2044	38	100	equation	equation	NOUN
ejpam-2044	38	101	depends	depend	VERB
ejpam-2044	38	102	on	on	ADP
ejpam-2044	38	103	the	the	DET
ejpam-2044	38	104	chosen	choose	VERB
ejpam-2044	38	105	method	method	NOUN
ejpam-2044	38	106	of	of	ADP
ejpam-2044	38	107	pricing	pricing	NOUN
ejpam-2044	38	108	)	)	PUNCT
ejpam-2044	38	109	will	will	AUX
ejpam-2044	38	110	preserve	preserve	VERB
ejpam-2044	38	111	their	their	PRON
ejpam-2044	38	112	correct	correct	ADJ
ejpam-2044	38	113	mathematical	mathematical	ADJ
ejpam-2044	38	114	meaning	meaning	NOUN
ejpam-2044	38	115	for	for	ADP
ejpam-2044	38	116	all	all	DET
ejpam-2044	38	117	risks	risk	NOUN
ejpam-2044	38	118	from	from	ADP
ejpam-2044	38	119	the	the	DET
ejpam-2044	38	120	considered	consider	VERB
ejpam-2044	38	121	class	class	NOUN
ejpam-2044	38	122	,	,	PUNCT
ejpam-2044	38	123	moreover	moreover	ADV
ejpam-2044	38	124	,	,	PUNCT
ejpam-2044	38	125	monotonicity	monotonicity	NOUN
ejpam-2044	38	126	and	and	CCONJ
ejpam-2044	38	127	concavity	concavity	NOUN
ejpam-2044	38	128	-	-	PUNCT
ejpam-2044	38	129	convexity	convexity	NOUN
ejpam-2044	38	130	properties	property	NOUN
ejpam-2044	38	131	of	of	ADP
ejpam-2044	38	132	the	the	DET
ejpam-2044	38	133	functions	function	NOUN
ejpam-2044	38	134	v(x	v(x	NUM
ejpam-2044	38	135	)	)	PUNCT
ejpam-2044	38	136	,	,	PUNCT
ejpam-2044	38	137	u(x	u(x	PROPN
ejpam-2044	38	138	)	)	PUNCT
ejpam-2044	38	139	,	,	PUNCT
ejpam-2044	38	140	u(x	u(x	PROPN
ejpam-2044	38	141	)	)	PUNCT
ejpam-2044	38	142	,	,	PUNCT
ejpam-2044	38	143	and	and	CCONJ
ejpam-2044	38	144	v	v	X
ejpam-2044	38	145	(	(	PUNCT
ejpam-2044	38	146	x	x	X
ejpam-2044	38	147	)	)	PUNCT
ejpam-2044	38	148	should	should	AUX
ejpam-2044	38	149	also	also	ADV
ejpam-2044	38	150	be	be	AUX
ejpam-2044	38	151	preserved	preserve	VERB
ejpam-2044	38	152	.	.	PUNCT
ejpam-2044	39	1	it	it	PRON
ejpam-2044	39	2	is	be	AUX
ejpam-2044	39	3	interesting	interesting	ADJ
ejpam-2044	39	4	to	to	PART
ejpam-2044	39	5	see	see	VERB
ejpam-2044	39	6	that	that	SCONJ
ejpam-2044	39	7	in	in	ADP
ejpam-2044	39	8	the	the	DET
ejpam-2044	39	9	case	case	NOUN
ejpam-2044	39	10	of	of	ADP
ejpam-2044	39	11	subjecting	subject	VERB
ejpam-2044	39	12	of	of	ADP
ejpam-2044	39	13	the	the	DET
ejpam-2044	39	14	describe	describe	NOUN
ejpam-2044	39	15	premium	premium	NOUN
ejpam-2044	39	16	principles	principle	NOUN
ejpam-2044	39	17	to	to	ADP
ejpam-2044	39	18	pricing	pricing	NOUN
ejpam-2044	39	19	of	of	ADP
ejpam-2044	39	20	some	some	DET
ejpam-2044	39	21	special	special	ADJ
ejpam-2044	39	22	classes	class	NOUN
ejpam-2044	39	23	of	of	ADP
ejpam-2044	39	24	risks	risk	NOUN
ejpam-2044	39	25	,	,	PUNCT
ejpam-2044	39	26	classes	class	NOUN
ejpam-2044	39	27	of	of	ADP
ejpam-2044	39	28	the	the	DET
ejpam-2044	39	29	auxiliary	auxiliary	ADJ
ejpam-2044	39	30	functions	function	NOUN
ejpam-2044	39	31	defining	define	VERB
ejpam-2044	39	32	scale	scale	NOUN
ejpam-2044	39	33	invariant	invariant	ADJ
ejpam-2044	39	34	premiums	premium	NOUN
ejpam-2044	39	35	can	can	AUX
ejpam-2044	39	36	be	be	AUX
ejpam-2044	39	37	larger	large	ADJ
ejpam-2044	39	38	than	than	ADP
ejpam-2044	39	39	in	in	ADP
ejpam-2044	39	40	the	the	DET
ejpam-2044	39	41	general	general	ADJ
ejpam-2044	39	42	case	case	NOUN
ejpam-2044	39	43	.	.	PUNCT
ejpam-2044	40	1	theorems	theorem	NOUN
ejpam-2044	40	2	2	2	NUM
ejpam-2044	40	3	and	and	CCONJ
ejpam-2044	40	4	5	5	NUM
ejpam-2044	40	5	as	as	ADV
ejpam-2044	40	6	well	well	ADV
ejpam-2044	40	7	as	as	ADP
ejpam-2044	40	8	corollary	corollary	ADJ
ejpam-2044	40	9	3	3	NUM
ejpam-2044	40	10	demonstrate	demonstrate	NOUN
ejpam-2044	40	11	examples	example	NOUN
ejpam-2044	40	12	of	of	ADP
ejpam-2044	40	13	just	just	ADV
ejpam-2044	40	14	such	such	ADJ
ejpam-2044	40	15	situations	situation	NOUN
ejpam-2044	40	16	.	.	PUNCT
ejpam-2044	41	1	we	we	PRON
ejpam-2044	41	2	will	will	AUX
ejpam-2044	41	3	say	say	VERB
ejpam-2044	41	4	that	that	SCONJ
ejpam-2044	41	5	a	a	DET
ejpam-2044	41	6	premium	premium	ADJ
ejpam-2044	41	7	calculation	calculation	NOUN
ejpam-2044	41	8	principle	principle	NOUN
ejpam-2044	41	9	π[x	π[x	X
ejpam-2044	41	10	]	]	PUNCT
ejpam-2044	41	11	possesses	possess	VERB
ejpam-2044	41	12	scale	scale	NOUN
ejpam-2044	41	13	invariance	invariance	NOUN
ejpam-2044	41	14	property	property	NOUN
ejpam-2044	41	15	if	if	SCONJ
ejpam-2044	41	16	for	for	ADP
ejpam-2044	41	17	any	any	DET
ejpam-2044	41	18	admissible	admissible	ADJ
ejpam-2044	41	19	risk	risk	NOUN
ejpam-2044	41	20	x	x	PUNCT
ejpam-2044	41	21	and	and	CCONJ
ejpam-2044	41	22	any	any	DET
ejpam-2044	41	23	positive	positive	ADJ
ejpam-2044	41	24	real	real	ADJ
ejpam-2044	41	25	constant	constant	ADJ
ejpam-2044	41	26	θ	θ	NOUN
ejpam-2044	41	27	the	the	DET
ejpam-2044	41	28	following	follow	VERB
ejpam-2044	41	29	equation	equation	NOUN
ejpam-2044	41	30	holds	hold	VERB
ejpam-2044	41	31	π[θx	π[θx	NOUN
ejpam-2044	41	32	]	]	PUNCT
ejpam-2044	41	33	=	=	PUNCT
ejpam-2044	41	34	θπ[x	θπ[x	NOUN
ejpam-2044	41	35	]	]	PUNCT
ejpam-2044	41	36	.	.	PUNCT
ejpam-2044	42	1	(	(	PUNCT
ejpam-2044	42	2	7	7	X
ejpam-2044	42	3	)	)	PUNCT
ejpam-2044	42	4	more	more	ADJ
ejpam-2044	42	5	information	information	NOUN
ejpam-2044	42	6	about	about	ADP
ejpam-2044	42	7	just	just	ADV
ejpam-2044	42	8	defined	define	VERB
ejpam-2044	42	9	methods	method	NOUN
ejpam-2044	42	10	of	of	ADP
ejpam-2044	42	11	pricing	pricing	NOUN
ejpam-2044	42	12	of	of	ADP
ejpam-2044	42	13	the	the	DET
ejpam-2044	42	14	insurance	insurance	NOUN
ejpam-2044	42	15	contracts	contract	NOUN
ejpam-2044	42	16	as	as	ADV
ejpam-2044	42	17	well	well	ADV
ejpam-2044	42	18	as	as	ADP
ejpam-2044	42	19	properties	property	NOUN
ejpam-2044	42	20	that	that	PRON
ejpam-2044	42	21	can	can	AUX
ejpam-2044	42	22	be	be	AUX
ejpam-2044	42	23	possessed	possess	VERB
ejpam-2044	42	24	by	by	ADP
ejpam-2044	42	25	an	an	DET
ejpam-2044	42	26	insurance	insurance	NOUN
ejpam-2044	42	27	premium	premium	NOUN
ejpam-2044	42	28	calculation	calculation	NOUN
ejpam-2044	42	29	principles	principle	NOUN
ejpam-2044	42	30	can	can	AUX
ejpam-2044	42	31	be	be	AUX
ejpam-2044	42	32	found	find	VERB
ejpam-2044	42	33	,	,	PUNCT
ejpam-2044	42	34	for	for	ADP
ejpam-2044	42	35	example	example	NOUN
ejpam-2044	42	36	,	,	PUNCT
ejpam-2044	42	37	in	in	ADP
ejpam-2044	42	38	asmussen	asmussen	NOUN
ejpam-2044	42	39	and	and	CCONJ
ejpam-2044	42	40	albrecher	albrecher	NOUN
ejpam-2044	42	41	[	[	X
ejpam-2044	42	42	1	1	NUM
ejpam-2044	42	43	]	]	PUNCT
ejpam-2044	42	44	,	,	PUNCT
ejpam-2044	42	45	boland	boland	X
ejpam-2044	43	1	[	[	X
ejpam-2044	43	2	2	2	NUM
ejpam-2044	43	3	]	]	PUNCT
ejpam-2044	43	4	,	,	PUNCT
ejpam-2044	43	5	bowers	bower	NOUN
ejpam-2044	43	6	et	et	PROPN
ejpam-2044	43	7	al	al	PROPN
ejpam-2044	43	8	.	.	PUNCT
ejpam-2044	44	1	[	[	X
ejpam-2044	44	2	3	3	NUM
ejpam-2044	44	3	]	]	PUNCT
ejpam-2044	44	4	,	,	PUNCT
ejpam-2044	44	5	bühlmann	bühlmann	VERB
ejpam-2044	44	6	[	[	X
ejpam-2044	44	7	4	4	NUM
ejpam-2044	44	8	]	]	PUNCT
ejpam-2044	44	9	,	,	PUNCT
ejpam-2044	44	10	dickson	dickson	PROPN
ejpam-2044	45	1	[	[	X
ejpam-2044	45	2	5	5	NUM
ejpam-2044	45	3	]	]	PUNCT
ejpam-2044	45	4	,	,	PUNCT
ejpam-2044	45	5	gerber	gerber	PROPN
ejpam-2044	46	1	[	[	X
ejpam-2044	46	2	6	6	NUM
ejpam-2044	46	3	]	]	PUNCT
ejpam-2044	46	4	,	,	PUNCT
ejpam-2044	46	5	de	de	X
ejpam-2044	46	6	vylder	vylder	NOUN
ejpam-2044	46	7	et	et	PROPN
ejpam-2044	46	8	al	al	PROPN
ejpam-2044	46	9	.	.	PUNCT
ejpam-2044	47	1	[	[	X
ejpam-2044	47	2	7	7	NUM
ejpam-2044	47	3	]	]	PUNCT
ejpam-2044	47	4	,	,	PUNCT
ejpam-2044	47	5	de	de	X
ejpam-2044	47	6	vylder	vylder	NOUN
ejpam-2044	47	7	et	et	PROPN
ejpam-2044	47	8	al	al	PROPN
ejpam-2044	47	9	.	.	PUNCT
ejpam-2044	48	1	[	[	X
ejpam-2044	48	2	8	8	NUM
ejpam-2044	48	3	]	]	PUNCT
ejpam-2044	48	4	,	,	PUNCT
ejpam-2044	48	5	kaas	kaas	NOUN
ejpam-2044	48	6	et	et	PROPN
ejpam-2044	48	7	al	al	PROPN
ejpam-2044	48	8	.	.	PUNCT
ejpam-2044	49	1	[	[	X
ejpam-2044	49	2	9	9	NUM
ejpam-2044	49	3	]	]	PUNCT
ejpam-2044	49	4	,	,	PUNCT
ejpam-2044	49	5	kremer	kremer	PROPN
ejpam-2044	50	1	[	[	X
ejpam-2044	50	2	10	10	NUM
ejpam-2044	50	3	]	]	PUNCT
ejpam-2044	50	4	,	,	PUNCT
ejpam-2044	50	5	rolski	rolski	PROPN
ejpam-2044	50	6	et	et	PROPN
ejpam-2044	50	7	al	al	PROPN
ejpam-2044	50	8	.	.	PUNCT
ejpam-2044	51	1	[	[	X
ejpam-2044	51	2	11	11	NUM
ejpam-2044	51	3	]	]	PUNCT
ejpam-2044	51	4	,	,	PUNCT
ejpam-2044	51	5	straub	straub	PROPN
ejpam-2044	52	1	[	[	X
ejpam-2044	52	2	12	12	NUM
ejpam-2044	52	3	]	]	PUNCT
ejpam-2044	52	4	.	.	PUNCT
ejpam-2044	53	1	we	we	PRON
ejpam-2044	53	2	would	would	AUX
ejpam-2044	53	3	like	like	VERB
ejpam-2044	53	4	to	to	PART
ejpam-2044	53	5	emphasize	emphasize	VERB
ejpam-2044	53	6	that	that	SCONJ
ejpam-2044	53	7	the	the	DET
ejpam-2044	53	8	research	research	NOUN
ejpam-2044	53	9	related	relate	VERB
ejpam-2044	53	10	to	to	ADP
ejpam-2044	53	11	theorems	theorem	NOUN
ejpam-2044	53	12	of	of	ADP
ejpam-2044	53	13	characterization	characterization	NOUN
ejpam-2044	53	14	type	type	NOUN
ejpam-2044	53	15	for	for	ADP
ejpam-2044	53	16	properties	property	NOUN
ejpam-2044	53	17	possessed	possess	VERB
ejpam-2044	53	18	by	by	ADP
ejpam-2044	53	19	certain	certain	ADJ
ejpam-2044	53	20	insurance	insurance	NOUN
ejpam-2044	53	21	premium	premium	NOUN
ejpam-2044	53	22	calculation	calculation	NOUN
ejpam-2044	53	23	principles	principle	NOUN
ejpam-2044	53	24	was	be	AUX
ejpam-2044	53	25	initiated	initiate	VERB
ejpam-2044	53	26	by	by	ADP
ejpam-2044	53	27	the	the	DET
ejpam-2044	53	28	swiss	swiss	ADJ
ejpam-2044	53	29	mathematician	mathematician	ADJ
ejpam-2044	53	30	hans	hans	PROPN
ejpam-2044	53	31	-	-	PUNCT
ejpam-2044	53	32	ulrich	ulrich	PROPN
ejpam-2044	53	33	gerber	gerber	NOUN
ejpam-2044	53	34	,	,	PUNCT
ejpam-2044	53	35	see	see	VERB
ejpam-2044	53	36	gerber	gerber	PROPN
ejpam-2044	54	1	[	[	X
ejpam-2044	54	2	6	6	NUM
ejpam-2044	54	3	]	]	PUNCT
ejpam-2044	54	4	.	.	PUNCT
ejpam-2044	55	1	corresponding	correspond	VERB
ejpam-2044	55	2	theorems	theorem	NOUN
ejpam-2044	55	3	for	for	ADP
ejpam-2044	55	4	the	the	DET
ejpam-2044	55	5	scale	scale	NOUN
ejpam-2044	55	6	invariance	invariance	NOUN
ejpam-2044	55	7	property	property	NOUN
ejpam-2044	55	8	were	be	AUX
ejpam-2044	55	9	still	still	ADV
ejpam-2044	55	10	missing	miss	VERB
ejpam-2044	55	11	in	in	ADP
ejpam-2044	55	12	the	the	DET
ejpam-2044	55	13	literature	literature	NOUN
ejpam-2044	55	14	.	.	PUNCT
ejpam-2044	56	1	2	2	X
ejpam-2044	56	2	.	.	X
ejpam-2044	56	3	mean	mean	ADJ
ejpam-2044	56	4	value	value	NOUN
ejpam-2044	56	5	premium	premium	NOUN
ejpam-2044	56	6	principle	principle	NOUN
ejpam-2044	56	7	the	the	DET
ejpam-2044	56	8	following	follow	VERB
ejpam-2044	56	9	theorem	theorem	NOUN
ejpam-2044	56	10	describes	describe	VERB
ejpam-2044	56	11	necessary	necessary	ADJ
ejpam-2044	56	12	and	and	CCONJ
ejpam-2044	56	13	sufficient	sufficient	ADJ
ejpam-2044	56	14	conditions	condition	NOUN
ejpam-2044	56	15	under	under	ADP
ejpam-2044	56	16	which	which	PRON
ejpam-2044	56	17	mean	mean	VERB
ejpam-2044	56	18	value	value	NOUN
ejpam-2044	56	19	premium	premium	NOUN
ejpam-2044	56	20	calculation	calculation	NOUN
ejpam-2044	56	21	principle	principle	NOUN
ejpam-2044	56	22	possesses	possess	VERB
ejpam-2044	56	23	scale	scale	NOUN
ejpam-2044	56	24	invariance	invariance	NOUN
ejpam-2044	56	25	property	property	NOUN
ejpam-2044	56	26	.	.	PUNCT
ejpam-2044	57	1	theorem	theorem	NOUN
ejpam-2044	57	2	1	1	NUM
ejpam-2044	57	3	.	.	PUNCT
ejpam-2044	57	4	mean	mean	ADJ
ejpam-2044	57	5	value	value	NOUN
ejpam-2044	57	6	premium	premium	NOUN
ejpam-2044	57	7	calculation	calculation	NOUN
ejpam-2044	57	8	principle	principle	NOUN
ejpam-2044	57	9	possesses	possess	VERB
ejpam-2044	57	10	scale	scale	NOUN
ejpam-2044	57	11	invariance	invariance	NOUN
ejpam-2044	57	12	property	property	NOUN
ejpam-2044	58	1	if	if	SCONJ
ejpam-2044	58	2	and	and	CCONJ
ejpam-2044	58	3	only	only	ADV
ejpam-2044	58	4	if	if	SCONJ
ejpam-2044	58	5	v(x	v(x	NUM
ejpam-2044	58	6	)	)	PUNCT
ejpam-2044	58	7	=	=	SYM
ejpam-2044	58	8	ax+b	ax+b	PROPN
ejpam-2044	58	9	,	,	PUNCT
ejpam-2044	58	10	for	for	ADP
ejpam-2044	58	11	a	a	DET
ejpam-2044	58	12	>	>	X
ejpam-2044	58	13	0	0	NUM
ejpam-2044	58	14	,	,	PUNCT
ejpam-2044	58	15	i.e.	i.e.	X
ejpam-2044	58	16	,	,	PUNCT
ejpam-2044	58	17	only	only	ADV
ejpam-2044	58	18	in	in	ADP
ejpam-2044	58	19	the	the	DET
ejpam-2044	58	20	case	case	NOUN
ejpam-2044	58	21	when	when	SCONJ
ejpam-2044	58	22	it	it	PRON
ejpam-2044	58	23	coincides	coincide	VERB
ejpam-2044	58	24	with	with	ADP
ejpam-2044	58	25	net	net	ADJ
ejpam-2044	58	26	premium	premium	ADJ
ejpam-2044	58	27	principle	principle	NOUN
ejpam-2044	58	28	.	.	PUNCT
ejpam-2044	59	1	proof	proof	NOUN
ejpam-2044	59	2	.	.	PUNCT
ejpam-2044	60	1	let	let	VERB
ejpam-2044	60	2	us	we	PRON
ejpam-2044	60	3	at	at	ADP
ejpam-2044	60	4	the	the	DET
ejpam-2044	60	5	beginning	beginning	NOUN
ejpam-2044	60	6	prove	prove	VERB
ejpam-2044	60	7	the	the	DET
ejpam-2044	60	8	sufficiency	sufficiency	NOUN
ejpam-2044	60	9	of	of	ADP
ejpam-2044	60	10	the	the	DET
ejpam-2044	60	11	statement	statement	NOUN
ejpam-2044	60	12	.	.	PUNCT
ejpam-2044	61	1	from	from	ADP
ejpam-2044	61	2	equation	equation	NOUN
ejpam-2044	61	3	(	(	PUNCT
ejpam-2044	61	4	1	1	NUM
ejpam-2044	61	5	)	)	PUNCT
ejpam-2044	61	6	in	in	ADP
ejpam-2044	61	7	the	the	DET
ejpam-2044	61	8	case	case	NOUN
ejpam-2044	61	9	of	of	ADP
ejpam-2044	61	10	v(x	v(x	PROPN
ejpam-2044	61	11	)	)	PUNCT
ejpam-2044	62	1	=	=	NOUN
ejpam-2044	62	2	ax	ax	NOUN
ejpam-2044	62	3	+	+	CCONJ
ejpam-2044	62	4	b	b	NOUN
ejpam-2044	62	5	,	,	PUNCT
ejpam-2044	62	6	for	for	ADP
ejpam-2044	62	7	a	a	DET
ejpam-2044	62	8	>	>	X
ejpam-2044	62	9	0	0	NUM
ejpam-2044	62	10	,	,	PUNCT
ejpam-2044	62	11	it	it	PRON
ejpam-2044	62	12	follows	follow	VERB
ejpam-2044	62	13	aπm.v.[x	aπm.v.[x	ADV
ejpam-2044	62	14	]	]	PUNCT
ejpam-2044	63	1	+	+	PUNCT
ejpam-2044	63	2	b	b	X
ejpam-2044	63	3	=	=	SYM
ejpam-2044	63	4	e[ax	e[ax	PROPN
ejpam-2044	63	5	+	+	PUNCT
ejpam-2044	63	6	b	b	X
ejpam-2044	63	7	]	]	X
ejpam-2044	63	8	=	=	PUNCT
ejpam-2044	63	9	ae[x	ae[x	PROPN
ejpam-2044	63	10	]	]	PUNCT
ejpam-2044	63	11	+	+	NUM
ejpam-2044	63	12	b	b	X
ejpam-2044	63	13	,	,	PUNCT
ejpam-2044	63	14	m.	m.	NOUN
ejpam-2044	63	15	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	63	16	,	,	PUNCT
ejpam-2044	63	17	v.	v.	ADP
ejpam-2044	63	18	drozdenko	drozdenko	PROPN
ejpam-2044	63	19	/	/	SYM
ejpam-2044	63	20	eur	eur	PROPN
ejpam-2044	63	21	.	.	PUNCT
ejpam-2044	64	1	j.	j.	PROPN
ejpam-2044	64	2	pure	pure	PROPN
ejpam-2044	64	3	appl	appl	PROPN
ejpam-2044	64	4	.	.	PROPN
ejpam-2044	64	5	math	math	PROPN
ejpam-2044	64	6	,	,	PUNCT
ejpam-2044	64	7	7	7	NUM
ejpam-2044	64	8	(	(	PUNCT
ejpam-2044	64	9	2014	2014	NUM
ejpam-2044	64	10	)	)	PUNCT
ejpam-2044	64	11	,	,	PUNCT
ejpam-2044	64	12	267	267	X
ejpam-2044	64	13	-	-	SYM
ejpam-2044	64	14	288	288	NUM
ejpam-2044	64	15	270	270	NUM
ejpam-2044	64	16	thus	thus	ADV
ejpam-2044	64	17	πm.v.[x	πm.v.[x	VERB
ejpam-2044	64	18	]	]	PUNCT
ejpam-2044	65	1	=	=	SYM
ejpam-2044	65	2	e[x	e[x	NOUN
ejpam-2044	65	3	]	]	X
ejpam-2044	65	4	=	=	PUNCT
ejpam-2044	65	5	πnet[x	πnet[x	X
ejpam-2044	65	6	]	]	X
ejpam-2044	65	7	.	.	PUNCT
ejpam-2044	66	1	on	on	ADP
ejpam-2044	66	2	the	the	DET
ejpam-2044	66	3	other	other	ADJ
ejpam-2044	66	4	hand	hand	NOUN
ejpam-2044	66	5	,	,	PUNCT
ejpam-2044	66	6	again	again	ADV
ejpam-2044	66	7	from	from	ADP
ejpam-2044	66	8	equation	equation	NOUN
ejpam-2044	66	9	(	(	PUNCT
ejpam-2044	66	10	1	1	NUM
ejpam-2044	66	11	)	)	PUNCT
ejpam-2044	66	12	for	for	ADP
ejpam-2044	66	13	any	any	DET
ejpam-2044	66	14	θ	θ	PROPN
ejpam-2044	66	15	>	>	X
ejpam-2044	66	16	0	0	NUM
ejpam-2044	66	17	it	it	PRON
ejpam-2044	66	18	follows	follow	VERB
ejpam-2044	66	19	aπm.v.[θx	aπm.v.[θx	PROPN
ejpam-2044	66	20	]	]	X
ejpam-2044	67	1	+	+	NUM
ejpam-2044	67	2	b	b	X
ejpam-2044	67	3	=	=	NOUN
ejpam-2044	67	4	e[aθx	e[aθx	NOUN
ejpam-2044	68	1	+	+	X
ejpam-2044	68	2	b	b	X
ejpam-2044	68	3	]	]	X
ejpam-2044	68	4	=	=	SYM
ejpam-2044	68	5	aθe[x	aθe[x	NOUN
ejpam-2044	68	6	]	]	PUNCT
ejpam-2044	69	1	+	+	CCONJ
ejpam-2044	69	2	b	b	X
ejpam-2044	69	3	,	,	PUNCT
ejpam-2044	69	4	so	so	SCONJ
ejpam-2044	69	5	we	we	PRON
ejpam-2044	69	6	get	get	VERB
ejpam-2044	69	7	πm.v.[θx	πm.v.[θx	NOUN
ejpam-2044	69	8	]	]	PUNCT
ejpam-2044	70	1	=	=	PUNCT
ejpam-2044	70	2	θe[x	θe[x	NOUN
ejpam-2044	70	3	]	]	PUNCT
ejpam-2044	70	4	=	=	VERB
ejpam-2044	70	5	θπm.v.[x	θπm.v.[x	VERB
ejpam-2044	70	6	]	]	PUNCT
ejpam-2044	70	7	,	,	PUNCT
ejpam-2044	70	8	and	and	CCONJ
ejpam-2044	70	9	we	we	PRON
ejpam-2044	70	10	see	see	VERB
ejpam-2044	70	11	that	that	DET
ejpam-2044	70	12	scale	scale	NOUN
ejpam-2044	70	13	invariance	invariance	NOUN
ejpam-2044	70	14	property	property	NOUN
ejpam-2044	70	15	holds	hold	VERB
ejpam-2044	70	16	in	in	ADP
ejpam-2044	70	17	this	this	DET
ejpam-2044	70	18	particular	particular	ADJ
ejpam-2044	70	19	case	case	NOUN
ejpam-2044	70	20	.	.	PUNCT
ejpam-2044	71	1	this	this	PRON
ejpam-2044	71	2	completes	complete	VERB
ejpam-2044	71	3	the	the	DET
ejpam-2044	71	4	proof	proof	NOUN
ejpam-2044	71	5	of	of	ADP
ejpam-2044	71	6	the	the	DET
ejpam-2044	71	7	sufficiency	sufficiency	NOUN
ejpam-2044	71	8	.	.	PUNCT
ejpam-2044	72	1	let	let	VERB
ejpam-2044	72	2	us	we	PRON
ejpam-2044	72	3	now	now	ADV
ejpam-2044	72	4	check	check	VERB
ejpam-2044	72	5	the	the	DET
ejpam-2044	72	6	necessity	necessity	NOUN
ejpam-2044	72	7	.	.	PUNCT
ejpam-2044	73	1	note	note	VERB
ejpam-2044	73	2	that	that	SCONJ
ejpam-2044	73	3	,	,	PUNCT
ejpam-2044	73	4	by	by	ADP
ejpam-2044	73	5	the	the	DET
ejpam-2044	73	6	definition	definition	NOUN
ejpam-2044	73	7	,	,	PUNCT
ejpam-2044	73	8	scale	scale	NOUN
ejpam-2044	73	9	invariance	invariance	NOUN
ejpam-2044	73	10	property	property	NOUN
ejpam-2044	73	11	for	for	ADP
ejpam-2044	73	12	a	a	DET
ejpam-2044	73	13	particular	particular	ADJ
ejpam-2044	73	14	premium	premium	NOUN
ejpam-2044	73	15	calculation	calculation	NOUN
ejpam-2044	73	16	principle	principle	NOUN
ejpam-2044	73	17	holds	hold	VERB
ejpam-2044	73	18	if	if	SCONJ
ejpam-2044	73	19	equation	equation	NOUN
ejpam-2044	73	20	(	(	PUNCT
ejpam-2044	73	21	7	7	X
ejpam-2044	73	22	)	)	PUNCT
ejpam-2044	73	23	holds	hold	VERB
ejpam-2044	73	24	for	for	ADP
ejpam-2044	73	25	any	any	DET
ejpam-2044	73	26	admissible	admissible	ADJ
ejpam-2044	73	27	risk	risk	NOUN
ejpam-2044	73	28	x	x	X
ejpam-2044	73	29	.	.	PUNCT
ejpam-2044	74	1	to	to	PART
ejpam-2044	74	2	show	show	VERB
ejpam-2044	74	3	that	that	PRON
ejpam-2044	74	4	mean	mean	NOUN
ejpam-2044	74	5	value	value	NOUN
ejpam-2044	74	6	premium	premium	NOUN
ejpam-2044	74	7	calculation	calculation	NOUN
ejpam-2044	74	8	principle	principle	NOUN
ejpam-2044	74	9	with	with	ADP
ejpam-2044	74	10	non	non	ADJ
ejpam-2044	74	11	-	-	ADJ
ejpam-2044	74	12	linear	linear	ADJ
ejpam-2044	74	13	functions	function	NOUN
ejpam-2044	74	14	v(x)will	v(x)will	VERB
ejpam-2044	74	15	not	not	PART
ejpam-2044	74	16	possess	possess	VERB
ejpam-2044	74	17	scale	scale	NOUN
ejpam-2044	74	18	invariance	invariance	NOUN
ejpam-2044	74	19	property	property	NOUN
ejpam-2044	74	20	,	,	PUNCT
ejpam-2044	74	21	we	we	PRON
ejpam-2044	74	22	will	will	AUX
ejpam-2044	74	23	consider	consider	VERB
ejpam-2044	74	24	a	a	DET
ejpam-2044	74	25	risk	risk	NOUN
ejpam-2044	74	26	x	x	PUNCT
ejpam-2044	74	27	which	which	PRON
ejpam-2044	74	28	takes	take	VERB
ejpam-2044	74	29	only	only	ADV
ejpam-2044	74	30	two	two	NUM
ejpam-2044	74	31	possible	possible	ADJ
ejpam-2044	74	32	values	value	NOUN
ejpam-2044	74	33	namely	namely	ADV
ejpam-2044	74	34	0	0	NUM
ejpam-2044	74	35	and	and	CCONJ
ejpam-2044	74	36	t	t	NOUN
ejpam-2044	74	37	with	with	ADP
ejpam-2044	74	38	probabilities	probability	NOUN
ejpam-2044	74	39	1−	1−	NUM
ejpam-2044	74	40	p	p	NOUN
ejpam-2044	74	41	and	and	CCONJ
ejpam-2044	74	42	p	p	NOUN
ejpam-2044	74	43	respectively	respectively	ADV
ejpam-2044	74	44	.	.	PUNCT
ejpam-2044	75	1	the	the	DET
ejpam-2044	75	2	risk	risk	NOUN
ejpam-2044	75	3	x	x	PUNCT
ejpam-2044	75	4	in	in	ADP
ejpam-2044	75	5	this	this	DET
ejpam-2044	75	6	case	case	NOUN
ejpam-2044	75	7	can	can	AUX
ejpam-2044	75	8	be	be	AUX
ejpam-2044	75	9	viewed	view	VERB
ejpam-2044	75	10	as	as	ADP
ejpam-2044	75	11	a	a	DET
ejpam-2044	75	12	random	random	ADJ
ejpam-2044	75	13	function	function	NOUN
ejpam-2044	75	14	of	of	ADP
ejpam-2044	75	15	two	two	NUM
ejpam-2044	75	16	parameters	parameter	NOUN
ejpam-2044	75	17	,	,	PUNCT
ejpam-2044	75	18	namely	namely	ADV
ejpam-2044	75	19	p	p	NOUN
ejpam-2044	75	20	and	and	CCONJ
ejpam-2044	75	21	t	t	PROPN
ejpam-2044	75	22	,	,	PUNCT
ejpam-2044	75	23	and	and	CCONJ
ejpam-2044	75	24	therefore	therefore	ADV
ejpam-2044	75	25	within	within	ADP
ejpam-2044	75	26	the	the	DET
ejpam-2044	75	27	proof	proof	NOUN
ejpam-2044	75	28	of	of	ADP
ejpam-2044	75	29	theorem	theorem	NOUN
ejpam-2044	75	30	1	1	NUM
ejpam-2044	75	31	will	will	AUX
ejpam-2044	75	32	be	be	AUX
ejpam-2044	75	33	denoted	denote	VERB
ejpam-2044	75	34	as	as	ADP
ejpam-2044	75	35	x	x	PROPN
ejpam-2044	75	36	t	t	PROPN
ejpam-2044	75	37	p.	p.	NOUN
ejpam-2044	75	38	for	for	ADP
ejpam-2044	75	39	the	the	DET
ejpam-2044	75	40	described	describe	VERB
ejpam-2044	75	41	risk	risk	NOUN
ejpam-2044	75	42	x	x	PUNCT
ejpam-2044	75	43	t	t	NOUN
ejpam-2044	75	44	p	p	NOUN
ejpam-2044	75	45	,	,	PUNCT
ejpam-2044	75	46	equation	equation	NOUN
ejpam-2044	75	47	(	(	PUNCT
ejpam-2044	75	48	1	1	X
ejpam-2044	75	49	)	)	PUNCT
ejpam-2044	75	50	will	will	AUX
ejpam-2044	75	51	take	take	VERB
ejpam-2044	75	52	the	the	DET
ejpam-2044	75	53	following	follow	VERB
ejpam-2044	75	54	form	form	NOUN
ejpam-2044	75	55	v(πm.v.[x	v(πm.v.[x	VERB
ejpam-2044	75	56	t	t	PROPN
ejpam-2044	75	57	p	p	X
ejpam-2044	75	58	]	]	X
ejpam-2044	75	59	)	)	PUNCT
ejpam-2044	75	60	=	=	SYM
ejpam-2044	75	61	pv(t	pv(t	NOUN
ejpam-2044	75	62	)	)	PUNCT
ejpam-2044	76	1	+	+	CCONJ
ejpam-2044	76	2	(	(	PUNCT
ejpam-2044	76	3	1−	1−	NUM
ejpam-2044	76	4	p)v(0	p)v(0	NOUN
ejpam-2044	76	5	)	)	PUNCT
ejpam-2044	76	6	.	.	PUNCT
ejpam-2044	77	1	(	(	PUNCT
ejpam-2044	77	2	8)	8)	NUM
ejpam-2044	77	3	substituting	substitute	VERB
ejpam-2044	77	4	p	p	NOUN
ejpam-2044	77	5	=	=	NOUN
ejpam-2044	77	6	0	0	PROPN
ejpam-2044	77	7	into	into	ADP
ejpam-2044	77	8	(	(	PUNCT
ejpam-2044	77	9	8)	8)	NUM
ejpam-2044	77	10	,	,	PUNCT
ejpam-2044	77	11	obtain	obtain	VERB
ejpam-2044	77	12	v(πm.v.[x	v(πm.v.[x	PROPN
ejpam-2044	77	13	t	t	PROPN
ejpam-2044	77	14	0	0	NUM
ejpam-2044	77	15	]	]	PUNCT
ejpam-2044	77	16	)	)	PUNCT
ejpam-2044	77	17	=	=	SYM
ejpam-2044	77	18	v(0	v(0	PROPN
ejpam-2044	77	19	)	)	PUNCT
ejpam-2044	77	20	.	.	PUNCT
ejpam-2044	78	1	(	(	PUNCT
ejpam-2044	78	2	9	9	X
ejpam-2044	78	3	)	)	PUNCT
ejpam-2044	78	4	since	since	SCONJ
ejpam-2044	78	5	the	the	DET
ejpam-2044	78	6	function	function	NOUN
ejpam-2044	78	7	v	v	NOUN
ejpam-2044	78	8	(	(	PUNCT
ejpam-2044	78	9	·	·	PUNCT
ejpam-2044	78	10	)	)	PUNCT
ejpam-2044	78	11	is	be	AUX
ejpam-2044	78	12	a	a	DET
ejpam-2044	78	13	strictly	strictly	ADV
ejpam-2044	78	14	increasing	increase	VERB
ejpam-2044	78	15	function	function	NOUN
ejpam-2044	78	16	,	,	PUNCT
ejpam-2044	78	17	then	then	ADV
ejpam-2044	78	18	from	from	ADP
ejpam-2044	78	19	the	the	DET
ejpam-2044	78	20	equation	equation	NOUN
ejpam-2044	78	21	(	(	PUNCT
ejpam-2044	78	22	9	9	X
ejpam-2044	78	23	)	)	PUNCT
ejpam-2044	78	24	it	it	PRON
ejpam-2044	78	25	follows	follow	VERB
ejpam-2044	78	26	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	78	27	t	t	PROPN
ejpam-2044	78	28	0	0	NUM
ejpam-2044	78	29	]	]	X
ejpam-2044	79	1	=	=	SYM
ejpam-2044	79	2	0	0	X
ejpam-2044	79	3	.	.	PUNCT
ejpam-2044	80	1	(	(	PUNCT
ejpam-2044	80	2	10	10	NUM
ejpam-2044	80	3	)	)	PUNCT
ejpam-2044	80	4	let	let	VERB
ejpam-2044	80	5	us	we	PRON
ejpam-2044	80	6	now	now	ADV
ejpam-2044	80	7	calculate	calculate	VERB
ejpam-2044	80	8	partial	partial	ADJ
ejpam-2044	80	9	derivatives	derivative	NOUN
ejpam-2044	80	10	with	with	ADP
ejpam-2044	80	11	respect	respect	NOUN
ejpam-2044	80	12	to	to	ADP
ejpam-2044	80	13	the	the	DET
ejpam-2044	80	14	parameter	parameter	NOUN
ejpam-2044	80	15	p	p	NOUN
ejpam-2044	80	16	from	from	ADP
ejpam-2044	80	17	both	both	DET
ejpam-2044	80	18	sides	side	NOUN
ejpam-2044	80	19	of	of	ADP
ejpam-2044	80	20	the	the	DET
ejpam-2044	80	21	equation	equation	NOUN
ejpam-2044	80	22	(	(	PUNCT
ejpam-2044	80	23	8)	8)	NUM
ejpam-2044	80	24	v′(πm.v.[x	v′(πm.v.[x	NOUN
ejpam-2044	80	25	t	t	NOUN
ejpam-2044	80	26	p	p	X
ejpam-2044	80	27	]	]	X
ejpam-2044	80	28	)	)	PUNCT
ejpam-2044	80	29	·	·	PUNCT
ejpam-2044	81	1	∂	∂	NUM
ejpam-2044	82	1	∂	∂	NUM
ejpam-2044	82	2	p	p	NOUN
ejpam-2044	82	3	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	82	4	t	t	NOUN
ejpam-2044	82	5	p	p	X
ejpam-2044	82	6	]	]	X
ejpam-2044	82	7	=	=	PUNCT
ejpam-2044	82	8	v(t)−	v(t)−	PROPN
ejpam-2044	82	9	v(0	v(0	PROPN
ejpam-2044	82	10	)	)	PUNCT
ejpam-2044	82	11	.	.	PUNCT
ejpam-2044	83	1	(	(	PUNCT
ejpam-2044	83	2	11	11	NUM
ejpam-2044	83	3	)	)	PUNCT
ejpam-2044	83	4	substitution	substitution	NOUN
ejpam-2044	83	5	of	of	ADP
ejpam-2044	83	6	the	the	DET
ejpam-2044	83	7	value	value	NOUN
ejpam-2044	83	8	p	p	NOUN
ejpam-2044	84	1	=	=	NOUN
ejpam-2044	84	2	0	0	PROPN
ejpam-2044	84	3	into	into	ADP
ejpam-2044	84	4	(	(	PUNCT
ejpam-2044	84	5	11	11	NUM
ejpam-2044	84	6	)	)	PUNCT
ejpam-2044	84	7	yields	yield	NOUN
ejpam-2044	84	8	v′(πm.v.[x	v′(πm.v.[x	VERB
ejpam-2044	84	9	t	t	PROPN
ejpam-2044	84	10	0	0	NUM
ejpam-2044	84	11	]	]	PUNCT
ejpam-2044	84	12	)	)	PUNCT
ejpam-2044	84	13	·	·	PUNCT
ejpam-2044	84	14	�	�	PROPN
ejpam-2044	84	15	∂	∂	NUM
ejpam-2044	84	16	∂	∂	NUM
ejpam-2044	85	1	p	p	NOUN
ejpam-2044	85	2	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	85	3	t	t	NOUN
ejpam-2044	85	4	p	p	X
ejpam-2044	85	5	]	]	X
ejpam-2044	85	6	�	�	PROPN
ejpam-2044	85	7	�	�	PROPN
ejpam-2044	85	8	�	�	PROPN
ejpam-2044	85	9	�	�	PROPN
ejpam-2044	85	10	p=0	p=0	PROPN
ejpam-2044	85	11	�	�	PROPN
ejpam-2044	85	12	=	=	SYM
ejpam-2044	85	13	v(t)−	v(t)−	PROPN
ejpam-2044	85	14	v(0	v(0	PROPN
ejpam-2044	85	15	)	)	PUNCT
ejpam-2044	85	16	.	.	PUNCT
ejpam-2044	86	1	(	(	PUNCT
ejpam-2044	86	2	12	12	NUM
ejpam-2044	86	3	)	)	PUNCT
ejpam-2044	86	4	since	since	SCONJ
ejpam-2044	86	5	the	the	DET
ejpam-2044	86	6	function	function	NOUN
ejpam-2044	86	7	v	v	NOUN
ejpam-2044	86	8	(	(	PUNCT
ejpam-2044	86	9	·	·	PUNCT
ejpam-2044	86	10	)	)	PUNCT
ejpam-2044	86	11	is	be	AUX
ejpam-2044	86	12	a	a	DET
ejpam-2044	86	13	strictly	strictly	ADV
ejpam-2044	86	14	increasing	increase	VERB
ejpam-2044	86	15	function	function	NOUN
ejpam-2044	86	16	,	,	PUNCT
ejpam-2044	86	17	then	then	ADV
ejpam-2044	86	18	v′(0	v′(0	NOUN
ejpam-2044	86	19	)	)	PUNCT
ejpam-2044	86	20	>	>	X
ejpam-2044	87	1	0	0	X
ejpam-2044	87	2	.	.	PUNCT
ejpam-2044	87	3	therefore	therefore	ADV
ejpam-2044	87	4	,	,	PUNCT
ejpam-2044	87	5	taking	take	VERB
ejpam-2044	87	6	into	into	ADP
ejpam-2044	87	7	account	account	NOUN
ejpam-2044	87	8	identity	identity	NOUN
ejpam-2044	87	9	(	(	PUNCT
ejpam-2044	87	10	10	10	NUM
ejpam-2044	87	11	)	)	PUNCT
ejpam-2044	87	12	we	we	PRON
ejpam-2044	87	13	get	get	VERB
ejpam-2044	87	14	from	from	ADP
ejpam-2044	87	15	(	(	PUNCT
ejpam-2044	87	16	12	12	NUM
ejpam-2044	87	17	)	)	PUNCT
ejpam-2044	87	18	a	a	DET
ejpam-2044	87	19	representation	representation	NOUN
ejpam-2044	87	20	for	for	ADP
ejpam-2044	87	21	the	the	DET
ejpam-2044	87	22	partial	partial	ADJ
ejpam-2044	87	23	derivative	derivative	NOUN
ejpam-2044	87	24	of	of	ADP
ejpam-2044	87	25	the	the	DET
ejpam-2044	87	26	premium	premium	NOUN
ejpam-2044	87	27	with	with	ADP
ejpam-2044	87	28	respect	respect	NOUN
ejpam-2044	87	29	to	to	ADP
ejpam-2044	87	30	the	the	DET
ejpam-2044	87	31	parameter	parameter	NOUN
ejpam-2044	87	32	p	p	NOUN
ejpam-2044	87	33	at	at	ADP
ejpam-2044	87	34	the	the	DET
ejpam-2044	87	35	point	point	NOUN
ejpam-2044	87	36	p	p	X
ejpam-2044	87	37	=	=	NOUN
ejpam-2044	87	38	0	0	NUM
ejpam-2044	87	39	,	,	PUNCT
ejpam-2044	87	40	namely	namely	ADV
ejpam-2044	87	41	,	,	PUNCT
ejpam-2044	87	42	∂	∂	NUM
ejpam-2044	87	43	∂	∂	NOUN
ejpam-2044	88	1	p	p	NOUN
ejpam-2044	88	2	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	88	3	t	t	NOUN
ejpam-2044	89	1	p	p	X
ejpam-2044	89	2	]	]	X
ejpam-2044	89	3	�	�	PROPN
ejpam-2044	89	4	�	�	PROPN
ejpam-2044	89	5	�	�	PROPN
ejpam-2044	89	6	�	�	PROPN
ejpam-2044	89	7	p=0	p=0	PROPN
ejpam-2044	89	8	=	=	PUNCT
ejpam-2044	89	9	v(t)−	v(t)−	PROPN
ejpam-2044	89	10	v(0	v(0	PROPN
ejpam-2044	89	11	)	)	PUNCT
ejpam-2044	89	12	v′(0	v′(0	NOUN
ejpam-2044	89	13	)	)	PUNCT
ejpam-2044	89	14	.	.	PUNCT
ejpam-2044	90	1	(	(	PUNCT
ejpam-2044	90	2	13	13	NUM
ejpam-2044	90	3	)	)	PUNCT
ejpam-2044	90	4	m.	m.	NOUN
ejpam-2044	90	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	90	6	,	,	PUNCT
ejpam-2044	90	7	v.	v.	ADP
ejpam-2044	90	8	drozdenko	drozdenko	PROPN
ejpam-2044	90	9	/	/	SYM
ejpam-2044	90	10	eur	eur	PROPN
ejpam-2044	90	11	.	.	PUNCT
ejpam-2044	91	1	j.	j.	PROPN
ejpam-2044	91	2	pure	pure	PROPN
ejpam-2044	91	3	appl	appl	PROPN
ejpam-2044	91	4	.	.	PROPN
ejpam-2044	91	5	math	math	PROPN
ejpam-2044	91	6	,	,	PUNCT
ejpam-2044	91	7	7	7	NUM
ejpam-2044	91	8	(	(	PUNCT
ejpam-2044	91	9	2014	2014	NUM
ejpam-2044	91	10	)	)	PUNCT
ejpam-2044	91	11	,	,	PUNCT
ejpam-2044	91	12	267	267	X
ejpam-2044	91	13	-	-	SYM
ejpam-2044	91	14	288	288	NUM
ejpam-2044	91	15	271	271	NUM
ejpam-2044	91	16	for	for	ADP
ejpam-2044	91	17	any	any	DET
ejpam-2044	91	18	θ	θ	PROPN
ejpam-2044	91	19	>	>	SYM
ejpam-2044	91	20	0	0	NUM
ejpam-2044	91	21	equation	equation	NOUN
ejpam-2044	91	22	(	(	PUNCT
ejpam-2044	91	23	1	1	NUM
ejpam-2044	91	24	)	)	PUNCT
ejpam-2044	91	25	for	for	ADP
ejpam-2044	91	26	the	the	DET
ejpam-2044	91	27	risk	risk	NOUN
ejpam-2044	91	28	θx	θx	ADP
ejpam-2044	91	29	t	t	PROPN
ejpam-2044	91	30	p	p	NOUN
ejpam-2044	91	31	in	in	ADP
ejpam-2044	91	32	the	the	DET
ejpam-2044	91	33	case	case	NOUN
ejpam-2044	91	34	of	of	ADP
ejpam-2044	91	35	scale	scale	NOUN
ejpam-2044	91	36	invariant	invariant	ADJ
ejpam-2044	91	37	mean	mean	NOUN
ejpam-2044	91	38	value	value	NOUN
ejpam-2044	91	39	principle	principle	NOUN
ejpam-2044	91	40	will	will	AUX
ejpam-2044	91	41	have	have	VERB
ejpam-2044	91	42	the	the	DET
ejpam-2044	91	43	following	follow	VERB
ejpam-2044	91	44	form	form	NOUN
ejpam-2044	91	45	v(θπm.v.[x	v(θπm.v.[x	VERB
ejpam-2044	91	46	t	t	NOUN
ejpam-2044	91	47	p	p	X
ejpam-2044	91	48	]	]	X
ejpam-2044	91	49	)	)	PUNCT
ejpam-2044	91	50	=	=	SYM
ejpam-2044	91	51	pv(θt	pv(θt	X
ejpam-2044	91	52	)	)	PUNCT
ejpam-2044	92	1	+	+	CCONJ
ejpam-2044	92	2	(	(	PUNCT
ejpam-2044	92	3	1−	1−	NUM
ejpam-2044	92	4	p)v(0	p)v(0	NOUN
ejpam-2044	92	5	)	)	PUNCT
ejpam-2044	92	6	.	.	PUNCT
ejpam-2044	93	1	(	(	PUNCT
ejpam-2044	93	2	14	14	X
ejpam-2044	93	3	)	)	PUNCT
ejpam-2044	93	4	taking	take	VERB
ejpam-2044	93	5	partial	partial	ADJ
ejpam-2044	93	6	derivatives	derivative	NOUN
ejpam-2044	93	7	with	with	ADP
ejpam-2044	93	8	respect	respect	NOUN
ejpam-2044	93	9	to	to	ADP
ejpam-2044	93	10	the	the	DET
ejpam-2044	93	11	parameter	parameter	NOUN
ejpam-2044	93	12	p	p	NOUN
ejpam-2044	93	13	from	from	ADP
ejpam-2044	93	14	both	both	DET
ejpam-2044	93	15	sides	side	NOUN
ejpam-2044	93	16	of	of	ADP
ejpam-2044	93	17	the	the	DET
ejpam-2044	93	18	equation	equation	NOUN
ejpam-2044	93	19	(	(	PUNCT
ejpam-2044	93	20	14	14	NUM
ejpam-2044	93	21	)	)	PUNCT
ejpam-2044	93	22	,	,	PUNCT
ejpam-2044	93	23	obtain	obtain	VERB
ejpam-2044	93	24	v′(θπm.v.[x	v′(θπm.v.[x	NOUN
ejpam-2044	93	25	t	t	NOUN
ejpam-2044	93	26	p	p	X
ejpam-2044	93	27	]	]	X
ejpam-2044	93	28	)	)	PUNCT
ejpam-2044	93	29	·	·	PUNCT
ejpam-2044	93	30	θ	θ	X
ejpam-2044	93	31	·	·	PUNCT
ejpam-2044	93	32	∂	∂	NUM
ejpam-2044	93	33	∂	∂	NOUN
ejpam-2044	93	34	p	p	NOUN
ejpam-2044	93	35	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	93	36	t	t	NOUN
ejpam-2044	94	1	p	p	X
ejpam-2044	94	2	]	]	X
ejpam-2044	94	3	=	=	X
ejpam-2044	94	4	v(θt)−	v(θt)−	X
ejpam-2044	94	5	v(0	v(0	PROPN
ejpam-2044	94	6	)	)	PUNCT
ejpam-2044	94	7	.	.	PUNCT
ejpam-2044	95	1	(	(	PUNCT
ejpam-2044	95	2	15	15	X
ejpam-2044	95	3	)	)	PUNCT
ejpam-2044	95	4	substituting	substitute	VERB
ejpam-2044	95	5	p	p	NOUN
ejpam-2044	95	6	=	=	NOUN
ejpam-2044	95	7	0	0	PROPN
ejpam-2044	95	8	into	into	ADP
ejpam-2044	95	9	(	(	PUNCT
ejpam-2044	95	10	15	15	NUM
ejpam-2044	95	11	)	)	PUNCT
ejpam-2044	95	12	,	,	PUNCT
ejpam-2044	95	13	using	use	VERB
ejpam-2044	95	14	identity	identity	NOUN
ejpam-2044	95	15	(	(	PUNCT
ejpam-2044	95	16	10	10	NUM
ejpam-2044	95	17	)	)	PUNCT
ejpam-2044	95	18	as	as	ADV
ejpam-2044	95	19	well	well	ADV
ejpam-2044	95	20	as	as	ADP
ejpam-2044	95	21	inequality	inequality	NOUN
ejpam-2044	95	22	v′(0	v′(0	NOUN
ejpam-2044	95	23	)	)	PUNCT
ejpam-2044	95	24	>	>	X
ejpam-2044	95	25	0	0	NUM
ejpam-2044	95	26	,	,	PUNCT
ejpam-2044	95	27	we	we	PRON
ejpam-2044	95	28	again	again	ADV
ejpam-2044	95	29	get	get	VERB
ejpam-2044	95	30	a	a	DET
ejpam-2044	95	31	representation	representation	NOUN
ejpam-2044	95	32	for	for	ADP
ejpam-2044	95	33	the	the	DET
ejpam-2044	95	34	partial	partial	ADJ
ejpam-2044	95	35	derivative	derivative	NOUN
ejpam-2044	95	36	of	of	ADP
ejpam-2044	95	37	the	the	DET
ejpam-2044	95	38	premium	premium	NOUN
ejpam-2044	95	39	with	with	ADP
ejpam-2044	95	40	respect	respect	NOUN
ejpam-2044	95	41	to	to	ADP
ejpam-2044	95	42	the	the	DET
ejpam-2044	95	43	parameter	parameter	NOUN
ejpam-2044	95	44	p	p	NOUN
ejpam-2044	95	45	at	at	ADP
ejpam-2044	95	46	the	the	DET
ejpam-2044	95	47	point	point	NOUN
ejpam-2044	95	48	p	p	X
ejpam-2044	95	49	=	=	NOUN
ejpam-2044	95	50	0	0	NUM
ejpam-2044	95	51	,	,	PUNCT
ejpam-2044	95	52	namely	namely	ADV
ejpam-2044	95	53	,	,	PUNCT
ejpam-2044	95	54	∂	∂	NUM
ejpam-2044	95	55	∂	∂	NOUN
ejpam-2044	96	1	p	p	NOUN
ejpam-2044	96	2	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	96	3	t	t	NOUN
ejpam-2044	97	1	p	p	X
ejpam-2044	97	2	]	]	X
ejpam-2044	97	3	�	�	PROPN
ejpam-2044	97	4	�	�	PROPN
ejpam-2044	97	5	�	�	PROPN
ejpam-2044	97	6	�	�	PROPN
ejpam-2044	97	7	p=0	p=0	PROPN
ejpam-2044	97	8	=	=	PRON
ejpam-2044	97	9	v(θt)−	v(θt)−	PROPN
ejpam-2044	97	10	v(0	v(0	PROPN
ejpam-2044	97	11	)	)	PUNCT
ejpam-2044	97	12	v′(0	v′(0	PROPN
ejpam-2044	97	13	)	)	PUNCT
ejpam-2044	97	14	·	·	PUNCT
ejpam-2044	97	15	θ	θ	NOUN
ejpam-2044	97	16	.	.	PUNCT
ejpam-2044	98	1	(	(	PUNCT
ejpam-2044	98	2	16	16	X
ejpam-2044	98	3	)	)	PUNCT
ejpam-2044	98	4	observe	observe	VERB
ejpam-2044	98	5	that	that	SCONJ
ejpam-2044	98	6	equations	equation	NOUN
ejpam-2044	98	7	(	(	PUNCT
ejpam-2044	98	8	13	13	NUM
ejpam-2044	98	9	)	)	PUNCT
ejpam-2044	98	10	and	and	CCONJ
ejpam-2044	98	11	(	(	PUNCT
ejpam-2044	98	12	16	16	NUM
ejpam-2044	98	13	)	)	PUNCT
ejpam-2044	98	14	have	have	VERB
ejpam-2044	98	15	equal	equal	ADJ
ejpam-2044	98	16	left	leave	VERB
ejpam-2044	98	17	-	-	PUNCT
ejpam-2044	98	18	hand	hand	NOUN
ejpam-2044	98	19	sides	side	NOUN
ejpam-2044	98	20	,	,	PUNCT
ejpam-2044	98	21	this	this	PRON
ejpam-2044	98	22	means	mean	VERB
ejpam-2044	98	23	that	that	SCONJ
ejpam-2044	98	24	their	their	PRON
ejpam-2044	98	25	right	right	ADJ
ejpam-2044	98	26	-	-	PUNCT
ejpam-2044	98	27	hand	hand	NOUN
ejpam-2044	98	28	sides	side	NOUN
ejpam-2044	98	29	also	also	ADV
ejpam-2044	98	30	have	have	VERB
ejpam-2044	98	31	to	to	PART
ejpam-2044	98	32	be	be	AUX
ejpam-2044	98	33	equal	equal	ADJ
ejpam-2044	98	34	.	.	PUNCT
ejpam-2044	99	1	in	in	ADP
ejpam-2044	99	2	this	this	DET
ejpam-2044	99	3	way	way	NOUN
ejpam-2044	99	4	we	we	PRON
ejpam-2044	99	5	finally	finally	ADV
ejpam-2044	99	6	get	get	VERB
ejpam-2044	99	7	an	an	DET
ejpam-2044	99	8	equation	equation	NOUN
ejpam-2044	99	9	which	which	PRON
ejpam-2044	99	10	function	function	VERB
ejpam-2044	99	11	v	v	NOUN
ejpam-2044	99	12	(	(	PUNCT
ejpam-2044	99	13	·	·	PUNCT
ejpam-2044	99	14	)	)	PUNCT
ejpam-2044	99	15	has	have	VERB
ejpam-2044	99	16	to	to	PART
ejpam-2044	99	17	satisfy	satisfy	VERB
ejpam-2044	99	18	in	in	ADP
ejpam-2044	99	19	the	the	DET
ejpam-2044	99	20	case	case	NOUN
ejpam-2044	99	21	of	of	ADP
ejpam-2044	99	22	scale	scale	NOUN
ejpam-2044	99	23	invariant	invariant	ADJ
ejpam-2044	99	24	mean	mean	NOUN
ejpam-2044	99	25	value	value	NOUN
ejpam-2044	99	26	premium	premium	NOUN
ejpam-2044	99	27	calculation	calculation	NOUN
ejpam-2044	99	28	principle	principle	NOUN
ejpam-2044	99	29	,	,	PUNCT
ejpam-2044	99	30	namely	namely	ADV
ejpam-2044	99	31	,	,	PUNCT
ejpam-2044	99	32	v(t)−	v(t)−	PROPN
ejpam-2044	99	33	v(0	v(0	PROPN
ejpam-2044	99	34	)	)	PUNCT
ejpam-2044	99	35	v′(0	v′(0	PROPN
ejpam-2044	99	36	)	)	PUNCT
ejpam-2044	99	37	=	=	PRON
ejpam-2044	99	38	v(θt)−	v(θt)−	X
ejpam-2044	99	39	v(0	v(0	PROPN
ejpam-2044	99	40	)	)	PUNCT
ejpam-2044	99	41	v′(0	v′(0	PROPN
ejpam-2044	99	42	)	)	PUNCT
ejpam-2044	99	43	·	·	PUNCT
ejpam-2044	99	44	θ	θ	NOUN
ejpam-2044	99	45	.	.	PUNCT
ejpam-2044	100	1	(	(	PUNCT
ejpam-2044	100	2	17	17	NUM
ejpam-2044	100	3	)	)	PUNCT
ejpam-2044	100	4	equation	equation	NOUN
ejpam-2044	100	5	(	(	PUNCT
ejpam-2044	100	6	17	17	NUM
ejpam-2044	100	7	)	)	PUNCT
ejpam-2044	100	8	can	can	AUX
ejpam-2044	100	9	be	be	AUX
ejpam-2044	100	10	simplified	simplify	VERB
ejpam-2044	100	11	to	to	ADP
ejpam-2044	100	12	the	the	DET
ejpam-2044	100	13	following	follow	VERB
ejpam-2044	100	14	one	one	NUM
ejpam-2044	100	15	v(θt)−	v(θt)−	X
ejpam-2044	100	16	v(0	v(0	NOUN
ejpam-2044	100	17	)	)	PUNCT
ejpam-2044	100	18	=	=	SYM
ejpam-2044	100	19	θ	θ	X
ejpam-2044	100	20	·	·	PUNCT
ejpam-2044	100	21	(	(	PUNCT
ejpam-2044	100	22	v(t)−	v(t)−	PROPN
ejpam-2044	100	23	v(0	v(0	PROPN
ejpam-2044	100	24	)	)	PUNCT
ejpam-2044	100	25	)	)	PUNCT
ejpam-2044	100	26	.	.	PUNCT
ejpam-2044	101	1	(	(	PUNCT
ejpam-2044	101	2	18	18	NUM
ejpam-2044	101	3	)	)	PUNCT
ejpam-2044	101	4	calculating	calculate	VERB
ejpam-2044	101	5	partial	partial	ADJ
ejpam-2044	101	6	derivatives	derivative	NOUN
ejpam-2044	101	7	with	with	ADP
ejpam-2044	101	8	respect	respect	NOUN
ejpam-2044	101	9	to	to	ADP
ejpam-2044	101	10	the	the	DET
ejpam-2044	101	11	parameter	parameter	NOUN
ejpam-2044	101	12	t	t	PROPN
ejpam-2044	101	13	from	from	ADP
ejpam-2044	101	14	both	both	DET
ejpam-2044	101	15	sides	side	NOUN
ejpam-2044	101	16	of	of	ADP
ejpam-2044	101	17	the	the	DET
ejpam-2044	101	18	equation	equation	NOUN
ejpam-2044	101	19	(	(	PUNCT
ejpam-2044	101	20	18	18	NUM
ejpam-2044	101	21	)	)	PUNCT
ejpam-2044	101	22	,	,	PUNCT
ejpam-2044	101	23	we	we	PRON
ejpam-2044	101	24	get	get	VERB
ejpam-2044	101	25	θv′(θt	θv′(θt	NOUN
ejpam-2044	101	26	)	)	PUNCT
ejpam-2044	102	1	=	=	SYM
ejpam-2044	102	2	θv′(t	θv′(t	VERB
ejpam-2044	102	3	)	)	PUNCT
ejpam-2044	102	4	or	or	CCONJ
ejpam-2044	102	5	equivalently	equivalently	ADV
ejpam-2044	102	6	,	,	PUNCT
ejpam-2044	102	7	after	after	ADP
ejpam-2044	102	8	cancelation	cancelation	NOUN
ejpam-2044	102	9	of	of	ADP
ejpam-2044	102	10	θ	θ	PROPN
ejpam-2044	102	11	factor	factor	NOUN
ejpam-2044	102	12	,	,	PUNCT
ejpam-2044	102	13	v′(θt	v′(θt	NOUN
ejpam-2044	102	14	)	)	PUNCT
ejpam-2044	102	15	=	=	SYM
ejpam-2044	103	1	v′(t	v′(t	PROPN
ejpam-2044	103	2	)	)	PUNCT
ejpam-2044	103	3	.	.	PUNCT
ejpam-2044	104	1	(	(	PUNCT
ejpam-2044	104	2	19	19	NUM
ejpam-2044	104	3	)	)	PUNCT
ejpam-2044	104	4	by	by	ADP
ejpam-2044	104	5	fixing	fix	VERB
ejpam-2044	104	6	the	the	DET
ejpam-2044	104	7	parameter	parameter	NOUN
ejpam-2044	104	8	t	t	PROPN
ejpam-2044	104	9	in	in	ADP
ejpam-2044	104	10	equation	equation	NOUN
ejpam-2044	104	11	(	(	PUNCT
ejpam-2044	104	12	19	19	NUM
ejpam-2044	104	13	)	)	PUNCT
ejpam-2044	104	14	to	to	ADP
ejpam-2044	104	15	a	a	DET
ejpam-2044	104	16	positive	positive	ADJ
ejpam-2044	104	17	value	value	NOUN
ejpam-2044	104	18	and	and	CCONJ
ejpam-2044	104	19	varying	vary	VERB
ejpam-2044	104	20	values	value	NOUN
ejpam-2044	104	21	of	of	ADP
ejpam-2044	104	22	the	the	DET
ejpam-2044	104	23	parameter	parameter	NOUN
ejpam-2044	104	24	θ	θ	PROPN
ejpam-2044	104	25	we	we	PRON
ejpam-2044	104	26	will	will	AUX
ejpam-2044	104	27	make	make	VERB
ejpam-2044	104	28	v′(θt	v′(θt	NOUN
ejpam-2044	104	29	)	)	PUNCT
ejpam-2044	104	30	a	a	DET
ejpam-2044	104	31	function	function	NOUN
ejpam-2044	104	32	of	of	ADP
ejpam-2044	104	33	changing	change	VERB
ejpam-2044	104	34	variable	variable	NOUN
ejpam-2044	104	35	defined	define	VERB
ejpam-2044	104	36	on	on	ADP
ejpam-2044	104	37	r+	r+	NOUN
ejpam-2044	104	38	while	while	SCONJ
ejpam-2044	104	39	the	the	DET
ejpam-2044	104	40	value	value	NOUN
ejpam-2044	104	41	v′(t	v′(t	NOUN
ejpam-2044	104	42	)	)	PUNCT
ejpam-2044	104	43	will	will	AUX
ejpam-2044	104	44	be	be	AUX
ejpam-2044	104	45	fixed	fix	VERB
ejpam-2044	104	46	to	to	ADP
ejpam-2044	104	47	a	a	DET
ejpam-2044	104	48	constant	constant	ADJ
ejpam-2044	104	49	.	.	PUNCT
ejpam-2044	105	1	by	by	ADP
ejpam-2044	105	2	doing	do	VERB
ejpam-2044	105	3	this	this	PRON
ejpam-2044	105	4	we	we	PRON
ejpam-2044	105	5	will	will	AUX
ejpam-2044	105	6	see	see	VERB
ejpam-2044	105	7	that	that	SCONJ
ejpam-2044	105	8	the	the	DET
ejpam-2044	105	9	function	function	NOUN
ejpam-2044	105	10	v′(x	v′(x	NOUN
ejpam-2044	105	11	)	)	PUNCT
ejpam-2044	105	12	will	will	AUX
ejpam-2044	105	13	take	take	VERB
ejpam-2044	105	14	for	for	ADP
ejpam-2044	105	15	all	all	PRON
ejpam-2044	105	16	x	x	SYM
ejpam-2044	105	17	>	>	X
ejpam-2044	105	18	0	0	NUM
ejpam-2044	105	19	one	one	NUM
ejpam-2044	105	20	and	and	CCONJ
ejpam-2044	105	21	the	the	DET
ejpam-2044	105	22	same	same	ADJ
ejpam-2044	105	23	value	value	NOUN
ejpam-2044	105	24	,	,	PUNCT
ejpam-2044	105	25	let	let	VERB
ejpam-2044	105	26	us	we	PRON
ejpam-2044	105	27	denote	denote	VERB
ejpam-2044	105	28	this	this	DET
ejpam-2044	105	29	value	value	NOUN
ejpam-2044	105	30	by	by	ADP
ejpam-2044	105	31	a1	a1	NOUN
ejpam-2044	105	32	.	.	PUNCT
ejpam-2044	106	1	in	in	ADP
ejpam-2044	106	2	a	a	DET
ejpam-2044	106	3	very	very	ADV
ejpam-2044	106	4	similar	similar	ADJ
ejpam-2044	106	5	way	way	NOUN
ejpam-2044	106	6	,	,	PUNCT
ejpam-2044	106	7	by	by	ADP
ejpam-2044	106	8	fixing	fix	VERB
ejpam-2044	106	9	the	the	DET
ejpam-2044	106	10	parameter	parameter	NOUN
ejpam-2044	106	11	t	t	PROPN
ejpam-2044	106	12	in	in	ADP
ejpam-2044	106	13	equation	equation	NOUN
ejpam-2044	106	14	(	(	PUNCT
ejpam-2044	106	15	19	19	NUM
ejpam-2044	106	16	)	)	PUNCT
ejpam-2044	106	17	to	to	ADP
ejpam-2044	106	18	a	a	DET
ejpam-2044	106	19	negative	negative	ADJ
ejpam-2044	106	20	value	value	NOUN
ejpam-2044	106	21	and	and	CCONJ
ejpam-2044	106	22	varying	vary	VERB
ejpam-2044	106	23	values	value	NOUN
ejpam-2044	106	24	of	of	ADP
ejpam-2044	106	25	the	the	DET
ejpam-2044	106	26	parameter	parameter	NOUN
ejpam-2044	106	27	θ	θ	PROPN
ejpam-2044	106	28	we	we	PRON
ejpam-2044	106	29	will	will	AUX
ejpam-2044	106	30	make	make	VERB
ejpam-2044	106	31	v′(θt	v′(θt	NOUN
ejpam-2044	106	32	)	)	PUNCT
ejpam-2044	106	33	a	a	DET
ejpam-2044	106	34	function	function	NOUN
ejpam-2044	106	35	of	of	ADP
ejpam-2044	106	36	changing	change	VERB
ejpam-2044	106	37	variable	variable	NOUN
ejpam-2044	106	38	defined	define	VERB
ejpam-2044	106	39	on	on	ADP
ejpam-2044	106	40	r−	r−	PROPN
ejpam-2044	106	41	while	while	SCONJ
ejpam-2044	106	42	the	the	DET
ejpam-2044	106	43	value	value	NOUN
ejpam-2044	106	44	v′(t	v′(t	NOUN
ejpam-2044	106	45	)	)	PUNCT
ejpam-2044	106	46	will	will	AUX
ejpam-2044	106	47	be	be	AUX
ejpam-2044	106	48	fixed	fix	VERB
ejpam-2044	106	49	to	to	ADP
ejpam-2044	106	50	a	a	DET
ejpam-2044	106	51	constant	constant	ADJ
ejpam-2044	106	52	.	.	PUNCT
ejpam-2044	107	1	in	in	ADP
ejpam-2044	107	2	this	this	DET
ejpam-2044	107	3	way	way	NOUN
ejpam-2044	107	4	we	we	PRON
ejpam-2044	107	5	will	will	AUX
ejpam-2044	107	6	see	see	VERB
ejpam-2044	107	7	that	that	SCONJ
ejpam-2044	107	8	the	the	DET
ejpam-2044	107	9	function	function	NOUN
ejpam-2044	107	10	v′(x	v′(x	NOUN
ejpam-2044	107	11	)	)	PUNCT
ejpam-2044	107	12	will	will	AUX
ejpam-2044	107	13	take	take	VERB
ejpam-2044	107	14	for	for	ADP
ejpam-2044	107	15	all	all	PRON
ejpam-2044	107	16	x	x	SYM
ejpam-2044	107	17	<	<	X
ejpam-2044	107	18	0	0	NUM
ejpam-2044	107	19	one	one	NUM
ejpam-2044	107	20	and	and	CCONJ
ejpam-2044	107	21	the	the	DET
ejpam-2044	107	22	same	same	ADJ
ejpam-2044	107	23	value	value	NOUN
ejpam-2044	107	24	,	,	PUNCT
ejpam-2044	107	25	let	let	VERB
ejpam-2044	107	26	us	we	PRON
ejpam-2044	107	27	denote	denote	VERB
ejpam-2044	107	28	this	this	DET
ejpam-2044	107	29	value	value	NOUN
ejpam-2044	107	30	by	by	ADP
ejpam-2044	107	31	a2	a2	PROPN
ejpam-2044	107	32	.	.	PUNCT
ejpam-2044	108	1	since	since	SCONJ
ejpam-2044	108	2	the	the	DET
ejpam-2044	108	3	function	function	NOUN
ejpam-2044	108	4	v(x	v(x	PROPN
ejpam-2044	108	5	)	)	PUNCT
ejpam-2044	108	6	was	be	AUX
ejpam-2044	108	7	twice	twice	ADV
ejpam-2044	108	8	differentiable	differentiable	ADJ
ejpam-2044	108	9	,	,	PUNCT
ejpam-2044	108	10	then	then	ADV
ejpam-2044	108	11	the	the	DET
ejpam-2044	108	12	function	function	NOUN
ejpam-2044	108	13	v′(x	v′(x	NOUN
ejpam-2044	108	14	)	)	PUNCT
ejpam-2044	108	15	must	must	AUX
ejpam-2044	108	16	be	be	AUX
ejpam-2044	108	17	continuous	continuous	ADJ
ejpam-2044	108	18	,	,	PUNCT
ejpam-2044	108	19	this	this	DET
ejpam-2044	108	20	yields	yield	NOUN
ejpam-2044	108	21	a1	a1	NOUN
ejpam-2044	108	22	=	=	SYM
ejpam-2044	108	23	a2	a2	PROPN
ejpam-2044	108	24	=	=	SYM
ejpam-2044	108	25	v′(0	v′(0	PROPN
ejpam-2044	108	26	)	)	PUNCT
ejpam-2044	108	27	=	=	NOUN
ejpam-2044	108	28	:	:	PUNCT
ejpam-2044	108	29	a	a	DET
ejpam-2044	108	30	,	,	PUNCT
ejpam-2044	108	31	m.	m.	NOUN
ejpam-2044	108	32	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	108	33	,	,	PUNCT
ejpam-2044	108	34	v.	v.	ADP
ejpam-2044	108	35	drozdenko	drozdenko	PROPN
ejpam-2044	108	36	/	/	SYM
ejpam-2044	108	37	eur	eur	PROPN
ejpam-2044	108	38	.	.	PUNCT
ejpam-2044	109	1	j.	j.	PROPN
ejpam-2044	109	2	pure	pure	PROPN
ejpam-2044	109	3	appl	appl	PROPN
ejpam-2044	109	4	.	.	PROPN
ejpam-2044	109	5	math	math	PROPN
ejpam-2044	109	6	,	,	PUNCT
ejpam-2044	109	7	7	7	NUM
ejpam-2044	109	8	(	(	PUNCT
ejpam-2044	109	9	2014	2014	NUM
ejpam-2044	109	10	)	)	PUNCT
ejpam-2044	109	11	,	,	PUNCT
ejpam-2044	109	12	267	267	X
ejpam-2044	109	13	-	-	SYM
ejpam-2044	109	14	288	288	NUM
ejpam-2044	109	15	272	272	NUM
ejpam-2044	109	16	hence	hence	ADV
ejpam-2044	109	17	v′(x	v′(x	NOUN
ejpam-2044	109	18	)	)	PUNCT
ejpam-2044	109	19	=	=	SYM
ejpam-2044	109	20	a	a	PRON
ejpam-2044	109	21	,	,	PUNCT
ejpam-2044	109	22	for	for	ADP
ejpam-2044	109	23	x	x	PROPN
ejpam-2044	109	24	∈	∈	PROPN
ejpam-2044	109	25	r.	r.	PROPN
ejpam-2044	109	26	integrating	integrating	PROPN
ejpam-2044	109	27	function	function	NOUN
ejpam-2044	109	28	v′(x	v′(x	NOUN
ejpam-2044	109	29	)	)	PUNCT
ejpam-2044	110	1	,	,	PUNCT
ejpam-2044	110	2	we	we	PRON
ejpam-2044	110	3	get	get	VERB
ejpam-2044	110	4	v(x	v(x	NOUN
ejpam-2044	110	5	)	)	PUNCT
ejpam-2044	111	1	=	=	NOUN
ejpam-2044	111	2	ax	ax	NOUN
ejpam-2044	111	3	+	+	CCONJ
ejpam-2044	111	4	b	b	NOUN
ejpam-2044	111	5	,	,	PUNCT
ejpam-2044	111	6	for	for	ADP
ejpam-2044	111	7	a	a	DET
ejpam-2044	111	8	constant	constant	ADJ
ejpam-2044	111	9	b	b	NOUN
ejpam-2044	111	10	,	,	PUNCT
ejpam-2044	111	11	initial	initial	ADJ
ejpam-2044	111	12	assumption	assumption	NOUN
ejpam-2044	111	13	of	of	ADP
ejpam-2044	111	14	positivity	positivity	NOUN
ejpam-2044	111	15	of	of	ADP
ejpam-2044	111	16	first	first	ADJ
ejpam-2044	111	17	derivative	derivative	NOUN
ejpam-2044	111	18	of	of	ADP
ejpam-2044	111	19	the	the	DET
ejpam-2044	111	20	function	function	NOUN
ejpam-2044	111	21	v(x	v(x	PROPN
ejpam-2044	111	22	)	)	PUNCT
ejpam-2044	111	23	gives	give	VERB
ejpam-2044	111	24	us	we	PRON
ejpam-2044	111	25	additional	additional	ADJ
ejpam-2044	111	26	restriction	restriction	NOUN
ejpam-2044	111	27	on	on	ADP
ejpam-2044	111	28	parameter	parameter	PROPN
ejpam-2044	111	29	a	a	DET
ejpam-2044	111	30	:	:	PUNCT
ejpam-2044	111	31	parameter	parameter	NOUN
ejpam-2044	111	32	a	a	PRON
ejpam-2044	111	33	must	must	AUX
ejpam-2044	111	34	be	be	AUX
ejpam-2044	111	35	a	a	DET
ejpam-2044	111	36	strictly	strictly	ADV
ejpam-2044	111	37	positive	positive	ADJ
ejpam-2044	111	38	constant	constant	ADJ
ejpam-2044	111	39	.	.	PUNCT
ejpam-2044	112	1	this	this	PRON
ejpam-2044	112	2	completes	complete	VERB
ejpam-2044	112	3	the	the	DET
ejpam-2044	112	4	proof	proof	NOUN
ejpam-2044	112	5	of	of	ADP
ejpam-2044	112	6	theorem	theorem	NOUN
ejpam-2044	112	7	1	1	NUM
ejpam-2044	112	8	.	.	PUNCT
ejpam-2044	112	9	from	from	ADP
ejpam-2044	112	10	the	the	DET
ejpam-2044	112	11	proof	proof	NOUN
ejpam-2044	112	12	of	of	ADP
ejpam-2044	112	13	theorem	theorem	NOUN
ejpam-2044	112	14	1	1	NUM
ejpam-2044	112	15	it	it	PRON
ejpam-2044	112	16	follows	follow	VERB
ejpam-2044	112	17	that	that	SCONJ
ejpam-2044	112	18	v(x	v(x	NOUN
ejpam-2044	112	19	)	)	PUNCT
ejpam-2044	112	20	=	=	PUNCT
ejpam-2044	112	21	ax+	ax+	PROPN
ejpam-2044	112	22	b	b	X
ejpam-2044	112	23	,	,	PUNCT
ejpam-2044	112	24	for	for	ADP
ejpam-2044	112	25	a	a	DET
ejpam-2044	112	26	>	>	X
ejpam-2044	112	27	0	0	NUM
ejpam-2044	112	28	,	,	PUNCT
ejpam-2044	112	29	is	be	AUX
ejpam-2044	112	30	the	the	DET
ejpam-2044	112	31	only	only	ADJ
ejpam-2044	112	32	case	case	NOUN
ejpam-2044	112	33	when	when	SCONJ
ejpam-2044	112	34	mean	mean	VERB
ejpam-2044	112	35	value	value	NOUN
ejpam-2044	112	36	premium	premium	NOUN
ejpam-2044	112	37	calculation	calculation	NOUN
ejpam-2044	112	38	principle	principle	NOUN
ejpam-2044	112	39	coincides	coincide	VERB
ejpam-2044	112	40	with	with	ADP
ejpam-2044	112	41	net	net	ADJ
ejpam-2044	112	42	premium	premium	NOUN
ejpam-2044	112	43	principle	principle	NOUN
ejpam-2044	112	44	.	.	PUNCT
ejpam-2044	113	1	indeed	indeed	ADV
ejpam-2044	113	2	,	,	PUNCT
ejpam-2044	113	3	let	let	VERB
ejpam-2044	113	4	us	we	PRON
ejpam-2044	113	5	assume	assume	VERB
ejpam-2044	113	6	that	that	SCONJ
ejpam-2044	113	7	for	for	ADP
ejpam-2044	113	8	some	some	DET
ejpam-2044	113	9	function	function	NOUN
ejpam-2044	113	10	v(x	v(x	PROPN
ejpam-2044	113	11	)	)	PUNCT
ejpam-2044	113	12	,	,	PUNCT
ejpam-2044	113	13	different	different	ADJ
ejpam-2044	113	14	from	from	ADP
ejpam-2044	113	15	the	the	DET
ejpam-2044	113	16	linear	linear	PROPN
ejpam-2044	113	17	function	function	NOUN
ejpam-2044	113	18	,	,	PUNCT
ejpam-2044	113	19	mean	mean	VERB
ejpam-2044	113	20	value	value	NOUN
ejpam-2044	113	21	premium	premium	NOUN
ejpam-2044	113	22	calculation	calculation	NOUN
ejpam-2044	113	23	principle	principle	NOUN
ejpam-2044	113	24	will	will	AUX
ejpam-2044	113	25	be	be	AUX
ejpam-2044	113	26	equivalent	equivalent	ADJ
ejpam-2044	113	27	to	to	ADP
ejpam-2044	113	28	net	net	ADJ
ejpam-2044	113	29	premium	premium	NOUN
ejpam-2044	113	30	principle	principle	NOUN
ejpam-2044	113	31	.	.	PUNCT
ejpam-2044	114	1	then	then	ADV
ejpam-2044	114	2	,	,	PUNCT
ejpam-2044	114	3	due	due	ADP
ejpam-2044	114	4	to	to	ADP
ejpam-2044	114	5	linearity	linearity	NOUN
ejpam-2044	114	6	property	property	NOUN
ejpam-2044	114	7	of	of	ADP
ejpam-2044	114	8	the	the	DET
ejpam-2044	114	9	expectation	expectation	NOUN
ejpam-2044	114	10	,	,	PUNCT
ejpam-2044	114	11	such	such	ADJ
ejpam-2044	114	12	method	method	NOUN
ejpam-2044	114	13	of	of	ADP
ejpam-2044	114	14	pricing	pricing	NOUN
ejpam-2044	114	15	must	must	AUX
ejpam-2044	114	16	be	be	AUX
ejpam-2044	114	17	scale	scale	NOUN
ejpam-2044	114	18	invariant	invariant	ADJ
ejpam-2044	114	19	,	,	PUNCT
ejpam-2044	114	20	however	however	ADV
ejpam-2044	114	21	,	,	PUNCT
ejpam-2044	114	22	in	in	ADP
ejpam-2044	114	23	the	the	DET
ejpam-2044	114	24	proof	proof	NOUN
ejpam-2044	114	25	of	of	ADP
ejpam-2044	114	26	theorem	theorem	NOUN
ejpam-2044	114	27	1	1	NUM
ejpam-2044	114	28	was	be	AUX
ejpam-2044	114	29	shown	show	VERB
ejpam-2044	114	30	that	that	SCONJ
ejpam-2044	114	31	mean	mean	VERB
ejpam-2044	114	32	value	value	NOUN
ejpam-2044	114	33	premium	premium	NOUN
ejpam-2044	114	34	calculation	calculation	NOUN
ejpam-2044	114	35	principle	principle	NOUN
ejpam-2044	114	36	possesses	possess	VERB
ejpam-2044	114	37	scale	scale	NOUN
ejpam-2044	114	38	invariance	invariance	NOUN
ejpam-2044	114	39	property	property	NOUN
ejpam-2044	115	1	if	if	SCONJ
ejpam-2044	115	2	and	and	CCONJ
ejpam-2044	115	3	only	only	ADV
ejpam-2044	115	4	if	if	SCONJ
ejpam-2044	115	5	v(x	v(x	NUM
ejpam-2044	115	6	)	)	PUNCT
ejpam-2044	116	1	=	=	NOUN
ejpam-2044	116	2	ax	ax	NOUN
ejpam-2044	116	3	+	+	CCONJ
ejpam-2044	116	4	b	b	NOUN
ejpam-2044	116	5	,	,	PUNCT
ejpam-2044	116	6	for	for	ADP
ejpam-2044	116	7	a	a	DET
ejpam-2044	116	8	>	>	X
ejpam-2044	116	9	0	0	NUM
ejpam-2044	116	10	,	,	PUNCT
ejpam-2044	116	11	so	so	SCONJ
ejpam-2044	116	12	we	we	PRON
ejpam-2044	116	13	come	come	VERB
ejpam-2044	116	14	to	to	ADP
ejpam-2044	116	15	a	a	DET
ejpam-2044	116	16	contradiction	contradiction	NOUN
ejpam-2044	116	17	.	.	PUNCT
ejpam-2044	117	1	using	use	VERB
ejpam-2044	117	2	similar	similar	ADJ
ejpam-2044	117	3	argumentations	argumentation	NOUN
ejpam-2044	117	4	one	one	PRON
ejpam-2044	117	5	can	can	AUX
ejpam-2044	117	6	conclude	conclude	VERB
ejpam-2044	117	7	that	that	PRON
ejpam-2044	117	8	:	:	PUNCT
ejpam-2044	117	9	u(x	u(x	PROPN
ejpam-2044	117	10	)	)	PUNCT
ejpam-2044	117	11	=	=	SYM
ejpam-2044	118	1	ax	ax	NOUN
ejpam-2044	118	2	+	+	CCONJ
ejpam-2044	118	3	b	b	NOUN
ejpam-2044	118	4	,	,	PUNCT
ejpam-2044	118	5	for	for	ADP
ejpam-2044	118	6	a	a	DET
ejpam-2044	118	7	>	>	X
ejpam-2044	118	8	0	0	NUM
ejpam-2044	118	9	,	,	PUNCT
ejpam-2044	118	10	is	be	AUX
ejpam-2044	118	11	the	the	DET
ejpam-2044	118	12	only	only	ADJ
ejpam-2044	118	13	case	case	NOUN
ejpam-2044	118	14	when	when	SCONJ
ejpam-2044	118	15	insurer	insurer	PROPN
ejpam-2044	118	16	’s	’s	PART
ejpam-2044	118	17	equivalent	equivalent	ADJ
ejpam-2044	118	18	/	/	SYM
ejpam-2044	118	19	zero	zero	NUM
ejpam-2044	118	20	utility	utility	NOUN
ejpam-2044	118	21	premium	premium	NOUN
ejpam-2044	118	22	calculation	calculation	NOUN
ejpam-2044	118	23	principle	principle	NOUN
ejpam-2044	118	24	coincides	coincide	VERB
ejpam-2044	118	25	with	with	ADP
ejpam-2044	118	26	net	net	ADJ
ejpam-2044	118	27	premium	premium	NOUN
ejpam-2044	118	28	principle	principle	NOUN
ejpam-2044	118	29	(	(	PUNCT
ejpam-2044	118	30	see	see	VERB
ejpam-2044	118	31	theorem	theorem	NOUN
ejpam-2044	118	32	3	3	NUM
ejpam-2044	118	33	)	)	PUNCT
ejpam-2044	118	34	;	;	PUNCT
ejpam-2044	118	35	u(x	u(x	PROPN
ejpam-2044	118	36	)	)	PUNCT
ejpam-2044	119	1	=	=	SYM
ejpam-2044	119	2	ax	ax	NOUN
ejpam-2044	119	3	+	+	CCONJ
ejpam-2044	119	4	b	b	NOUN
ejpam-2044	119	5	,	,	PUNCT
ejpam-2044	119	6	for	for	ADP
ejpam-2044	119	7	a	a	DET
ejpam-2044	119	8	>	>	X
ejpam-2044	119	9	0	0	NUM
ejpam-2044	119	10	,	,	PUNCT
ejpam-2044	119	11	is	be	AUX
ejpam-2044	119	12	the	the	DET
ejpam-2044	119	13	only	only	ADJ
ejpam-2044	119	14	case	case	NOUN
ejpam-2044	119	15	when	when	SCONJ
ejpam-2044	119	16	customer	customer	NOUN
ejpam-2044	119	17	’s	’s	PART
ejpam-2044	119	18	equivalent	equivalent	ADJ
ejpam-2044	119	19	/	/	SYM
ejpam-2044	119	20	zero	zero	NUM
ejpam-2044	119	21	utility	utility	NOUN
ejpam-2044	119	22	premium	premium	NOUN
ejpam-2044	119	23	calculation	calculation	NOUN
ejpam-2044	119	24	principle	principle	NOUN
ejpam-2044	119	25	coincides	coincide	VERB
ejpam-2044	119	26	with	with	ADP
ejpam-2044	119	27	net	net	ADJ
ejpam-2044	119	28	premium	premium	NOUN
ejpam-2044	119	29	principle	principle	NOUN
ejpam-2044	119	30	(	(	PUNCT
ejpam-2044	119	31	see	see	VERB
ejpam-2044	119	32	theorem	theorem	NOUN
ejpam-2044	119	33	4	4	NUM
ejpam-2044	119	34	)	)	PUNCT
ejpam-2044	119	35	;	;	PUNCT
ejpam-2044	119	36	and	and	CCONJ
ejpam-2044	119	37	v	v	X
ejpam-2044	119	38	(	(	PUNCT
ejpam-2044	119	39	x	x	NOUN
ejpam-2044	119	40	)	)	PUNCT
ejpam-2044	119	41	=	=	PUNCT
ejpam-2044	119	42	ax+	ax+	PROPN
ejpam-2044	119	43	b	b	X
ejpam-2044	119	44	,	,	PUNCT
ejpam-2044	119	45	for	for	ADP
ejpam-2044	119	46	a	a	DET
ejpam-2044	119	47	>	>	X
ejpam-2044	119	48	0	0	NUM
ejpam-2044	119	49	,	,	PUNCT
ejpam-2044	119	50	is	be	AUX
ejpam-2044	119	51	the	the	DET
ejpam-2044	119	52	only	only	ADJ
ejpam-2044	119	53	case	case	NOUN
ejpam-2044	119	54	when	when	SCONJ
ejpam-2044	119	55	swiss	swiss	ADJ
ejpam-2044	119	56	premium	premium	NOUN
ejpam-2044	119	57	calculation	calculation	NOUN
ejpam-2044	119	58	principle	principle	NOUN
ejpam-2044	119	59	coincides	coincide	VERB
ejpam-2044	119	60	with	with	ADP
ejpam-2044	119	61	net	net	ADJ
ejpam-2044	119	62	premium	premium	NOUN
ejpam-2044	119	63	principle	principle	NOUN
ejpam-2044	119	64	(	(	PUNCT
ejpam-2044	119	65	see	see	VERB
ejpam-2044	119	66	theorem	theorem	NOUN
ejpam-2044	119	67	6	6	NUM
ejpam-2044	119	68	)	)	PUNCT
ejpam-2044	119	69	.	.	PUNCT
ejpam-2044	120	1	as	as	SCONJ
ejpam-2044	120	2	was	be	AUX
ejpam-2044	120	3	already	already	ADV
ejpam-2044	120	4	mentioned	mention	VERB
ejpam-2044	120	5	,	,	PUNCT
ejpam-2044	120	6	in	in	ADP
ejpam-2044	120	7	the	the	DET
ejpam-2044	120	8	case	case	NOUN
ejpam-2044	120	9	when	when	SCONJ
ejpam-2044	120	10	mean	mean	VERB
ejpam-2044	120	11	value	value	NOUN
ejpam-2044	120	12	premium	premium	NOUN
ejpam-2044	120	13	principle	principle	NOUN
ejpam-2044	120	14	is	be	AUX
ejpam-2044	120	15	applied	apply	VERB
ejpam-2044	120	16	to	to	ADP
ejpam-2044	120	17	a	a	DET
ejpam-2044	120	18	special	special	ADJ
ejpam-2044	120	19	class	class	NOUN
ejpam-2044	120	20	of	of	ADP
ejpam-2044	120	21	risks	risk	NOUN
ejpam-2044	120	22	,	,	PUNCT
ejpam-2044	120	23	it	it	PRON
ejpam-2044	120	24	is	be	AUX
ejpam-2044	120	25	enough	enough	ADJ
ejpam-2044	120	26	to	to	PART
ejpam-2044	120	27	define	define	VERB
ejpam-2044	120	28	the	the	DET
ejpam-2044	120	29	function	function	NOUN
ejpam-2044	120	30	v(x	v(x	PROPN
ejpam-2044	120	31	)	)	PUNCT
ejpam-2044	120	32	on	on	ADP
ejpam-2044	120	33	a	a	DET
ejpam-2044	120	34	subset	subset	NOUN
ejpam-2044	120	35	a	a	DET
ejpam-2044	120	36	⊂	⊂	X
ejpam-2044	120	37	r	r	NOUN
ejpam-2044	120	38	preserving	preserve	VERB
ejpam-2044	120	39	monotonicity	monotonicity	NOUN
ejpam-2044	120	40	and	and	CCONJ
ejpam-2044	120	41	convexity	convexity	NOUN
ejpam-2044	120	42	properties	property	NOUN
ejpam-2044	120	43	,	,	PUNCT
ejpam-2044	120	44	i.e.	i.e.	X
ejpam-2044	120	45	,	,	PUNCT
ejpam-2044	120	46	v(x	v(x	PROPN
ejpam-2044	120	47	)	)	PUNCT
ejpam-2044	120	48	must	must	AUX
ejpam-2044	120	49	be	be	AUX
ejpam-2044	120	50	such	such	ADJ
ejpam-2044	120	51	that	that	SCONJ
ejpam-2044	120	52	v′(x	v′(x	NOUN
ejpam-2044	120	53	)	)	PUNCT
ejpam-2044	120	54	>	>	X
ejpam-2044	120	55	0	0	PUNCT
ejpam-2044	120	56	and	and	CCONJ
ejpam-2044	120	57	v′′(x	v′′(x	NOUN
ejpam-2044	120	58	)	)	PUNCT
ejpam-2044	120	59	≥	≥	NOUN
ejpam-2044	120	60	0	0	NUM
ejpam-2044	120	61	for	for	SCONJ
ejpam-2044	120	62	all	all	DET
ejpam-2044	120	63	x	x	SYM
ejpam-2044	120	64	∈	∈	PROPN
ejpam-2044	120	65	a	a	PRON
ejpam-2044	120	66	,	,	PUNCT
ejpam-2044	120	67	and	and	CCONJ
ejpam-2044	120	68	,	,	PUNCT
ejpam-2044	120	69	moreover	moreover	ADV
ejpam-2044	120	70	,	,	PUNCT
ejpam-2044	120	71	equation	equation	NOUN
ejpam-2044	120	72	(	(	PUNCT
ejpam-2044	120	73	1	1	X
ejpam-2044	120	74	)	)	PUNCT
ejpam-2044	120	75	must	must	AUX
ejpam-2044	120	76	preserve	preserve	VERB
ejpam-2044	120	77	its	its	PRON
ejpam-2044	120	78	correct	correct	ADJ
ejpam-2044	120	79	mathematical	mathematical	ADJ
ejpam-2044	120	80	meaning	meaning	NOUN
ejpam-2044	120	81	for	for	ADP
ejpam-2044	120	82	all	all	DET
ejpam-2044	120	83	risks	risk	NOUN
ejpam-2044	120	84	from	from	ADP
ejpam-2044	120	85	the	the	DET
ejpam-2044	120	86	mentioned	mention	VERB
ejpam-2044	120	87	class	class	NOUN
ejpam-2044	120	88	.	.	PUNCT
ejpam-2044	121	1	it	it	PRON
ejpam-2044	121	2	is	be	AUX
ejpam-2044	121	3	interesting	interesting	ADJ
ejpam-2044	121	4	to	to	PART
ejpam-2044	121	5	see	see	VERB
ejpam-2044	121	6	that	that	SCONJ
ejpam-2044	121	7	in	in	ADP
ejpam-2044	121	8	the	the	DET
ejpam-2044	121	9	case	case	NOUN
ejpam-2044	121	10	of	of	ADP
ejpam-2044	121	11	subjecting	subject	VERB
ejpam-2044	121	12	of	of	ADP
ejpam-2044	121	13	mean	mean	ADJ
ejpam-2044	121	14	value	value	NOUN
ejpam-2044	121	15	principle	principle	NOUN
ejpam-2044	121	16	to	to	ADP
ejpam-2044	121	17	pricing	pricing	NOUN
ejpam-2044	121	18	of	of	ADP
ejpam-2044	121	19	only	only	ADV
ejpam-2044	121	20	strictly	strictly	ADV
ejpam-2044	121	21	positive	positive	ADJ
ejpam-2044	121	22	risks	risk	NOUN
ejpam-2044	121	23	,	,	PUNCT
ejpam-2044	121	24	the	the	DET
ejpam-2044	121	25	class	class	NOUN
ejpam-2044	121	26	of	of	ADP
ejpam-2044	121	27	functions	function	NOUN
ejpam-2044	121	28	v(x	v(x	NOUN
ejpam-2044	121	29	)	)	PUNCT
ejpam-2044	121	30	producing	produce	VERB
ejpam-2044	121	31	scale	scale	NOUN
ejpam-2044	121	32	invariant	invariant	ADJ
ejpam-2044	121	33	premiums	premium	NOUN
ejpam-2044	121	34	is	be	AUX
ejpam-2044	121	35	larger	large	ADJ
ejpam-2044	121	36	than	than	ADP
ejpam-2044	121	37	in	in	ADP
ejpam-2044	121	38	the	the	DET
ejpam-2044	121	39	general	general	ADJ
ejpam-2044	121	40	case	case	NOUN
ejpam-2044	121	41	.	.	PUNCT
ejpam-2044	122	1	we	we	PRON
ejpam-2044	122	2	believe	believe	VERB
ejpam-2044	122	3	that	that	SCONJ
ejpam-2044	122	4	this	this	DET
ejpam-2044	122	5	observation	observation	NOUN
ejpam-2044	122	6	deserves	deserve	VERB
ejpam-2044	122	7	to	to	PART
ejpam-2044	122	8	be	be	AUX
ejpam-2044	122	9	formulated	formulate	VERB
ejpam-2044	122	10	in	in	ADP
ejpam-2044	122	11	a	a	DET
ejpam-2044	122	12	form	form	NOUN
ejpam-2044	122	13	of	of	ADP
ejpam-2044	122	14	theorem	theorem	PROPN
ejpam-2044	122	15	.	.	PUNCT
ejpam-2044	122	16	theorem	theorem	NOUN
ejpam-2044	122	17	2	2	NUM
ejpam-2044	122	18	.	.	NOUN
ejpam-2044	123	1	mean	mean	ADJ
ejpam-2044	123	2	value	value	NOUN
ejpam-2044	123	3	premium	premium	NOUN
ejpam-2044	123	4	calculation	calculation	NOUN
ejpam-2044	123	5	principle	principle	NOUN
ejpam-2044	123	6	subjected	subject	VERB
ejpam-2044	123	7	to	to	ADP
ejpam-2044	123	8	consideration	consideration	NOUN
ejpam-2044	123	9	of	of	ADP
ejpam-2044	123	10	only	only	ADV
ejpam-2044	123	11	strictly	strictly	ADV
ejpam-2044	123	12	positive	positive	ADJ
ejpam-2044	123	13	risks	risk	NOUN
ejpam-2044	123	14	possesses	possess	VERB
ejpam-2044	123	15	scale	scale	NOUN
ejpam-2044	123	16	invariance	invariance	NOUN
ejpam-2044	123	17	property	property	NOUN
ejpam-2044	124	1	if	if	SCONJ
ejpam-2044	124	2	and	and	CCONJ
ejpam-2044	124	3	only	only	ADV
ejpam-2044	124	4	if	if	SCONJ
ejpam-2044	124	5	v(x	v(x	NUM
ejpam-2044	124	6	)	)	PUNCT
ejpam-2044	124	7	=	=	VERB
ejpam-2044	124	8	axκ	axκ	PROPN
ejpam-2044	124	9	+	+	CCONJ
ejpam-2044	124	10	b	b	X
ejpam-2044	124	11	,	,	PUNCT
ejpam-2044	124	12	for	for	ADP
ejpam-2044	124	13	a	a	DET
ejpam-2044	124	14	>	>	X
ejpam-2044	124	15	0	0	PUNCT
ejpam-2044	124	16	and	and	CCONJ
ejpam-2044	124	17	κ≥	κ≥	PROPN
ejpam-2044	124	18	1	1	NUM
ejpam-2044	124	19	,	,	PUNCT
ejpam-2044	124	20	defined	define	VERB
ejpam-2044	124	21	for	for	ADP
ejpam-2044	124	22	x	x	PROPN
ejpam-2044	124	23	∈	∈	PROPN
ejpam-2044	124	24	(	(	PUNCT
ejpam-2044	124	25	0,+∞	0,+∞	NUM
ejpam-2044	124	26	)	)	PUNCT
ejpam-2044	124	27	.	.	PUNCT
ejpam-2044	125	1	observe	observe	VERB
ejpam-2044	125	2	that	that	SCONJ
ejpam-2044	125	3	for	for	ADP
ejpam-2044	125	4	the	the	DET
ejpam-2044	125	5	function	function	NOUN
ejpam-2044	125	6	v(x	v(x	PROPN
ejpam-2044	125	7	)	)	PUNCT
ejpam-2044	125	8	=	=	VERB
ejpam-2044	126	1	axκ	axκ	PROPN
ejpam-2044	126	2	+	+	CCONJ
ejpam-2044	126	3	b	b	X
ejpam-2044	126	4	with	with	ADP
ejpam-2044	126	5	a	a	DET
ejpam-2044	126	6	>	>	X
ejpam-2044	126	7	0	0	NUM
ejpam-2044	126	8	and	and	CCONJ
ejpam-2044	126	9	κ	κ	X
ejpam-2044	126	10	>	>	X
ejpam-2044	126	11	1	1	NUM
ejpam-2044	126	12	condition	condition	NOUN
ejpam-2044	126	13	v′(x	v′(x	NOUN
ejpam-2044	126	14	)	)	PUNCT
ejpam-2044	126	15	>	>	X
ejpam-2044	126	16	0	0	NUM
ejpam-2044	126	17	violates	violate	VERB
ejpam-2044	126	18	at	at	ADP
ejpam-2044	126	19	the	the	DET
ejpam-2044	126	20	point	point	NOUN
ejpam-2044	126	21	x	x	PUNCT
ejpam-2044	126	22	=	=	SYM
ejpam-2044	126	23	0	0	NUM
ejpam-2044	126	24	,	,	PUNCT
ejpam-2044	126	25	therefore	therefore	ADV
ejpam-2044	126	26	,	,	PUNCT
ejpam-2044	126	27	statement	statement	NOUN
ejpam-2044	126	28	of	of	ADP
ejpam-2044	126	29	theorem	theorem	ADJ
ejpam-2044	126	30	2	2	NUM
ejpam-2044	126	31	does	do	AUX
ejpam-2044	126	32	not	not	PART
ejpam-2044	126	33	contradict	contradict	VERB
ejpam-2044	126	34	statement	statement	NOUN
ejpam-2044	126	35	of	of	ADP
ejpam-2044	126	36	theorem	theorem	NOUN
ejpam-2044	126	37	1	1	NUM
ejpam-2044	126	38	.	.	PUNCT
ejpam-2044	127	1	proof	proof	NOUN
ejpam-2044	127	2	.	.	PUNCT
ejpam-2044	128	1	since	since	SCONJ
ejpam-2044	128	2	in	in	ADP
ejpam-2044	128	3	the	the	DET
ejpam-2044	128	4	case	case	NOUN
ejpam-2044	128	5	of	of	ADP
ejpam-2044	128	6	strictly	strictly	ADV
ejpam-2044	128	7	positive	positive	ADJ
ejpam-2044	128	8	risk	risk	NOUN
ejpam-2044	128	9	x	x	VERB
ejpam-2044	128	10	we	we	PRON
ejpam-2044	128	11	get	get	VERB
ejpam-2044	128	12	e[x	e[x	NOUN
ejpam-2044	128	13	]	]	PUNCT
ejpam-2044	128	14	>	>	X
ejpam-2044	128	15	0	0	NUM
ejpam-2044	128	16	,	,	PUNCT
ejpam-2044	128	17	then	then	ADV
ejpam-2044	128	18	,	,	PUNCT
ejpam-2044	128	19	combining	combine	VERB
ejpam-2044	128	20	jensen	jensen	PROPN
ejpam-2044	128	21	inequality	inequality	NOUN
ejpam-2044	128	22	v(e[x	v(e[x	NOUN
ejpam-2044	128	23	]	]	PUNCT
ejpam-2044	128	24	)	)	PUNCT
ejpam-2044	128	25	≤	≤	PROPN
ejpam-2044	128	26	e[v(x	e[v(x	PROPN
ejpam-2044	128	27	)	)	PUNCT
ejpam-2044	128	28	]	]	PUNCT
ejpam-2044	128	29	with	with	ADP
ejpam-2044	128	30	definition	definition	NOUN
ejpam-2044	128	31	equation	equation	NOUN
ejpam-2044	128	32	(	(	PUNCT
ejpam-2044	128	33	1	1	NUM
ejpam-2044	128	34	)	)	PUNCT
ejpam-2044	128	35	,	,	PUNCT
ejpam-2044	128	36	we	we	PRON
ejpam-2044	128	37	see	see	VERB
ejpam-2044	128	38	that	that	PRON
ejpam-2044	128	39	mean	mean	NOUN
ejpam-2044	128	40	value	value	NOUN
ejpam-2044	128	41	premium	premium	NOUN
ejpam-2044	128	42	calculation	calculation	NOUN
ejpam-2044	128	43	principle	principle	NOUN
ejpam-2044	128	44	will	will	AUX
ejpam-2044	128	45	be	be	AUX
ejpam-2044	128	46	well	well	ADV
ejpam-2044	128	47	-	-	PUNCT
ejpam-2044	128	48	defined	define	VERB
ejpam-2044	128	49	if	if	SCONJ
ejpam-2044	128	50	the	the	DET
ejpam-2044	128	51	function	function	NOUN
ejpam-2044	128	52	v(x	v(x	PROPN
ejpam-2044	128	53	)	)	PUNCT
ejpam-2044	128	54	will	will	AUX
ejpam-2044	128	55	be	be	AUX
ejpam-2044	128	56	defined	define	VERB
ejpam-2044	128	57	just	just	ADV
ejpam-2044	128	58	for	for	ADP
ejpam-2044	128	59	x	x	PROPN
ejpam-2044	128	60	∈	∈	PROPN
ejpam-2044	128	61	(	(	PUNCT
ejpam-2044	128	62	0,+∞	0,+∞	NUM
ejpam-2044	128	63	)	)	PUNCT
ejpam-2044	128	64	with	with	ADP
ejpam-2044	128	65	preservation	preservation	NOUN
ejpam-2044	128	66	of	of	ADP
ejpam-2044	128	67	m.	m.	NOUN
ejpam-2044	128	68	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	128	69	,	,	PUNCT
ejpam-2044	128	70	v.	v.	ADP
ejpam-2044	128	71	drozdenko	drozdenko	PROPN
ejpam-2044	128	72	/	/	SYM
ejpam-2044	128	73	eur	eur	PROPN
ejpam-2044	128	74	.	.	PUNCT
ejpam-2044	129	1	j.	j.	PROPN
ejpam-2044	129	2	pure	pure	PROPN
ejpam-2044	129	3	appl	appl	PROPN
ejpam-2044	129	4	.	.	PROPN
ejpam-2044	129	5	math	math	PROPN
ejpam-2044	129	6	,	,	PUNCT
ejpam-2044	129	7	7	7	NUM
ejpam-2044	129	8	(	(	PUNCT
ejpam-2044	129	9	2014	2014	NUM
ejpam-2044	129	10	)	)	PUNCT
ejpam-2044	129	11	,	,	PUNCT
ejpam-2044	129	12	267	267	X
ejpam-2044	129	13	-	-	SYM
ejpam-2044	129	14	288	288	NUM
ejpam-2044	129	15	273	273	NUM
ejpam-2044	129	16	monotonicity	monotonicity	NOUN
ejpam-2044	129	17	and	and	CCONJ
ejpam-2044	129	18	convexity	convexity	NOUN
ejpam-2044	129	19	assumptions	assumption	NOUN
ejpam-2044	129	20	,	,	PUNCT
ejpam-2044	129	21	i.e.	i.e.	X
ejpam-2044	129	22	,	,	PUNCT
ejpam-2044	129	23	the	the	DET
ejpam-2044	129	24	function	function	NOUN
ejpam-2044	129	25	v(x	v(x	PROPN
ejpam-2044	129	26	)	)	PUNCT
ejpam-2044	129	27	must	must	AUX
ejpam-2044	129	28	be	be	AUX
ejpam-2044	129	29	defined	define	VERB
ejpam-2044	129	30	on	on	ADP
ejpam-2044	129	31	(	(	PUNCT
ejpam-2044	129	32	0,+∞	0,+∞	NUM
ejpam-2044	129	33	)	)	PUNCT
ejpam-2044	129	34	such	such	ADJ
ejpam-2044	129	35	that	that	PRON
ejpam-2044	129	36	v′(x	v′(x	NOUN
ejpam-2044	129	37	)	)	PUNCT
ejpam-2044	129	38	>	>	X
ejpam-2044	129	39	0	0	PUNCT
ejpam-2044	129	40	and	and	CCONJ
ejpam-2044	129	41	v′′(x)≥	v′′(x)≥	NOUN
ejpam-2044	129	42	0	0	NUM
ejpam-2044	129	43	for	for	ADP
ejpam-2044	129	44	all	all	DET
ejpam-2044	129	45	x	x	SYM
ejpam-2044	129	46	∈	∈	PROPN
ejpam-2044	129	47	(	(	PUNCT
ejpam-2044	129	48	0,+∞	0,+∞	NUM
ejpam-2044	129	49	)	)	PUNCT
ejpam-2044	129	50	.	.	PUNCT
ejpam-2044	130	1	let	let	VERB
ejpam-2044	130	2	us	we	PRON
ejpam-2044	130	3	from	from	ADP
ejpam-2044	130	4	the	the	DET
ejpam-2044	130	5	beginning	beginning	NOUN
ejpam-2044	130	6	prove	prove	VERB
ejpam-2044	130	7	the	the	DET
ejpam-2044	130	8	sufficiency	sufficiency	NOUN
ejpam-2044	130	9	of	of	ADP
ejpam-2044	130	10	the	the	DET
ejpam-2044	130	11	statement	statement	NOUN
ejpam-2044	130	12	.	.	PUNCT
ejpam-2044	131	1	indeed	indeed	ADV
ejpam-2044	131	2	in	in	ADP
ejpam-2044	131	3	the	the	DET
ejpam-2044	131	4	case	case	NOUN
ejpam-2044	131	5	of	of	ADP
ejpam-2044	131	6	v(x	v(x	PROPN
ejpam-2044	131	7	)	)	PUNCT
ejpam-2044	131	8	=	=	VERB
ejpam-2044	131	9	axκ	axκ	PROPN
ejpam-2044	131	10	+	+	CCONJ
ejpam-2044	131	11	b	b	X
ejpam-2044	131	12	,	,	PUNCT
ejpam-2044	131	13	with	with	ADP
ejpam-2044	131	14	a	a	DET
ejpam-2044	131	15	>	>	X
ejpam-2044	131	16	0	0	NUM
ejpam-2044	131	17	and	and	CCONJ
ejpam-2044	131	18	κ	κ	X
ejpam-2044	131	19	≥	≥	NOUN
ejpam-2044	131	20	1	1	NUM
ejpam-2044	131	21	,	,	PUNCT
ejpam-2044	131	22	for	for	ADP
ejpam-2044	131	23	any	any	DET
ejpam-2044	131	24	strictly	strictly	ADV
ejpam-2044	131	25	positive	positive	ADJ
ejpam-2044	131	26	risk	risk	NOUN
ejpam-2044	132	1	x	x	X
ejpam-2044	132	2	equation	equation	NOUN
ejpam-2044	132	3	(	(	PUNCT
ejpam-2044	132	4	1	1	X
ejpam-2044	132	5	)	)	PUNCT
ejpam-2044	132	6	will	will	AUX
ejpam-2044	132	7	have	have	VERB
ejpam-2044	132	8	the	the	DET
ejpam-2044	132	9	following	follow	VERB
ejpam-2044	132	10	form	form	NOUN
ejpam-2044	132	11	a(πm.v.[x	a(πm.v.[x	PROPN
ejpam-2044	132	12	]	]	PUNCT
ejpam-2044	132	13	)	)	PUNCT
ejpam-2044	132	14	κ	κ	PROPN
ejpam-2044	133	1	+	+	PROPN
ejpam-2044	133	2	b	b	X
ejpam-2044	133	3	=	=	SYM
ejpam-2044	133	4	e[ax	e[ax	PROPN
ejpam-2044	133	5	κ	κ	PROPN
ejpam-2044	133	6	+	+	NOUN
ejpam-2044	133	7	b	b	X
ejpam-2044	133	8	]	]	X
ejpam-2044	133	9	=	=	PUNCT
ejpam-2044	134	1	ae[x	ae[x	PROPN
ejpam-2044	134	2	κ	κ	X
ejpam-2044	134	3	]	]	X
ejpam-2044	134	4	+	+	CCONJ
ejpam-2044	134	5	b	b	X
ejpam-2044	134	6	,	,	PUNCT
ejpam-2044	134	7	therefore	therefore	ADV
ejpam-2044	134	8	,	,	PUNCT
ejpam-2044	134	9	in	in	ADP
ejpam-2044	134	10	the	the	DET
ejpam-2044	134	11	considered	considered	ADJ
ejpam-2044	134	12	case	case	NOUN
ejpam-2044	134	13	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	134	14	]	]	PUNCT
ejpam-2044	134	15	=	=	SYM
ejpam-2044	134	16	(	(	PUNCT
ejpam-2044	134	17	e[x	e[x	NUM
ejpam-2044	134	18	κ])1	κ])1	PROPN
ejpam-2044	134	19	/	/	SYM
ejpam-2044	134	20	κ	κ	NOUN
ejpam-2044	134	21	.	.	NOUN
ejpam-2044	135	1	on	on	ADP
ejpam-2044	135	2	the	the	DET
ejpam-2044	135	3	other	other	ADJ
ejpam-2044	135	4	hand	hand	NOUN
ejpam-2044	135	5	,	,	PUNCT
ejpam-2044	135	6	for	for	ADP
ejpam-2044	135	7	the	the	DET
ejpam-2044	135	8	same	same	ADJ
ejpam-2044	135	9	function	function	NOUN
ejpam-2044	135	10	v(x	v(x	PROPN
ejpam-2044	135	11	)	)	PUNCT
ejpam-2044	135	12	,	,	PUNCT
ejpam-2044	135	13	the	the	DET
ejpam-2044	135	14	same	same	ADJ
ejpam-2044	135	15	risk	risk	NOUN
ejpam-2044	135	16	x	x	X
ejpam-2044	135	17	,	,	PUNCT
ejpam-2044	135	18	and	and	CCONJ
ejpam-2044	135	19	any	any	DET
ejpam-2044	135	20	θ	θ	PROPN
ejpam-2044	135	21	>	>	X
ejpam-2044	135	22	0	0	NUM
ejpam-2044	135	23	,	,	PUNCT
ejpam-2044	135	24	from	from	ADP
ejpam-2044	135	25	equation	equation	NOUN
ejpam-2044	135	26	(	(	PUNCT
ejpam-2044	135	27	1	1	X
ejpam-2044	135	28	)	)	PUNCT
ejpam-2044	135	29	it	it	PRON
ejpam-2044	135	30	follows	follow	VERB
ejpam-2044	135	31	a(πm.v.[θx	a(πm.v.[θx	PROPN
ejpam-2044	135	32	]	]	PUNCT
ejpam-2044	135	33	)	)	PUNCT
ejpam-2044	135	34	κ	κ	PROPN
ejpam-2044	136	1	+	+	NUM
ejpam-2044	136	2	b	b	NOUN
ejpam-2044	136	3	=	=	SYM
ejpam-2044	136	4	e[a(θx	e[a(θx	NOUN
ejpam-2044	136	5	)	)	PUNCT
ejpam-2044	136	6	κ	κ	NOUN
ejpam-2044	136	7	+	+	NOUN
ejpam-2044	136	8	b	b	X
ejpam-2044	136	9	]	]	X
ejpam-2044	136	10	=	=	PUNCT
ejpam-2044	136	11	aθκe[x	aθκe[x	PROPN
ejpam-2044	136	12	κ	κ	X
ejpam-2044	136	13	]	]	X
ejpam-2044	137	1	+	+	CCONJ
ejpam-2044	137	2	b	b	X
ejpam-2044	137	3	so	so	ADV
ejpam-2044	137	4	,	,	PUNCT
ejpam-2044	137	5	here	here	ADV
ejpam-2044	137	6	we	we	PRON
ejpam-2044	137	7	get	get	VERB
ejpam-2044	137	8	πm.v.[θx	πm.v.[θx	NOUN
ejpam-2044	137	9	]	]	PUNCT
ejpam-2044	138	1	=	=	PUNCT
ejpam-2044	138	2	θ(e[x	θ(e[x	PROPN
ejpam-2044	138	3	κ])1	κ])1	PROPN
ejpam-2044	138	4	/	/	SYM
ejpam-2044	138	5	κ	κ	X
ejpam-2044	138	6	=	=	VERB
ejpam-2044	138	7	θπm.v.[x	θπm.v.[x	ADJ
ejpam-2044	138	8	]	]	PUNCT
ejpam-2044	138	9	,	,	PUNCT
ejpam-2044	138	10	and	and	CCONJ
ejpam-2044	138	11	as	as	SCONJ
ejpam-2044	138	12	we	we	PRON
ejpam-2044	138	13	see	see	VERB
ejpam-2044	138	14	,	,	PUNCT
ejpam-2044	138	15	mean	mean	VERB
ejpam-2044	138	16	value	value	NOUN
ejpam-2044	138	17	premium	premium	NOUN
ejpam-2044	138	18	calculation	calculation	NOUN
ejpam-2044	138	19	principle	principle	NOUN
ejpam-2044	138	20	subjected	subject	VERB
ejpam-2044	138	21	to	to	ADP
ejpam-2044	138	22	consideration	consideration	NOUN
ejpam-2044	138	23	of	of	ADP
ejpam-2044	138	24	only	only	ADV
ejpam-2044	138	25	strictly	strictly	ADV
ejpam-2044	138	26	positive	positive	ADJ
ejpam-2044	138	27	risks	risk	NOUN
ejpam-2044	138	28	possesses	possess	VERB
ejpam-2044	138	29	scale	scale	NOUN
ejpam-2044	138	30	invariance	invariance	NOUN
ejpam-2044	138	31	property	property	NOUN
ejpam-2044	138	32	in	in	ADP
ejpam-2044	138	33	the	the	DET
ejpam-2044	138	34	case	case	NOUN
ejpam-2044	138	35	of	of	ADP
ejpam-2044	138	36	v(x	v(x	PROPN
ejpam-2044	138	37	)	)	PUNCT
ejpam-2044	139	1	=	=	VERB
ejpam-2044	139	2	axκ	axκ	PROPN
ejpam-2044	139	3	+	+	CCONJ
ejpam-2044	139	4	b	b	X
ejpam-2044	139	5	,	,	PUNCT
ejpam-2044	139	6	for	for	ADP
ejpam-2044	139	7	a	a	DET
ejpam-2044	139	8	>	>	X
ejpam-2044	139	9	0	0	PUNCT
ejpam-2044	139	10	and	and	CCONJ
ejpam-2044	139	11	κ≥	κ≥	PROPN
ejpam-2044	139	12	1	1	NUM
ejpam-2044	139	13	,	,	PUNCT
ejpam-2044	139	14	defined	define	VERB
ejpam-2044	139	15	for	for	ADP
ejpam-2044	139	16	x	x	PROPN
ejpam-2044	139	17	∈	∈	PROPN
ejpam-2044	139	18	(	(	PUNCT
ejpam-2044	139	19	0,+∞	0,+∞	NUM
ejpam-2044	139	20	)	)	PUNCT
ejpam-2044	139	21	.	.	PUNCT
ejpam-2044	140	1	let	let	VERB
ejpam-2044	140	2	us	we	PRON
ejpam-2044	140	3	now	now	ADV
ejpam-2044	140	4	switch	switch	VERB
ejpam-2044	140	5	to	to	ADP
ejpam-2044	140	6	the	the	DET
ejpam-2044	140	7	statement	statement	NOUN
ejpam-2044	140	8	of	of	ADP
ejpam-2044	140	9	the	the	DET
ejpam-2044	140	10	necessity	necessity	NOUN
ejpam-2044	140	11	.	.	PUNCT
ejpam-2044	141	1	in	in	ADP
ejpam-2044	141	2	order	order	NOUN
ejpam-2044	141	3	to	to	PART
ejpam-2044	141	4	show	show	VERB
ejpam-2044	141	5	that	that	PRON
ejpam-2044	141	6	mean	mean	NOUN
ejpam-2044	141	7	value	value	NOUN
ejpam-2044	141	8	premium	premium	NOUN
ejpam-2044	141	9	calculation	calculation	NOUN
ejpam-2044	141	10	principle	principle	NOUN
ejpam-2044	141	11	subjected	subject	VERB
ejpam-2044	141	12	to	to	ADP
ejpam-2044	141	13	consideration	consideration	NOUN
ejpam-2044	141	14	of	of	ADP
ejpam-2044	141	15	only	only	ADV
ejpam-2044	141	16	strictly	strictly	ADV
ejpam-2044	141	17	positive	positive	ADJ
ejpam-2044	141	18	risks	risk	NOUN
ejpam-2044	141	19	with	with	ADP
ejpam-2044	141	20	all	all	DET
ejpam-2044	141	21	other	other	ADJ
ejpam-2044	141	22	types	type	NOUN
ejpam-2044	141	23	of	of	ADP
ejpam-2044	141	24	function	function	NOUN
ejpam-2044	141	25	v(x)will	v(x)will	VERB
ejpam-2044	141	26	not	not	PART
ejpam-2044	141	27	possess	possess	VERB
ejpam-2044	141	28	scale	scale	NOUN
ejpam-2044	141	29	invariance	invariance	NOUN
ejpam-2044	141	30	property	property	NOUN
ejpam-2044	141	31	,	,	PUNCT
ejpam-2044	141	32	we	we	PRON
ejpam-2044	141	33	will	will	AUX
ejpam-2044	141	34	consider	consider	VERB
ejpam-2044	141	35	a	a	DET
ejpam-2044	141	36	risk	risk	NOUN
ejpam-2044	141	37	x	x	ADP
ejpam-2044	141	38	taking	take	VERB
ejpam-2044	141	39	values	value	NOUN
ejpam-2044	141	40	ε	ε	X
ejpam-2044	141	41	>	>	PUNCT
ejpam-2044	141	42	0	0	PUNCT
ejpam-2044	141	43	and	and	CCONJ
ejpam-2044	141	44	1	1	NUM
ejpam-2044	141	45	with	with	ADP
ejpam-2044	141	46	probabilities	probability	NOUN
ejpam-2044	141	47	p	p	NOUN
ejpam-2044	141	48	and	and	CCONJ
ejpam-2044	141	49	1−	1−	NUM
ejpam-2044	141	50	p	p	NOUN
ejpam-2044	141	51	respectively	respectively	ADV
ejpam-2044	141	52	.	.	PUNCT
ejpam-2044	142	1	being	be	AUX
ejpam-2044	142	2	a	a	DET
ejpam-2044	142	3	random	random	ADJ
ejpam-2044	142	4	function	function	NOUN
ejpam-2044	142	5	of	of	ADP
ejpam-2044	142	6	the	the	DET
ejpam-2044	142	7	parameters	parameter	NOUN
ejpam-2044	142	8	ε	ε	PROPN
ejpam-2044	142	9	and	and	CCONJ
ejpam-2044	142	10	p	p	X
ejpam-2044	142	11	,	,	PUNCT
ejpam-2044	142	12	the	the	DET
ejpam-2044	142	13	risk	risk	NOUN
ejpam-2044	142	14	x	x	PUNCT
ejpam-2044	142	15	within	within	ADP
ejpam-2044	142	16	the	the	DET
ejpam-2044	142	17	proof	proof	NOUN
ejpam-2044	142	18	of	of	ADP
ejpam-2044	142	19	theorem	theorem	ADJ
ejpam-2044	142	20	2	2	NUM
ejpam-2044	142	21	will	will	AUX
ejpam-2044	142	22	be	be	AUX
ejpam-2044	142	23	denoted	denote	VERB
ejpam-2044	142	24	as	as	ADP
ejpam-2044	142	25	x	x	PROPN
ejpam-2044	142	26	εp	εp	NOUN
ejpam-2044	142	27	.	.	NOUN
ejpam-2044	142	28	for	for	ADP
ejpam-2044	142	29	the	the	DET
ejpam-2044	142	30	described	describe	VERB
ejpam-2044	142	31	risk	risk	NOUN
ejpam-2044	142	32	x	x	X
ejpam-2044	142	33	εp	εp	ADP
ejpam-2044	142	34	equation	equation	NOUN
ejpam-2044	142	35	(	(	PUNCT
ejpam-2044	142	36	1	1	X
ejpam-2044	142	37	)	)	PUNCT
ejpam-2044	142	38	will	will	AUX
ejpam-2044	142	39	have	have	VERB
ejpam-2044	142	40	the	the	DET
ejpam-2044	142	41	following	follow	VERB
ejpam-2044	142	42	form	form	NOUN
ejpam-2044	142	43	v(πm.v.[x	v(πm.v.[x	VERB
ejpam-2044	142	44	ε	ε	PROPN
ejpam-2044	142	45	p	p	X
ejpam-2044	142	46	]	]	X
ejpam-2044	142	47	)	)	PUNCT
ejpam-2044	142	48	=	=	SYM
ejpam-2044	142	49	pv(ε	pv(ε	NOUN
ejpam-2044	142	50	)	)	PUNCT
ejpam-2044	143	1	+	+	CCONJ
ejpam-2044	143	2	(	(	PUNCT
ejpam-2044	143	3	1−	1−	NUM
ejpam-2044	143	4	p)v(1	p)v(1	ADJ
ejpam-2044	143	5	)	)	PUNCT
ejpam-2044	143	6	.	.	PUNCT
ejpam-2044	144	1	(	(	PUNCT
ejpam-2044	144	2	20	20	NUM
ejpam-2044	144	3	)	)	PUNCT
ejpam-2044	144	4	from	from	ADP
ejpam-2044	144	5	the	the	DET
ejpam-2044	144	6	equation	equation	NOUN
ejpam-2044	144	7	(	(	PUNCT
ejpam-2044	144	8	20	20	NUM
ejpam-2044	144	9	)	)	PUNCT
ejpam-2044	144	10	it	it	PRON
ejpam-2044	144	11	follows	follow	VERB
ejpam-2044	144	12	v(πm.v.[x	v(πm.v.[x	PROPN
ejpam-2044	144	13	ε	ε	PROPN
ejpam-2044	144	14	0	0	NUM
ejpam-2044	144	15	]	]	PUNCT
ejpam-2044	144	16	)	)	PUNCT
ejpam-2044	145	1	=	=	SYM
ejpam-2044	145	2	0	0	NUM
ejpam-2044	145	3	·	·	PUNCT
ejpam-2044	145	4	v(ε	v(ε	PROPN
ejpam-2044	145	5	)	)	PUNCT
ejpam-2044	146	1	+	+	CCONJ
ejpam-2044	146	2	1	1	NUM
ejpam-2044	146	3	·	·	SYM
ejpam-2044	146	4	v(1	v(1	NUM
ejpam-2044	146	5	)	)	PUNCT
ejpam-2044	146	6	,	,	PUNCT
ejpam-2044	146	7	moreover	moreover	ADV
ejpam-2044	146	8	,	,	PUNCT
ejpam-2044	146	9	since	since	SCONJ
ejpam-2044	146	10	v(x	v(x	PROPN
ejpam-2044	146	11	)	)	PUNCT
ejpam-2044	146	12	is	be	AUX
ejpam-2044	146	13	a	a	DET
ejpam-2044	146	14	strictly	strictly	ADV
ejpam-2044	146	15	increasing	increase	VERB
ejpam-2044	146	16	function	function	NOUN
ejpam-2044	146	17	,	,	PUNCT
ejpam-2044	146	18	then	then	ADV
ejpam-2044	146	19	πm.v.[x	πm.v.[x	PROPN
ejpam-2044	146	20	ε	ε	PROPN
ejpam-2044	146	21	0	0	NUM
ejpam-2044	146	22	]	]	X
ejpam-2044	146	23	=	=	SYM
ejpam-2044	146	24	1	1	X
ejpam-2044	146	25	.	.	PUNCT
ejpam-2044	146	26	(	(	PUNCT
ejpam-2044	146	27	21	21	NUM
ejpam-2044	146	28	)	)	PUNCT
ejpam-2044	146	29	calculating	calculate	VERB
ejpam-2044	146	30	partial	partial	ADJ
ejpam-2044	146	31	derivatives	derivative	NOUN
ejpam-2044	146	32	with	with	ADP
ejpam-2044	146	33	respect	respect	NOUN
ejpam-2044	146	34	to	to	ADP
ejpam-2044	146	35	the	the	DET
ejpam-2044	146	36	parameter	parameter	NOUN
ejpam-2044	146	37	p	p	NOUN
ejpam-2044	146	38	from	from	ADP
ejpam-2044	146	39	both	both	DET
ejpam-2044	146	40	sides	side	NOUN
ejpam-2044	146	41	of	of	ADP
ejpam-2044	146	42	the	the	DET
ejpam-2044	146	43	equation	equation	NOUN
ejpam-2044	146	44	(	(	PUNCT
ejpam-2044	146	45	20	20	NUM
ejpam-2044	146	46	)	)	PUNCT
ejpam-2044	146	47	,	,	PUNCT
ejpam-2044	146	48	obtain	obtain	VERB
ejpam-2044	146	49	v′(πm.v.[x	v′(πm.v.[x	NOUN
ejpam-2044	146	50	ε	ε	PROPN
ejpam-2044	146	51	p	p	X
ejpam-2044	146	52	]	]	X
ejpam-2044	146	53	)	)	PUNCT
ejpam-2044	146	54	·	·	PUNCT
ejpam-2044	146	55	∂	∂	NUM
ejpam-2044	146	56	∂	∂	NUM
ejpam-2044	146	57	p	p	NOUN
ejpam-2044	146	58	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	146	59	ε	ε	NOUN
ejpam-2044	147	1	p	p	X
ejpam-2044	147	2	]	]	X
ejpam-2044	147	3	=	=	SYM
ejpam-2044	147	4	v(ε)−	v(ε)−	NOUN
ejpam-2044	147	5	v(1	v(1	PROPN
ejpam-2044	147	6	)	)	PUNCT
ejpam-2044	147	7	.	.	PUNCT
ejpam-2044	148	1	(	(	PUNCT
ejpam-2044	148	2	22	22	X
ejpam-2044	148	3	)	)	PUNCT
ejpam-2044	148	4	substituting	substitute	VERB
ejpam-2044	148	5	p	p	NOUN
ejpam-2044	148	6	=	=	NOUN
ejpam-2044	148	7	0	0	NUM
ejpam-2044	148	8	into	into	ADP
ejpam-2044	148	9	equation	equation	NOUN
ejpam-2044	148	10	(	(	PUNCT
ejpam-2044	148	11	22	22	NUM
ejpam-2044	148	12	)	)	PUNCT
ejpam-2044	148	13	,	,	PUNCT
ejpam-2044	148	14	we	we	PRON
ejpam-2044	148	15	get	get	VERB
ejpam-2044	148	16	v′(πm.v.[x	v′(πm.v.[x	ADJ
ejpam-2044	148	17	ε	ε	PROPN
ejpam-2044	148	18	0	0	NUM
ejpam-2044	148	19	]	]	PUNCT
ejpam-2044	148	20	)	)	PUNCT
ejpam-2044	148	21	·	·	PUNCT
ejpam-2044	148	22	∂	∂	NUM
ejpam-2044	148	23	∂	∂	NUM
ejpam-2044	148	24	p	p	NOUN
ejpam-2044	148	25	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	148	26	ε	ε	NOUN
ejpam-2044	149	1	p	p	X
ejpam-2044	149	2	]	]	X
ejpam-2044	149	3	�	�	PROPN
ejpam-2044	149	4	�	�	PROPN
ejpam-2044	149	5	�	�	PROPN
ejpam-2044	149	6	�	�	PROPN
ejpam-2044	149	7	p=0	p=0	PROPN
ejpam-2044	149	8	=	=	PROPN
ejpam-2044	149	9	v(ε)−	v(ε)−	ADJ
ejpam-2044	149	10	v(1	v(1	PROPN
ejpam-2044	149	11	)	)	PUNCT
ejpam-2044	149	12	.	.	PUNCT
ejpam-2044	150	1	(	(	PUNCT
ejpam-2044	150	2	23	23	X
ejpam-2044	150	3	)	)	PUNCT
ejpam-2044	150	4	m.	m.	NOUN
ejpam-2044	150	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	150	6	,	,	PUNCT
ejpam-2044	150	7	v.	v.	ADP
ejpam-2044	150	8	drozdenko	drozdenko	PROPN
ejpam-2044	150	9	/	/	SYM
ejpam-2044	150	10	eur	eur	PROPN
ejpam-2044	150	11	.	.	PUNCT
ejpam-2044	151	1	j.	j.	PROPN
ejpam-2044	151	2	pure	pure	PROPN
ejpam-2044	151	3	appl	appl	PROPN
ejpam-2044	151	4	.	.	PROPN
ejpam-2044	151	5	math	math	PROPN
ejpam-2044	151	6	,	,	PUNCT
ejpam-2044	151	7	7	7	NUM
ejpam-2044	151	8	(	(	PUNCT
ejpam-2044	151	9	2014	2014	NUM
ejpam-2044	151	10	)	)	PUNCT
ejpam-2044	151	11	,	,	PUNCT
ejpam-2044	151	12	267	267	X
ejpam-2044	151	13	-	-	SYM
ejpam-2044	151	14	288	288	NUM
ejpam-2044	151	15	274	274	NUM
ejpam-2044	151	16	using	use	VERB
ejpam-2044	151	17	(	(	PUNCT
ejpam-2044	151	18	21	21	NUM
ejpam-2044	151	19	)	)	PUNCT
ejpam-2044	151	20	equation	equation	NOUN
ejpam-2044	151	21	(	(	PUNCT
ejpam-2044	151	22	23	23	NUM
ejpam-2044	151	23	)	)	PUNCT
ejpam-2044	151	24	can	can	AUX
ejpam-2044	151	25	be	be	AUX
ejpam-2044	151	26	rewritten	rewrite	VERB
ejpam-2044	151	27	as	as	ADP
ejpam-2044	151	28	v′(1	v′(1	NOUN
ejpam-2044	151	29	)	)	PUNCT
ejpam-2044	151	30	·	·	PUNCT
ejpam-2044	152	1	∂	∂	NUM
ejpam-2044	153	1	∂	∂	NUM
ejpam-2044	153	2	p	p	NOUN
ejpam-2044	153	3	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	153	4	ε	ε	NOUN
ejpam-2044	153	5	p	p	X
ejpam-2044	153	6	]	]	X
ejpam-2044	153	7	�	�	PROPN
ejpam-2044	153	8	�	�	PROPN
ejpam-2044	153	9	�	�	PROPN
ejpam-2044	153	10	�	�	PROPN
ejpam-2044	153	11	p=0	p=0	PROPN
ejpam-2044	153	12	=	=	PROPN
ejpam-2044	153	13	v(ε)−	v(ε)−	ADJ
ejpam-2044	153	14	v(1	v(1	PROPN
ejpam-2044	153	15	)	)	PUNCT
ejpam-2044	153	16	.	.	PUNCT
ejpam-2044	154	1	(	(	PUNCT
ejpam-2044	154	2	24	24	NUM
ejpam-2044	154	3	)	)	PUNCT
ejpam-2044	154	4	let	let	VERB
ejpam-2044	154	5	us	we	PRON
ejpam-2044	154	6	now	now	ADV
ejpam-2044	154	7	calculate	calculate	VERB
ejpam-2044	154	8	partial	partial	ADJ
ejpam-2044	154	9	derivatives	derivative	NOUN
ejpam-2044	154	10	with	with	ADP
ejpam-2044	154	11	respect	respect	NOUN
ejpam-2044	154	12	to	to	ADP
ejpam-2044	154	13	the	the	DET
ejpam-2044	154	14	parameter	parameter	NOUN
ejpam-2044	154	15	p	p	NOUN
ejpam-2044	154	16	from	from	ADP
ejpam-2044	154	17	both	both	DET
ejpam-2044	154	18	sides	side	NOUN
ejpam-2044	154	19	of	of	ADP
ejpam-2044	154	20	the	the	DET
ejpam-2044	154	21	equation	equation	NOUN
ejpam-2044	154	22	(	(	PUNCT
ejpam-2044	154	23	22	22	NUM
ejpam-2044	154	24	)	)	PUNCT
ejpam-2044	154	25	v′′(πm.v.[x	v′′(πm.v.[x	NOUN
ejpam-2044	155	1	ε	ε	X
ejpam-2044	155	2	p	p	X
ejpam-2044	155	3	]	]	X
ejpam-2044	155	4	)	)	PUNCT
ejpam-2044	155	5	·	·	PUNCT
ejpam-2044	155	6	�	�	PROPN
ejpam-2044	155	7	∂	∂	NUM
ejpam-2044	155	8	∂	∂	NUM
ejpam-2044	155	9	p	p	NOUN
ejpam-2044	155	10	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	155	11	ε	ε	NOUN
ejpam-2044	155	12	p	p	X
ejpam-2044	155	13	]	]	X
ejpam-2044	155	14	�	�	X
ejpam-2044	155	15	2	2	NUM
ejpam-2044	155	16	+	+	NUM
ejpam-2044	155	17	v′(πm.v.[x	v′(πm.v.[x	X
ejpam-2044	155	18	ε	ε	PROPN
ejpam-2044	155	19	p	p	X
ejpam-2044	155	20	]	]	X
ejpam-2044	155	21	)	)	PUNCT
ejpam-2044	155	22	·	·	PUNCT
ejpam-2044	155	23	∂	∂	NUM
ejpam-2044	155	24	2	2	NUM
ejpam-2044	155	25	(	(	PUNCT
ejpam-2044	155	26	∂	∂	NUM
ejpam-2044	155	27	p)2	p)2	NOUN
ejpam-2044	155	28	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	155	29	ε	ε	NOUN
ejpam-2044	156	1	p	p	X
ejpam-2044	156	2	]	]	X
ejpam-2044	156	3	=	=	SYM
ejpam-2044	156	4	0	0	X
ejpam-2044	156	5	.	.	PUNCT
ejpam-2044	157	1	(	(	PUNCT
ejpam-2044	157	2	25	25	NUM
ejpam-2044	157	3	)	)	PUNCT
ejpam-2044	157	4	substituting	substitute	VERB
ejpam-2044	157	5	p	p	NOUN
ejpam-2044	157	6	=	=	NOUN
ejpam-2044	157	7	0	0	NUM
ejpam-2044	157	8	into	into	ADP
ejpam-2044	157	9	the	the	DET
ejpam-2044	157	10	equation	equation	NOUN
ejpam-2044	157	11	(	(	PUNCT
ejpam-2044	157	12	25	25	NUM
ejpam-2044	157	13	)	)	PUNCT
ejpam-2044	157	14	,	,	PUNCT
ejpam-2044	157	15	and	and	CCONJ
ejpam-2044	157	16	using	use	VERB
ejpam-2044	157	17	identity	identity	NOUN
ejpam-2044	157	18	(	(	PUNCT
ejpam-2044	157	19	21	21	NUM
ejpam-2044	157	20	)	)	PUNCT
ejpam-2044	157	21	,	,	PUNCT
ejpam-2044	157	22	obtain	obtain	VERB
ejpam-2044	157	23	v′′(1	v′′(1	PROPN
ejpam-2044	157	24	)	)	PUNCT
ejpam-2044	157	25	·	·	PUNCT
ejpam-2044	157	26	�	�	PROPN
ejpam-2044	157	27	∂	∂	NUM
ejpam-2044	157	28	∂	∂	NUM
ejpam-2044	157	29	p	p	NOUN
ejpam-2044	157	30	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	157	31	ε	ε	NOUN
ejpam-2044	158	1	p	p	X
ejpam-2044	158	2	]	]	X
ejpam-2044	158	3	�	�	PROPN
ejpam-2044	158	4	�	�	PROPN
ejpam-2044	158	5	�	�	PROPN
ejpam-2044	158	6	�	�	PROPN
ejpam-2044	158	7	p=0	p=0	PROPN
ejpam-2044	158	8	�	�	PROPN
ejpam-2044	158	9	2	2	NUM
ejpam-2044	158	10	+	+	SYM
ejpam-2044	158	11	v′(1	v′(1	NOUN
ejpam-2044	158	12	)	)	PUNCT
ejpam-2044	158	13	·	·	PUNCT
ejpam-2044	158	14	�	�	PROPN
ejpam-2044	158	15	∂	∂	NUM
ejpam-2044	158	16	2	2	NUM
ejpam-2044	158	17	(	(	PUNCT
ejpam-2044	158	18	∂	∂	NUM
ejpam-2044	158	19	p)2	p)2	NOUN
ejpam-2044	158	20	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	158	21	ε	ε	PROPN
ejpam-2044	159	1	p	p	X
ejpam-2044	159	2	]	]	X
ejpam-2044	159	3	�	�	PROPN
ejpam-2044	159	4	�	�	PROPN
ejpam-2044	159	5	�	�	PROPN
ejpam-2044	159	6	�	�	PROPN
ejpam-2044	159	7	p=0	p=0	PROPN
ejpam-2044	159	8	�	�	PROPN
ejpam-2044	159	9	=	=	PUNCT
ejpam-2044	159	10	0	0	PROPN
ejpam-2044	159	11	.	.	PUNCT
ejpam-2044	160	1	(	(	PUNCT
ejpam-2044	160	2	26	26	NUM
ejpam-2044	160	3	)	)	PUNCT
ejpam-2044	160	4	taking	take	VERB
ejpam-2044	160	5	ε	ε	PROPN
ejpam-2044	160	6	small	small	ADJ
ejpam-2044	160	7	enough	enough	ADV
ejpam-2044	160	8	,	,	PUNCT
ejpam-2044	160	9	namely	namely	ADV
ejpam-2044	160	10	ε	ε	X
ejpam-2044	160	11	<	<	X
ejpam-2044	160	12	1	1	NUM
ejpam-2044	160	13	,	,	PUNCT
ejpam-2044	160	14	and	and	CCONJ
ejpam-2044	160	15	taking	take	VERB
ejpam-2044	160	16	into	into	ADP
ejpam-2044	160	17	account	account	NOUN
ejpam-2044	160	18	strict	strict	ADJ
ejpam-2044	160	19	monotonicity	monotonicity	NOUN
ejpam-2044	160	20	of	of	ADP
ejpam-2044	160	21	the	the	DET
ejpam-2044	160	22	function	function	NOUN
ejpam-2044	160	23	v(x	v(x	PROPN
ejpam-2044	160	24	)	)	PUNCT
ejpam-2044	160	25	,	,	PUNCT
ejpam-2044	160	26	without	without	ADP
ejpam-2044	160	27	of	of	ADP
ejpam-2044	160	28	loss	loss	NOUN
ejpam-2044	160	29	of	of	ADP
ejpam-2044	160	30	generality	generality	NOUN
ejpam-2044	160	31	,	,	PUNCT
ejpam-2044	160	32	using	use	VERB
ejpam-2044	160	33	(	(	PUNCT
ejpam-2044	160	34	24	24	NUM
ejpam-2044	160	35	)	)	PUNCT
ejpam-2044	160	36	,	,	PUNCT
ejpam-2044	160	37	we	we	PRON
ejpam-2044	160	38	may	may	AUX
ejpam-2044	160	39	conclude	conclude	VERB
ejpam-2044	160	40	that	that	DET
ejpam-2044	160	41	∂	∂	NOUN
ejpam-2044	160	42	∂	∂	NUM
ejpam-2044	160	43	p	p	NOUN
ejpam-2044	160	44	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	160	45	ε	ε	NOUN
ejpam-2044	160	46	p	p	X
ejpam-2044	160	47	]	]	X
ejpam-2044	160	48	�	�	PROPN
ejpam-2044	160	49	�	�	PROPN
ejpam-2044	160	50	�	�	PROPN
ejpam-2044	160	51	�	�	PROPN
ejpam-2044	160	52	p=0	p=0	PROPN
ejpam-2044	160	53	6=	6=	ADP
ejpam-2044	160	54	0	0	NUM
ejpam-2044	160	55	,	,	PUNCT
ejpam-2044	160	56	(	(	PUNCT
ejpam-2044	160	57	27	27	NUM
ejpam-2044	160	58	)	)	PUNCT
ejpam-2044	160	59	hence	hence	ADV
ejpam-2044	160	60	,	,	PUNCT
ejpam-2044	160	61	equation	equation	NOUN
ejpam-2044	160	62	(	(	PUNCT
ejpam-2044	160	63	26	26	NUM
ejpam-2044	160	64	)	)	PUNCT
ejpam-2044	160	65	can	can	AUX
ejpam-2044	160	66	be	be	AUX
ejpam-2044	160	67	rewritten	rewrite	VERB
ejpam-2044	160	68	as	as	ADP
ejpam-2044	160	69	v′′(1	v′′(1	NOUN
ejpam-2044	160	70	)	)	PUNCT
ejpam-2044	160	71	v′(1	v′(1	PROPN
ejpam-2044	160	72	)	)	PUNCT
ejpam-2044	160	73	=	=	SYM
ejpam-2044	160	74	−	−	PROPN
ejpam-2044	160	75	�	�	PROPN
ejpam-2044	160	76	∂	∂	NUM
ejpam-2044	160	77	2	2	NUM
ejpam-2044	160	78	(	(	PUNCT
ejpam-2044	160	79	∂	∂	NUM
ejpam-2044	160	80	p)2	p)2	NOUN
ejpam-2044	160	81	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	160	82	ε	ε	PROPN
ejpam-2044	160	83	p	p	X
ejpam-2044	160	84	]	]	X
ejpam-2044	160	85	�	�	PROPN
ejpam-2044	160	86	�	�	PROPN
ejpam-2044	160	87	�	�	PROPN
ejpam-2044	160	88	�	�	PROPN
ejpam-2044	160	89	p=0	p=0	PROPN
ejpam-2044	160	90	�	�	PROPN
ejpam-2044	160	91	â	â	PART
ejpam-2044	160	92	�	�	PROPN
ejpam-2044	160	93	∂	∂	NUM
ejpam-2044	160	94	∂	∂	NUM
ejpam-2044	160	95	p	p	NOUN
ejpam-2044	160	96	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	160	97	ε	ε	NOUN
ejpam-2044	160	98	p	p	X
ejpam-2044	160	99	]	]	X
ejpam-2044	160	100	�	�	PROPN
ejpam-2044	160	101	�	�	PROPN
ejpam-2044	160	102	�	�	PROPN
ejpam-2044	160	103	�	�	PROPN
ejpam-2044	160	104	p=0	p=0	PROPN
ejpam-2044	160	105	�	�	PROPN
ejpam-2044	160	106	2	2	NUM
ejpam-2044	160	107	.	.	PUNCT
ejpam-2044	161	1	(	(	PUNCT
ejpam-2044	161	2	28	28	NUM
ejpam-2044	161	3	)	)	PUNCT
ejpam-2044	161	4	for	for	ADP
ejpam-2044	161	5	any	any	DET
ejpam-2044	161	6	θ	θ	PROPN
ejpam-2044	161	7	>	>	X
ejpam-2044	161	8	0	0	NUM
ejpam-2044	161	9	,	,	PUNCT
ejpam-2044	161	10	equation	equation	NOUN
ejpam-2044	161	11	(	(	PUNCT
ejpam-2044	161	12	1	1	NUM
ejpam-2044	161	13	)	)	PUNCT
ejpam-2044	161	14	for	for	ADP
ejpam-2044	161	15	the	the	DET
ejpam-2044	161	16	risk	risk	NOUN
ejpam-2044	161	17	θx	θx	PART
ejpam-2044	161	18	εp	εp	NOUN
ejpam-2044	161	19	will	will	AUX
ejpam-2044	161	20	take	take	VERB
ejpam-2044	161	21	the	the	DET
ejpam-2044	161	22	following	follow	VERB
ejpam-2044	161	23	form	form	NOUN
ejpam-2044	161	24	v(πm.v.[θx	v(πm.v.[θx	NOUN
ejpam-2044	161	25	εp	εp	ADP
ejpam-2044	161	26	]	]	PUNCT
ejpam-2044	161	27	)	)	PUNCT
ejpam-2044	161	28	=	=	SYM
ejpam-2044	161	29	pv(θε	pv(θε	ADJ
ejpam-2044	161	30	)	)	PUNCT
ejpam-2044	162	1	+	+	CCONJ
ejpam-2044	162	2	(	(	PUNCT
ejpam-2044	162	3	1−	1−	NUM
ejpam-2044	162	4	p)v(θ	p)v(θ	NOUN
ejpam-2044	162	5	)	)	PUNCT
ejpam-2044	162	6	.	.	PUNCT
ejpam-2044	163	1	(	(	PUNCT
ejpam-2044	163	2	29	29	NUM
ejpam-2044	163	3	)	)	PUNCT
ejpam-2044	163	4	in	in	ADP
ejpam-2044	163	5	the	the	DET
ejpam-2044	163	6	case	case	NOUN
ejpam-2044	163	7	of	of	ADP
ejpam-2044	163	8	scale	scale	NOUN
ejpam-2044	163	9	invariant	invariant	ADJ
ejpam-2044	163	10	mean	mean	NOUN
ejpam-2044	163	11	value	value	NOUN
ejpam-2044	163	12	premium	premium	NOUN
ejpam-2044	163	13	principle	principle	NOUN
ejpam-2044	163	14	equation	equation	NOUN
ejpam-2044	163	15	(	(	PUNCT
ejpam-2044	163	16	29	29	NUM
ejpam-2044	163	17	)	)	PUNCT
ejpam-2044	163	18	can	can	AUX
ejpam-2044	163	19	be	be	AUX
ejpam-2044	163	20	rewritten	rewrite	VERB
ejpam-2044	163	21	as	as	ADP
ejpam-2044	163	22	v(θπm.v.[x	v(θπm.v.[x	X
ejpam-2044	163	23	ε	ε	PROPN
ejpam-2044	163	24	p	p	X
ejpam-2044	163	25	]	]	X
ejpam-2044	163	26	)	)	PUNCT
ejpam-2044	163	27	=	=	SYM
ejpam-2044	163	28	pv(θε	pv(θε	ADJ
ejpam-2044	163	29	)	)	PUNCT
ejpam-2044	164	1	+	+	CCONJ
ejpam-2044	164	2	(	(	PUNCT
ejpam-2044	164	3	1−	1−	NUM
ejpam-2044	164	4	p)v(θ	p)v(θ	NOUN
ejpam-2044	164	5	)	)	PUNCT
ejpam-2044	164	6	.	.	PUNCT
ejpam-2044	165	1	(	(	PUNCT
ejpam-2044	165	2	30	30	X
ejpam-2044	165	3	)	)	PUNCT
ejpam-2044	165	4	calculating	calculate	VERB
ejpam-2044	165	5	second	second	ADJ
ejpam-2044	165	6	partial	partial	ADJ
ejpam-2044	165	7	derivative	derivative	NOUN
ejpam-2044	165	8	with	with	ADP
ejpam-2044	165	9	respect	respect	NOUN
ejpam-2044	165	10	to	to	ADP
ejpam-2044	165	11	p	p	NOUN
ejpam-2044	165	12	from	from	ADP
ejpam-2044	165	13	both	both	DET
ejpam-2044	165	14	sides	side	NOUN
ejpam-2044	165	15	of	of	ADP
ejpam-2044	165	16	the	the	DET
ejpam-2044	165	17	equation	equation	NOUN
ejpam-2044	165	18	(	(	PUNCT
ejpam-2044	165	19	30	30	NUM
ejpam-2044	165	20	)	)	PUNCT
ejpam-2044	165	21	,	,	PUNCT
ejpam-2044	165	22	obtain	obtain	VERB
ejpam-2044	165	23	v′′(θπm.v.[x	v′′(θπm.v.[x	NUM
ejpam-2044	165	24	ε	ε	PROPN
ejpam-2044	165	25	p	p	X
ejpam-2044	165	26	]	]	X
ejpam-2044	165	27	)	)	PUNCT
ejpam-2044	165	28	·	·	PUNCT
ejpam-2044	165	29	θ	θ	NOUN
ejpam-2044	165	30	2	2	NUM
ejpam-2044	165	31	·	·	SYM
ejpam-2044	165	32	�	�	PROPN
ejpam-2044	165	33	∂	∂	NUM
ejpam-2044	165	34	∂	∂	NUM
ejpam-2044	165	35	p	p	NOUN
ejpam-2044	165	36	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	165	37	ε	ε	NOUN
ejpam-2044	165	38	p	p	X
ejpam-2044	165	39	]	]	X
ejpam-2044	165	40	�	�	X
ejpam-2044	165	41	2	2	NUM
ejpam-2044	165	42	+	+	CCONJ
ejpam-2044	165	43	v′(θπm.v.[x	v′(θπm.v.[x	NOUN
ejpam-2044	165	44	ε	ε	X
ejpam-2044	165	45	p	p	X
ejpam-2044	165	46	]	]	X
ejpam-2044	165	47	)	)	PUNCT
ejpam-2044	165	48	·	·	PUNCT
ejpam-2044	165	49	θ	θ	X
ejpam-2044	165	50	·	·	PUNCT
ejpam-2044	165	51	∂	∂	NUM
ejpam-2044	165	52	2	2	NUM
ejpam-2044	165	53	(	(	PUNCT
ejpam-2044	165	54	∂	∂	NUM
ejpam-2044	165	55	p)2	p)2	NOUN
ejpam-2044	165	56	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	165	57	ε	ε	NOUN
ejpam-2044	166	1	p	p	X
ejpam-2044	166	2	]	]	X
ejpam-2044	166	3	=	=	SYM
ejpam-2044	166	4	0	0	X
ejpam-2044	166	5	.	.	PUNCT
ejpam-2044	167	1	(	(	PUNCT
ejpam-2044	167	2	31	31	NUM
ejpam-2044	167	3	)	)	PUNCT
ejpam-2044	167	4	substituting	substitute	VERB
ejpam-2044	167	5	p	p	NOUN
ejpam-2044	167	6	=	=	NOUN
ejpam-2044	167	7	0	0	NUM
ejpam-2044	167	8	into	into	ADP
ejpam-2044	167	9	the	the	DET
ejpam-2044	167	10	equation	equation	NOUN
ejpam-2044	167	11	(	(	PUNCT
ejpam-2044	167	12	31	31	NUM
ejpam-2044	167	13	)	)	PUNCT
ejpam-2044	167	14	,	,	PUNCT
ejpam-2044	167	15	canceling	cancel	VERB
ejpam-2044	167	16	θ	θ	PROPN
ejpam-2044	167	17	factor	factor	NOUN
ejpam-2044	167	18	,	,	PUNCT
ejpam-2044	167	19	and	and	CCONJ
ejpam-2044	167	20	using	use	VERB
ejpam-2044	167	21	identity	identity	NOUN
ejpam-2044	167	22	(	(	PUNCT
ejpam-2044	167	23	21	21	NUM
ejpam-2044	167	24	)	)	PUNCT
ejpam-2044	167	25	,	,	PUNCT
ejpam-2044	167	26	we	we	PRON
ejpam-2044	167	27	get	get	VERB
ejpam-2044	167	28	v′′(θ	v′′(θ	NOUN
ejpam-2044	167	29	)	)	PUNCT
ejpam-2044	167	30	·	·	PUNCT
ejpam-2044	167	31	θ	θ	X
ejpam-2044	167	32	·	·	PUNCT
ejpam-2044	167	33	�	�	PROPN
ejpam-2044	167	34	∂	∂	NUM
ejpam-2044	167	35	∂	∂	NUM
ejpam-2044	167	36	p	p	NOUN
ejpam-2044	167	37	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	167	38	ε	ε	NOUN
ejpam-2044	167	39	p	p	X
ejpam-2044	167	40	]	]	X
ejpam-2044	167	41	�	�	PROPN
ejpam-2044	167	42	�	�	PROPN
ejpam-2044	167	43	�	�	PROPN
ejpam-2044	167	44	�	�	PROPN
ejpam-2044	167	45	p=0	p=0	PROPN
ejpam-2044	167	46	�	�	PROPN
ejpam-2044	167	47	2	2	NUM
ejpam-2044	167	48	+	+	SYM
ejpam-2044	167	49	v′(θ	v′(θ	NOUN
ejpam-2044	167	50	)	)	PUNCT
ejpam-2044	167	51	·	·	PUNCT
ejpam-2044	167	52	�	�	PROPN
ejpam-2044	167	53	∂	∂	NUM
ejpam-2044	167	54	2	2	NUM
ejpam-2044	167	55	(	(	PUNCT
ejpam-2044	167	56	∂	∂	NUM
ejpam-2044	167	57	p)2	p)2	NOUN
ejpam-2044	167	58	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	167	59	ε	ε	PROPN
ejpam-2044	167	60	p	p	X
ejpam-2044	167	61	]	]	X
ejpam-2044	167	62	�	�	PROPN
ejpam-2044	167	63	�	�	PROPN
ejpam-2044	167	64	�	�	PROPN
ejpam-2044	167	65	�	�	PROPN
ejpam-2044	167	66	p=0	p=0	PROPN
ejpam-2044	167	67	�	�	PROPN
ejpam-2044	168	1	=	=	PUNCT
ejpam-2044	168	2	0	0	PROPN
ejpam-2044	168	3	.	.	PUNCT
ejpam-2044	169	1	(	(	PUNCT
ejpam-2044	169	2	32	32	NUM
ejpam-2044	169	3	)	)	PUNCT
ejpam-2044	169	4	m.	m.	NOUN
ejpam-2044	169	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	169	6	,	,	PUNCT
ejpam-2044	169	7	v.	v.	ADP
ejpam-2044	169	8	drozdenko	drozdenko	PROPN
ejpam-2044	169	9	/	/	SYM
ejpam-2044	169	10	eur	eur	PROPN
ejpam-2044	169	11	.	.	PUNCT
ejpam-2044	170	1	j.	j.	PROPN
ejpam-2044	170	2	pure	pure	PROPN
ejpam-2044	170	3	appl	appl	PROPN
ejpam-2044	170	4	.	.	PROPN
ejpam-2044	170	5	math	math	PROPN
ejpam-2044	170	6	,	,	PUNCT
ejpam-2044	170	7	7	7	NUM
ejpam-2044	170	8	(	(	PUNCT
ejpam-2044	170	9	2014	2014	NUM
ejpam-2044	170	10	)	)	PUNCT
ejpam-2044	170	11	,	,	PUNCT
ejpam-2044	170	12	267	267	X
ejpam-2044	170	13	-	-	SYM
ejpam-2044	170	14	288	288	NUM
ejpam-2044	170	15	275	275	NUM
ejpam-2044	170	16	since	since	SCONJ
ejpam-2044	170	17	v′(θ	v′(θ	NUM
ejpam-2044	170	18	)	)	PUNCT
ejpam-2044	170	19	>	>	X
ejpam-2044	170	20	0	0	NUM
ejpam-2044	170	21	,	,	PUNCT
ejpam-2044	170	22	then	then	ADV
ejpam-2044	170	23	using	use	VERB
ejpam-2044	170	24	relation	relation	NOUN
ejpam-2044	170	25	(	(	PUNCT
ejpam-2044	170	26	27	27	NUM
ejpam-2044	170	27	)	)	PUNCT
ejpam-2044	170	28	,	,	PUNCT
ejpam-2044	170	29	equation	equation	NOUN
ejpam-2044	170	30	(	(	PUNCT
ejpam-2044	170	31	32	32	NUM
ejpam-2044	170	32	)	)	PUNCT
ejpam-2044	170	33	can	can	AUX
ejpam-2044	170	34	be	be	AUX
ejpam-2044	170	35	rewritten	rewrite	VERB
ejpam-2044	170	36	as	as	ADP
ejpam-2044	170	37	v′′(θ	v′′(θ	NOUN
ejpam-2044	170	38	)	)	PUNCT
ejpam-2044	170	39	·	·	PUNCT
ejpam-2044	170	40	θ	θ	NOUN
ejpam-2044	170	41	v′(θ	v′(θ	NOUN
ejpam-2044	170	42	)	)	PUNCT
ejpam-2044	170	43	=	=	SYM
ejpam-2044	171	1	−	−	PROPN
ejpam-2044	171	2	�	�	PROPN
ejpam-2044	171	3	∂	∂	NUM
ejpam-2044	171	4	2	2	NUM
ejpam-2044	171	5	(	(	PUNCT
ejpam-2044	171	6	∂	∂	NUM
ejpam-2044	171	7	p)2	p)2	NOUN
ejpam-2044	171	8	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	171	9	ε	ε	PROPN
ejpam-2044	171	10	p	p	X
ejpam-2044	171	11	]	]	X
ejpam-2044	171	12	�	�	PROPN
ejpam-2044	171	13	�	�	PROPN
ejpam-2044	171	14	�	�	PROPN
ejpam-2044	171	15	�	�	PROPN
ejpam-2044	171	16	p=0	p=0	PROPN
ejpam-2044	171	17	�	�	PROPN
ejpam-2044	171	18	â	â	PART
ejpam-2044	171	19	�	�	PROPN
ejpam-2044	171	20	∂	∂	NUM
ejpam-2044	171	21	∂	∂	NUM
ejpam-2044	171	22	p	p	NOUN
ejpam-2044	171	23	πm.v.[x	πm.v.[x	NOUN
ejpam-2044	171	24	ε	ε	NOUN
ejpam-2044	171	25	p	p	X
ejpam-2044	171	26	]	]	X
ejpam-2044	171	27	�	�	PROPN
ejpam-2044	171	28	�	�	PROPN
ejpam-2044	171	29	�	�	PROPN
ejpam-2044	171	30	�	�	PROPN
ejpam-2044	171	31	p=0	p=0	PROPN
ejpam-2044	171	32	�	�	PROPN
ejpam-2044	171	33	2	2	NUM
ejpam-2044	171	34	.	.	PUNCT
ejpam-2044	172	1	(	(	PUNCT
ejpam-2044	172	2	33	33	NUM
ejpam-2044	172	3	)	)	PUNCT
ejpam-2044	172	4	observe	observe	VERB
ejpam-2044	172	5	that	that	SCONJ
ejpam-2044	172	6	equations	equation	NOUN
ejpam-2044	172	7	(	(	PUNCT
ejpam-2044	172	8	28	28	NUM
ejpam-2044	172	9	)	)	PUNCT
ejpam-2044	172	10	and	and	CCONJ
ejpam-2044	172	11	(	(	PUNCT
ejpam-2044	172	12	33	33	NUM
ejpam-2044	172	13	)	)	PUNCT
ejpam-2044	172	14	have	have	VERB
ejpam-2044	172	15	equal	equal	ADJ
ejpam-2044	172	16	right	right	ADJ
ejpam-2044	172	17	-	-	PUNCT
ejpam-2044	172	18	hand	hand	NOUN
ejpam-2044	172	19	sides	side	NOUN
ejpam-2044	172	20	,	,	PUNCT
ejpam-2044	172	21	this	this	PRON
ejpam-2044	172	22	means	mean	VERB
ejpam-2044	172	23	that	that	SCONJ
ejpam-2044	172	24	their	their	PRON
ejpam-2044	172	25	left	leave	VERB
ejpam-2044	172	26	-	-	PUNCT
ejpam-2044	172	27	hand	hand	NOUN
ejpam-2044	172	28	sides	side	NOUN
ejpam-2044	172	29	also	also	ADV
ejpam-2044	172	30	have	have	VERB
ejpam-2044	172	31	to	to	PART
ejpam-2044	172	32	be	be	AUX
ejpam-2044	172	33	equal	equal	ADJ
ejpam-2044	172	34	,	,	PUNCT
ejpam-2044	172	35	in	in	ADP
ejpam-2044	172	36	this	this	DET
ejpam-2044	172	37	way	way	NOUN
ejpam-2044	172	38	we	we	PRON
ejpam-2044	172	39	finally	finally	ADV
ejpam-2044	172	40	get	get	VERB
ejpam-2044	172	41	an	an	DET
ejpam-2044	172	42	equation	equation	NOUN
ejpam-2044	172	43	which	which	PRON
ejpam-2044	172	44	the	the	DET
ejpam-2044	172	45	function	function	NOUN
ejpam-2044	172	46	v(x	v(x	PROPN
ejpam-2044	172	47	)	)	PUNCT
ejpam-2044	172	48	has	have	VERB
ejpam-2044	172	49	to	to	PART
ejpam-2044	172	50	satisfy	satisfy	VERB
ejpam-2044	172	51	in	in	ADP
ejpam-2044	172	52	the	the	DET
ejpam-2044	172	53	case	case	NOUN
ejpam-2044	172	54	of	of	ADP
ejpam-2044	172	55	scale	scale	NOUN
ejpam-2044	172	56	invariant	invariant	ADJ
ejpam-2044	172	57	mean	mean	NOUN
ejpam-2044	172	58	value	value	NOUN
ejpam-2044	172	59	premium	premium	NOUN
ejpam-2044	172	60	calculation	calculation	NOUN
ejpam-2044	172	61	principle	principle	NOUN
ejpam-2044	172	62	subjected	subject	VERB
ejpam-2044	172	63	to	to	ADP
ejpam-2044	172	64	consideration	consideration	NOUN
ejpam-2044	172	65	of	of	ADP
ejpam-2044	172	66	only	only	ADV
ejpam-2044	172	67	strictly	strictly	ADV
ejpam-2044	172	68	positive	positive	ADJ
ejpam-2044	172	69	risks	risk	NOUN
ejpam-2044	172	70	,	,	PUNCT
ejpam-2044	172	71	namely	namely	ADV
ejpam-2044	172	72	,	,	PUNCT
ejpam-2044	172	73	v′′(θ	v′′(θ	NOUN
ejpam-2044	172	74	)	)	PUNCT
ejpam-2044	172	75	·	·	PUNCT
ejpam-2044	172	76	θ	θ	NOUN
ejpam-2044	172	77	v′(θ	v′(θ	NOUN
ejpam-2044	172	78	)	)	PUNCT
ejpam-2044	172	79	=	=	SYM
ejpam-2044	172	80	v′′(1	v′′(1	ADJ
ejpam-2044	172	81	)	)	PUNCT
ejpam-2044	172	82	v′(1	v′(1	PROPN
ejpam-2044	172	83	)	)	PUNCT
ejpam-2044	172	84	,	,	PUNCT
ejpam-2044	172	85	for	for	ADP
ejpam-2044	172	86	all	all	DET
ejpam-2044	172	87	θ	θ	PROPN
ejpam-2044	172	88	>	>	X
ejpam-2044	172	89	0	0	NUM
ejpam-2044	172	90	.	.	PUNCT
ejpam-2044	173	1	(	(	PUNCT
ejpam-2044	173	2	34	34	NUM
ejpam-2044	173	3	)	)	PUNCT
ejpam-2044	173	4	assigning	assign	VERB
ejpam-2044	173	5	v′′(1)/v′(1	v′′(1)/v′(1	NOUN
ejpam-2044	173	6	)	)	PUNCT
ejpam-2044	173	7	=	=	NOUN
ejpam-2044	173	8	:	:	PUNCT
ejpam-2044	173	9	c	c	X
ejpam-2044	173	10	(	(	PUNCT
ejpam-2044	173	11	since	since	SCONJ
ejpam-2044	173	12	v′′(1	v′′(1	PROPN
ejpam-2044	173	13	)	)	PUNCT
ejpam-2044	173	14	≥	≥	NOUN
ejpam-2044	173	15	0	0	NUM
ejpam-2044	173	16	and	and	CCONJ
ejpam-2044	173	17	v′(1	v′(1	PROPN
ejpam-2044	173	18	)	)	PUNCT
ejpam-2044	173	19	>	>	X
ejpam-2044	173	20	0	0	PUNCT
ejpam-2044	174	1	then	then	ADV
ejpam-2044	174	2	c	c	X
ejpam-2044	174	3	≥	≥	PROPN
ejpam-2044	174	4	0	0	NUM
ejpam-2044	174	5	)	)	PUNCT
ejpam-2044	174	6	and	and	CCONJ
ejpam-2044	174	7	making	make	VERB
ejpam-2044	174	8	substitution	substitution	NOUN
ejpam-2044	174	9	z(θ	z(θ	NOUN
ejpam-2044	174	10	)	)	PUNCT
ejpam-2044	174	11	:	:	PUNCT
ejpam-2044	174	12	=	=	SYM
ejpam-2044	174	13	v′(θ	v′(θ	NOUN
ejpam-2044	174	14	)	)	PUNCT
ejpam-2044	174	15	equation	equation	NOUN
ejpam-2044	174	16	(	(	PUNCT
ejpam-2044	174	17	34	34	NUM
ejpam-2044	174	18	)	)	PUNCT
ejpam-2044	174	19	can	can	AUX
ejpam-2044	174	20	be	be	AUX
ejpam-2044	174	21	rewritten	rewrite	VERB
ejpam-2044	174	22	in	in	ADP
ejpam-2044	174	23	the	the	DET
ejpam-2044	174	24	following	follow	VERB
ejpam-2044	174	25	equivalent	equivalent	ADJ
ejpam-2044	174	26	form	form	NOUN
ejpam-2044	174	27	dz	dz	PROPN
ejpam-2044	174	28	z	z	NOUN
ejpam-2044	174	29	=	=	PUNCT
ejpam-2044	174	30	c	c	PROPN
ejpam-2044	174	31	dθ	dθ	PROPN
ejpam-2044	174	32	θ	θ	PROPN
ejpam-2044	174	33	,	,	PUNCT
ejpam-2044	174	34	therefore	therefore	ADV
ejpam-2044	174	35	log(z(θ	log(z(θ	NOUN
ejpam-2044	174	36	)	)	PUNCT
ejpam-2044	174	37	)	)	PUNCT
ejpam-2044	175	1	=	=	PUNCT
ejpam-2044	175	2	c	c	X
ejpam-2044	175	3	log(θ	log(θ	PROPN
ejpam-2044	175	4	)	)	PUNCT
ejpam-2044	175	5	+	+	X
ejpam-2044	175	6	log(c1	log(c1	NOUN
ejpam-2044	175	7	)	)	PUNCT
ejpam-2044	175	8	,	,	PUNCT
ejpam-2044	175	9	for	for	ADP
ejpam-2044	175	10	some	some	DET
ejpam-2044	175	11	constant	constant	ADJ
ejpam-2044	175	12	c1	c1	NOUN
ejpam-2044	175	13	>	>	X
ejpam-2044	175	14	0	0	PROPN
ejpam-2044	175	15	,	,	PUNCT
ejpam-2044	175	16	and	and	CCONJ
ejpam-2044	175	17	the	the	DET
ejpam-2044	175	18	function	function	NOUN
ejpam-2044	175	19	z(θ	z(θ	NOUN
ejpam-2044	175	20	)	)	PUNCT
ejpam-2044	175	21	itself	itself	PRON
ejpam-2044	175	22	will	will	AUX
ejpam-2044	175	23	have	have	VERB
ejpam-2044	175	24	a	a	DET
ejpam-2044	175	25	form	form	NOUN
ejpam-2044	175	26	z(θ	z(θ	NUM
ejpam-2044	175	27	)	)	PUNCT
ejpam-2044	176	1	=	=	PUNCT
ejpam-2044	176	2	c1θ	c1θ	PROPN
ejpam-2044	176	3	c.	c.	NOUN
ejpam-2044	176	4	switching	switch	VERB
ejpam-2044	176	5	back	back	ADV
ejpam-2044	176	6	to	to	ADP
ejpam-2044	176	7	the	the	DET
ejpam-2044	176	8	function	function	NOUN
ejpam-2044	176	9	v′	v′	NOUN
ejpam-2044	176	10	(	(	PUNCT
ejpam-2044	176	11	·	·	PUNCT
ejpam-2044	176	12	)	)	PUNCT
ejpam-2044	176	13	,	,	PUNCT
ejpam-2044	176	14	and	and	CCONJ
ejpam-2044	176	15	switching	switch	VERB
ejpam-2044	176	16	to	to	ADP
ejpam-2044	176	17	the	the	DET
ejpam-2044	176	18	original	original	ADJ
ejpam-2044	176	19	parameter	parameter	NOUN
ejpam-2044	176	20	x	x	X
ejpam-2044	176	21	∈	∈	PROPN
ejpam-2044	176	22	(	(	PUNCT
ejpam-2044	176	23	0,+∞	0,+∞	NUM
ejpam-2044	176	24	)	)	PUNCT
ejpam-2044	176	25	,	,	PUNCT
ejpam-2044	176	26	obtain	obtain	VERB
ejpam-2044	176	27	v′(x	v′(x	SYM
ejpam-2044	176	28	)	)	PUNCT
ejpam-2044	176	29	=	=	SYM
ejpam-2044	176	30	c1	c1	PROPN
ejpam-2044	176	31	xc	xc	PROPN
ejpam-2044	176	32	.	.	PUNCT
ejpam-2044	177	1	taking	take	VERB
ejpam-2044	177	2	antiderivative	antiderivative	ADJ
ejpam-2044	177	3	,	,	PUNCT
ejpam-2044	177	4	we	we	PRON
ejpam-2044	177	5	get	get	VERB
ejpam-2044	177	6	v(x	v(x	NOUN
ejpam-2044	177	7	)	)	PUNCT
ejpam-2044	178	1	=	=	SYM
ejpam-2044	178	2	c1	c1	NOUN
ejpam-2044	178	3	c+	c+	VERB
ejpam-2044	178	4	1	1	NUM
ejpam-2044	178	5	xc+1	xc+1	PROPN
ejpam-2044	178	6	+	+	CCONJ
ejpam-2044	178	7	c2	c2	PROPN
ejpam-2044	178	8	,	,	PUNCT
ejpam-2044	178	9	therefore	therefore	ADV
ejpam-2044	178	10	,	,	PUNCT
ejpam-2044	178	11	the	the	DET
ejpam-2044	178	12	function	function	NOUN
ejpam-2044	178	13	v(x	v(x	PROPN
ejpam-2044	178	14	)	)	PUNCT
ejpam-2044	178	15	must	must	AUX
ejpam-2044	178	16	be	be	AUX
ejpam-2044	178	17	a	a	DET
ejpam-2044	178	18	function	function	NOUN
ejpam-2044	178	19	of	of	ADP
ejpam-2044	178	20	the	the	DET
ejpam-2044	178	21	form	form	NOUN
ejpam-2044	178	22	v(x	v(x	NUM
ejpam-2044	178	23	)	)	PUNCT
ejpam-2044	178	24	=	=	VERB
ejpam-2044	179	1	axκ	axκ	PROPN
ejpam-2044	179	2	+	+	CCONJ
ejpam-2044	179	3	b	b	X
ejpam-2044	179	4	,	,	PUNCT
ejpam-2044	179	5	for	for	ADP
ejpam-2044	179	6	some	some	DET
ejpam-2044	179	7	real	real	ADJ
ejpam-2044	179	8	constants	constant	NOUN
ejpam-2044	179	9	a	a	DET
ejpam-2044	179	10	,	,	PUNCT
ejpam-2044	179	11	b	b	NOUN
ejpam-2044	179	12	,	,	PUNCT
ejpam-2044	179	13	and	and	CCONJ
ejpam-2044	179	14	κ	κ	X
ejpam-2044	179	15	.	.	PUNCT
ejpam-2044	180	1	moreover	moreover	ADV
ejpam-2044	180	2	,	,	PUNCT
ejpam-2044	180	3	since	since	SCONJ
ejpam-2044	180	4	c1	c1	PROPN
ejpam-2044	180	5	>	>	X
ejpam-2044	180	6	0	0	PUNCT
ejpam-2044	180	7	and	and	CCONJ
ejpam-2044	180	8	c≥	c≥	PROPN
ejpam-2044	180	9	0	0	NUM
ejpam-2044	181	1	then	then	ADV
ejpam-2044	181	2	a	a	DET
ejpam-2044	181	3	>	>	X
ejpam-2044	181	4	0	0	NUM
ejpam-2044	181	5	,	,	PUNCT
ejpam-2044	181	6	and	and	CCONJ
ejpam-2044	181	7	since	since	SCONJ
ejpam-2044	181	8	c≥	c≥	PROPN
ejpam-2044	181	9	0	0	NUM
ejpam-2044	182	1	then	then	ADV
ejpam-2044	182	2	κ≥	κ≥	PROPN
ejpam-2044	182	3	1	1	PROPN
ejpam-2044	182	4	.	.	PUNCT
ejpam-2044	183	1	this	this	PRON
ejpam-2044	183	2	completes	complete	VERB
ejpam-2044	183	3	the	the	DET
ejpam-2044	183	4	proof	proof	NOUN
ejpam-2044	183	5	of	of	ADP
ejpam-2044	183	6	theorem	theorem	NOUN
ejpam-2044	183	7	2	2	NUM
ejpam-2044	183	8	.	.	NOUN
ejpam-2044	183	9	3	3	NUM
ejpam-2044	183	10	.	.	X
ejpam-2044	183	11	insurer	insurer	NOUN
ejpam-2044	183	12	equivalent	equivalent	ADJ
ejpam-2044	183	13	utility	utility	NOUN
ejpam-2044	183	14	premium	premium	NOUN
ejpam-2044	183	15	principle	principle	NOUN
ejpam-2044	183	16	conditions	condition	NOUN
ejpam-2044	183	17	under	under	ADP
ejpam-2044	183	18	which	which	PRON
ejpam-2044	183	19	scale	scale	NOUN
ejpam-2044	183	20	invariance	invariance	NOUN
ejpam-2044	183	21	property	property	NOUN
ejpam-2044	183	22	will	will	AUX
ejpam-2044	183	23	be	be	AUX
ejpam-2044	183	24	satisfied	satisfy	VERB
ejpam-2044	183	25	by	by	ADP
ejpam-2044	183	26	insurer	insurer	NOUN
ejpam-2044	183	27	equivalent	equivalent	ADJ
ejpam-2044	183	28	utility	utility	NOUN
ejpam-2044	183	29	premium	premium	NOUN
ejpam-2044	183	30	calculation	calculation	NOUN
ejpam-2044	183	31	principle	principle	NOUN
ejpam-2044	183	32	are	be	AUX
ejpam-2044	183	33	described	describe	VERB
ejpam-2044	183	34	by	by	ADP
ejpam-2044	183	35	the	the	DET
ejpam-2044	183	36	following	follow	VERB
ejpam-2044	183	37	theorem	theorem	PROPN
ejpam-2044	183	38	.	.	PUNCT
ejpam-2044	184	1	theorem	theorem	NOUN
ejpam-2044	184	2	3	3	NUM
ejpam-2044	184	3	.	.	PUNCT
ejpam-2044	184	4	insurer	insurer	NOUN
ejpam-2044	184	5	equivalent	equivalent	ADJ
ejpam-2044	184	6	utility	utility	NOUN
ejpam-2044	184	7	premium	premium	NOUN
ejpam-2044	184	8	calculation	calculation	NOUN
ejpam-2044	184	9	principle	principle	NOUN
ejpam-2044	184	10	possesses	possess	VERB
ejpam-2044	184	11	scale	scale	NOUN
ejpam-2044	184	12	invariance	invariance	NOUN
ejpam-2044	184	13	property	property	NOUN
ejpam-2044	185	1	if	if	SCONJ
ejpam-2044	185	2	and	and	CCONJ
ejpam-2044	185	3	only	only	ADV
ejpam-2044	185	4	if	if	SCONJ
ejpam-2044	185	5	u(x	u(x	NOUN
ejpam-2044	185	6	)	)	PUNCT
ejpam-2044	185	7	=	=	SYM
ejpam-2044	185	8	ax	ax	NOUN
ejpam-2044	185	9	+	+	CCONJ
ejpam-2044	185	10	b	b	NOUN
ejpam-2044	185	11	,	,	PUNCT
ejpam-2044	185	12	for	for	ADP
ejpam-2044	185	13	a	a	DET
ejpam-2044	185	14	>	>	X
ejpam-2044	185	15	0	0	NUM
ejpam-2044	185	16	,	,	PUNCT
ejpam-2044	185	17	i.e.	i.e.	X
ejpam-2044	185	18	,	,	PUNCT
ejpam-2044	185	19	only	only	ADV
ejpam-2044	185	20	in	in	ADP
ejpam-2044	185	21	the	the	DET
ejpam-2044	185	22	case	case	NOUN
ejpam-2044	185	23	when	when	SCONJ
ejpam-2044	185	24	it	it	PRON
ejpam-2044	185	25	coincides	coincide	VERB
ejpam-2044	185	26	with	with	ADP
ejpam-2044	185	27	net	net	ADJ
ejpam-2044	185	28	premium	premium	ADJ
ejpam-2044	185	29	principle	principle	NOUN
ejpam-2044	185	30	.	.	PUNCT
ejpam-2044	186	1	m.	m.	NOUN
ejpam-2044	186	2	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	186	3	,	,	PUNCT
ejpam-2044	186	4	v.	v.	ADP
ejpam-2044	186	5	drozdenko	drozdenko	PROPN
ejpam-2044	186	6	/	/	SYM
ejpam-2044	186	7	eur	eur	PROPN
ejpam-2044	186	8	.	.	PUNCT
ejpam-2044	187	1	j.	j.	PROPN
ejpam-2044	187	2	pure	pure	PROPN
ejpam-2044	187	3	appl	appl	PROPN
ejpam-2044	187	4	.	.	PROPN
ejpam-2044	187	5	math	math	PROPN
ejpam-2044	187	6	,	,	PUNCT
ejpam-2044	187	7	7	7	NUM
ejpam-2044	187	8	(	(	PUNCT
ejpam-2044	187	9	2014	2014	NUM
ejpam-2044	187	10	)	)	PUNCT
ejpam-2044	187	11	,	,	PUNCT
ejpam-2044	187	12	267	267	NUM
ejpam-2044	187	13	-	-	SYM
ejpam-2044	187	14	288	288	NUM
ejpam-2044	187	15	276	276	NUM
ejpam-2044	187	16	proof	proof	NOUN
ejpam-2044	187	17	.	.	PUNCT
ejpam-2044	188	1	we	we	PRON
ejpam-2044	188	2	start	start	VERB
ejpam-2044	188	3	from	from	ADP
ejpam-2044	188	4	the	the	DET
ejpam-2044	188	5	sufficiency	sufficiency	NOUN
ejpam-2044	188	6	.	.	PUNCT
ejpam-2044	189	1	in	in	ADP
ejpam-2044	189	2	the	the	DET
ejpam-2044	189	3	case	case	NOUN
ejpam-2044	189	4	of	of	ADP
ejpam-2044	189	5	u(x	u(x	NOUN
ejpam-2044	189	6	)	)	PUNCT
ejpam-2044	189	7	=	=	PUNCT
ejpam-2044	189	8	ax+	ax+	PROPN
ejpam-2044	189	9	b	b	X
ejpam-2044	189	10	,	,	PUNCT
ejpam-2044	189	11	for	for	ADP
ejpam-2044	189	12	a	a	DET
ejpam-2044	189	13	>	>	X
ejpam-2044	189	14	0	0	NUM
ejpam-2044	189	15	,	,	PUNCT
ejpam-2044	189	16	and	and	CCONJ
ejpam-2044	189	17	any	any	DET
ejpam-2044	189	18	initial	initial	ADJ
ejpam-2044	189	19	capital	capital	NOUN
ejpam-2044	189	20	w	w	PROPN
ejpam-2044	189	21	,	,	PUNCT
ejpam-2044	189	22	from	from	ADP
ejpam-2044	189	23	the	the	DET
ejpam-2044	189	24	equation	equation	NOUN
ejpam-2044	189	25	(	(	PUNCT
ejpam-2044	189	26	2	2	X
ejpam-2044	189	27	)	)	PUNCT
ejpam-2044	189	28	it	it	PRON
ejpam-2044	189	29	follows	follow	VERB
ejpam-2044	189	30	aw	aw	INTJ
ejpam-2044	190	1	+	+	CCONJ
ejpam-2044	190	2	b	b	X
ejpam-2044	190	3	=	=	X
ejpam-2044	191	1	e[aw	e[aw	NOUN
ejpam-2044	192	1	+	+	PUNCT
ejpam-2044	193	1	aπi.e.u.[x	aπi.e.u.[x	ADJ
ejpam-2044	193	2	]	]	PUNCT
ejpam-2044	193	3	−	−	NOUN
ejpam-2044	193	4	ax	ax	NOUN
ejpam-2044	193	5	+	+	CCONJ
ejpam-2044	193	6	b	b	X
ejpam-2044	193	7	]	]	X
ejpam-2044	193	8	=	=	PUNCT
ejpam-2044	194	1	aw	aw	INTJ
ejpam-2044	195	1	+	+	CCONJ
ejpam-2044	195	2	aπi.e.u.[x	aπi.e.u.[x	ADJ
ejpam-2044	195	3	]	]	PUNCT
ejpam-2044	195	4	−	−	X
ejpam-2044	196	1	ae[x	ae[x	PROPN
ejpam-2044	196	2	]	]	PUNCT
ejpam-2044	197	1	+	+	NUM
ejpam-2044	197	2	b	b	X
ejpam-2044	197	3	,	,	PUNCT
ejpam-2044	197	4	thus	thus	ADV
ejpam-2044	197	5	πi.e.u.[x	πi.e.u.[x	VERB
ejpam-2044	197	6	]	]	PUNCT
ejpam-2044	198	1	=	=	PUNCT
ejpam-2044	198	2	e[x	e[x	NOUN
ejpam-2044	198	3	]	]	X
ejpam-2044	198	4	=	=	PUNCT
ejpam-2044	198	5	πnet[x	πnet[x	X
ejpam-2044	198	6	]	]	X
ejpam-2044	198	7	.	.	PUNCT
ejpam-2044	199	1	from	from	ADP
ejpam-2044	199	2	the	the	DET
ejpam-2044	199	3	equation	equation	NOUN
ejpam-2044	199	4	(	(	PUNCT
ejpam-2044	199	5	2	2	NUM
ejpam-2044	199	6	)	)	PUNCT
ejpam-2044	199	7	,	,	PUNCT
ejpam-2044	199	8	for	for	ADP
ejpam-2044	199	9	any	any	DET
ejpam-2044	199	10	θ	θ	PROPN
ejpam-2044	199	11	>	>	X
ejpam-2044	199	12	0	0	NUM
ejpam-2044	199	13	,	,	PUNCT
ejpam-2044	199	14	any	any	DET
ejpam-2044	199	15	initial	initial	ADJ
ejpam-2044	199	16	capital	capital	NOUN
ejpam-2044	199	17	w	w	NOUN
ejpam-2044	199	18	,	,	PUNCT
ejpam-2044	199	19	and	and	CCONJ
ejpam-2044	199	20	the	the	DET
ejpam-2044	199	21	same	same	ADJ
ejpam-2044	199	22	utility	utility	NOUN
ejpam-2044	199	23	function	function	NOUN
ejpam-2044	199	24	,	,	PUNCT
ejpam-2044	199	25	it	it	PRON
ejpam-2044	199	26	follows	follow	VERB
ejpam-2044	199	27	aw	aw	INTJ
ejpam-2044	200	1	+	+	CCONJ
ejpam-2044	200	2	b	b	X
ejpam-2044	200	3	=	=	X
ejpam-2044	201	1	e[aw	e[aw	NOUN
ejpam-2044	202	1	+	+	PUNCT
ejpam-2044	202	2	aπi.e.u.[θx	aπi.e.u.[θx	NOUN
ejpam-2044	202	3	]	]	SYM
ejpam-2044	202	4	−	−	PROPN
ejpam-2044	202	5	aθx	aθx	ADP
ejpam-2044	202	6	+	+	X
ejpam-2044	202	7	b	b	NOUN
ejpam-2044	202	8	]	]	X
ejpam-2044	202	9	=	=	PUNCT
ejpam-2044	203	1	aw	aw	INTJ
ejpam-2044	204	1	+	+	CCONJ
ejpam-2044	204	2	aπi.e.u.[θx	aπi.e.u.[θx	NOUN
ejpam-2044	204	3	]	]	PUNCT
ejpam-2044	204	4	−	−	X
ejpam-2044	204	5	aθe[x	aθe[x	NOUN
ejpam-2044	204	6	]	]	X
ejpam-2044	205	1	+	+	CCONJ
ejpam-2044	205	2	b	b	X
ejpam-2044	205	3	,	,	PUNCT
ejpam-2044	205	4	hence	hence	ADV
ejpam-2044	205	5	πi.e.u.[θx	πi.e.u.[θx	VERB
ejpam-2044	205	6	]	]	PUNCT
ejpam-2044	205	7	=	=	PUNCT
ejpam-2044	205	8	θe[x	θe[x	NOUN
ejpam-2044	205	9	]	]	PUNCT
ejpam-2044	205	10	=	=	PUNCT
ejpam-2044	206	1	θπi.e.u.[x	θπi.e.u.[x	VERB
ejpam-2044	206	2	]	]	PUNCT
ejpam-2044	206	3	,	,	PUNCT
ejpam-2044	206	4	and	and	CCONJ
ejpam-2044	206	5	we	we	PRON
ejpam-2044	206	6	see	see	VERB
ejpam-2044	206	7	that	that	DET
ejpam-2044	206	8	scale	scale	NOUN
ejpam-2044	206	9	invariance	invariance	NOUN
ejpam-2044	206	10	property	property	NOUN
ejpam-2044	206	11	holds	hold	VERB
ejpam-2044	206	12	in	in	ADP
ejpam-2044	206	13	this	this	DET
ejpam-2044	206	14	particular	particular	ADJ
ejpam-2044	206	15	case	case	NOUN
ejpam-2044	206	16	.	.	PUNCT
ejpam-2044	207	1	the	the	DET
ejpam-2044	207	2	proof	proof	NOUN
ejpam-2044	207	3	of	of	ADP
ejpam-2044	207	4	sufficiency	sufficiency	NOUN
ejpam-2044	207	5	was	be	AUX
ejpam-2044	207	6	completed	complete	VERB
ejpam-2044	207	7	,	,	PUNCT
ejpam-2044	207	8	so	so	SCONJ
ejpam-2044	207	9	we	we	PRON
ejpam-2044	207	10	switch	switch	VERB
ejpam-2044	207	11	to	to	ADP
ejpam-2044	207	12	the	the	DET
ejpam-2044	207	13	necessity	necessity	NOUN
ejpam-2044	207	14	.	.	PUNCT
ejpam-2044	208	1	to	to	PART
ejpam-2044	208	2	show	show	VERB
ejpam-2044	208	3	that	that	SCONJ
ejpam-2044	208	4	insurer	insurer	NOUN
ejpam-2044	208	5	equivalent	equivalent	ADJ
ejpam-2044	208	6	utility	utility	NOUN
ejpam-2044	208	7	premium	premium	NOUN
ejpam-2044	208	8	calculation	calculation	NOUN
ejpam-2044	208	9	principle	principle	NOUN
ejpam-2044	208	10	with	with	ADP
ejpam-2044	208	11	non	non	ADJ
ejpam-2044	208	12	-	-	ADJ
ejpam-2044	208	13	linear	linear	ADJ
ejpam-2044	208	14	insurer	insurer	NOUN
ejpam-2044	208	15	’s	’s	PART
ejpam-2044	208	16	utility	utility	NOUN
ejpam-2044	208	17	function	function	NOUN
ejpam-2044	208	18	u(x	u(x	NOUN
ejpam-2044	208	19	)	)	PUNCT
ejpam-2044	208	20	will	will	AUX
ejpam-2044	208	21	not	not	PART
ejpam-2044	208	22	possess	possess	VERB
ejpam-2044	208	23	scale	scale	NOUN
ejpam-2044	208	24	invariance	invariance	NOUN
ejpam-2044	208	25	property	property	NOUN
ejpam-2044	208	26	,	,	PUNCT
ejpam-2044	208	27	we	we	PRON
ejpam-2044	208	28	will	will	AUX
ejpam-2044	208	29	choose	choose	VERB
ejpam-2044	208	30	a	a	DET
ejpam-2044	208	31	risk	risk	NOUN
ejpam-2044	208	32	x	x	PUNCT
ejpam-2044	208	33	which	which	PRON
ejpam-2044	208	34	takes	take	VERB
ejpam-2044	208	35	only	only	ADV
ejpam-2044	208	36	two	two	NUM
ejpam-2044	208	37	possible	possible	ADJ
ejpam-2044	208	38	values	value	NOUN
ejpam-2044	208	39	,	,	PUNCT
ejpam-2044	208	40	namely	namely	ADV
ejpam-2044	208	41	,	,	PUNCT
ejpam-2044	208	42	0	0	NUM
ejpam-2044	208	43	and	and	CCONJ
ejpam-2044	208	44	t	t	NOUN
ejpam-2044	208	45	with	with	ADP
ejpam-2044	208	46	probabilities	probability	NOUN
ejpam-2044	208	47	1	1	NUM
ejpam-2044	208	48	−	−	NOUN
ejpam-2044	208	49	p	p	NOUN
ejpam-2044	208	50	and	and	CCONJ
ejpam-2044	208	51	p	p	NOUN
ejpam-2044	208	52	respectively	respectively	ADV
ejpam-2044	208	53	.	.	PUNCT
ejpam-2044	209	1	the	the	DET
ejpam-2044	209	2	risk	risk	NOUN
ejpam-2044	209	3	x	x	X
ejpam-2044	209	4	can	can	AUX
ejpam-2044	209	5	in	in	ADP
ejpam-2044	209	6	this	this	DET
ejpam-2044	209	7	case	case	NOUN
ejpam-2044	209	8	be	be	AUX
ejpam-2044	209	9	considered	consider	VERB
ejpam-2044	209	10	as	as	ADP
ejpam-2044	209	11	a	a	DET
ejpam-2044	209	12	random	random	ADJ
ejpam-2044	209	13	function	function	NOUN
ejpam-2044	209	14	of	of	ADP
ejpam-2044	209	15	two	two	NUM
ejpam-2044	209	16	parameters	parameter	NOUN
ejpam-2044	209	17	,	,	PUNCT
ejpam-2044	209	18	namely	namely	ADV
ejpam-2044	209	19	p	p	NOUN
ejpam-2044	209	20	and	and	CCONJ
ejpam-2044	209	21	t	t	PROPN
ejpam-2044	209	22	,	,	PUNCT
ejpam-2044	209	23	and	and	CCONJ
ejpam-2044	209	24	,	,	PUNCT
ejpam-2044	209	25	therefore	therefore	ADV
ejpam-2044	209	26	,	,	PUNCT
ejpam-2044	209	27	within	within	ADP
ejpam-2044	209	28	the	the	DET
ejpam-2044	209	29	proof	proof	NOUN
ejpam-2044	209	30	of	of	ADP
ejpam-2044	209	31	theorem	theorem	NOUN
ejpam-2044	209	32	3	3	NUM
ejpam-2044	209	33	it	it	PRON
ejpam-2044	209	34	will	will	AUX
ejpam-2044	209	35	be	be	AUX
ejpam-2044	209	36	denoted	denote	VERB
ejpam-2044	209	37	by	by	ADP
ejpam-2044	209	38	x	x	PROPN
ejpam-2044	209	39	t	t	PROPN
ejpam-2044	209	40	p.	p.	NOUN
ejpam-2044	209	41	for	for	ADP
ejpam-2044	209	42	any	any	DET
ejpam-2044	209	43	insurer	insurer	NOUN
ejpam-2044	209	44	’s	’s	PART
ejpam-2044	209	45	initial	initial	ADJ
ejpam-2044	209	46	capital	capital	NOUN
ejpam-2044	209	47	w	w	PROPN
ejpam-2044	209	48	,	,	PUNCT
ejpam-2044	209	49	equivalent	equivalent	ADJ
ejpam-2044	209	50	utility	utility	NOUN
ejpam-2044	209	51	equation	equation	NOUN
ejpam-2044	209	52	(	(	PUNCT
ejpam-2044	209	53	2	2	NUM
ejpam-2044	209	54	)	)	PUNCT
ejpam-2044	209	55	for	for	ADP
ejpam-2044	209	56	the	the	DET
ejpam-2044	209	57	risk	risk	NOUN
ejpam-2044	209	58	x	x	X
ejpam-2044	209	59	t	t	NOUN
ejpam-2044	209	60	p	p	NOUN
ejpam-2044	209	61	will	will	AUX
ejpam-2044	209	62	take	take	VERB
ejpam-2044	209	63	the	the	DET
ejpam-2044	209	64	following	follow	VERB
ejpam-2044	209	65	form	form	NOUN
ejpam-2044	209	66	u(w	u(w	PROPN
ejpam-2044	209	67	)	)	PUNCT
ejpam-2044	210	1	=	=	SYM
ejpam-2044	211	1	u(w	u(w	PROPN
ejpam-2044	211	2	+	+	PROPN
ejpam-2044	211	3	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	211	4	t	t	PROPN
ejpam-2044	211	5	p]−	p]−	PROPN
ejpam-2044	211	6	t	t	PROPN
ejpam-2044	211	7	)	)	PUNCT
ejpam-2044	211	8	·	·	PUNCT
ejpam-2044	211	9	p+	p+	VERB
ejpam-2044	211	10	u(w	u(w	PROPN
ejpam-2044	211	11	+	+	PROPN
ejpam-2044	211	12	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	211	13	t	t	NOUN
ejpam-2044	211	14	p	p	X
ejpam-2044	211	15	]	]	X
ejpam-2044	211	16	)	)	PUNCT
ejpam-2044	211	17	·	·	PUNCT
ejpam-2044	212	1	(	(	PUNCT
ejpam-2044	212	2	1−	1−	NUM
ejpam-2044	212	3	p	p	NOUN
ejpam-2044	212	4	)	)	PUNCT
ejpam-2044	212	5	.	.	PUNCT
ejpam-2044	213	1	(	(	PUNCT
ejpam-2044	213	2	35	35	NUM
ejpam-2044	213	3	)	)	PUNCT
ejpam-2044	213	4	substituting	substitute	VERB
ejpam-2044	213	5	p	p	NOUN
ejpam-2044	213	6	=	=	NOUN
ejpam-2044	213	7	1	1	NUM
ejpam-2044	213	8	into	into	ADP
ejpam-2044	213	9	equation	equation	NOUN
ejpam-2044	213	10	(	(	PUNCT
ejpam-2044	213	11	35	35	NUM
ejpam-2044	213	12	)	)	PUNCT
ejpam-2044	213	13	,	,	PUNCT
ejpam-2044	213	14	we	we	PRON
ejpam-2044	213	15	get	get	VERB
ejpam-2044	213	16	u(w	u(w	PRON
ejpam-2044	213	17	)	)	PUNCT
ejpam-2044	214	1	=	=	VERB
ejpam-2044	214	2	u(w	u(w	PROPN
ejpam-2044	214	3	+	+	PROPN
ejpam-2044	214	4	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	214	5	t	t	PROPN
ejpam-2044	214	6	1]−	1]−	NUM
ejpam-2044	214	7	t	t	NOUN
ejpam-2044	214	8	)	)	PUNCT
ejpam-2044	214	9	·	·	PUNCT
ejpam-2044	215	1	1	1	X
ejpam-2044	215	2	+	+	CCONJ
ejpam-2044	215	3	u(w	u(w	PROPN
ejpam-2044	215	4	+	+	PROPN
ejpam-2044	215	5	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	215	6	t	t	NOUN
ejpam-2044	215	7	1	1	NUM
ejpam-2044	215	8	]	]	PUNCT
ejpam-2044	215	9	)	)	PUNCT
ejpam-2044	215	10	·	·	PUNCT
ejpam-2044	215	11	0	0	PUNCT
ejpam-2044	216	1	=	=	NOUN
ejpam-2044	216	2	u(w	u(w	PROPN
ejpam-2044	216	3	+	+	PROPN
ejpam-2044	216	4	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	216	5	t	t	PROPN
ejpam-2044	216	6	1]−	1]−	NUM
ejpam-2044	216	7	t	t	NOUN
ejpam-2044	216	8	)	)	PUNCT
ejpam-2044	216	9	.	.	PUNCT
ejpam-2044	217	1	(	(	PUNCT
ejpam-2044	217	2	36	36	NUM
ejpam-2044	217	3	)	)	PUNCT
ejpam-2044	217	4	since	since	SCONJ
ejpam-2044	217	5	u(x	u(x	NOUN
ejpam-2044	217	6	)	)	PUNCT
ejpam-2044	217	7	is	be	AUX
ejpam-2044	217	8	a	a	DET
ejpam-2044	217	9	strictly	strictly	ADV
ejpam-2044	217	10	increasing	increase	VERB
ejpam-2044	217	11	function	function	NOUN
ejpam-2044	217	12	,	,	PUNCT
ejpam-2044	217	13	then	then	ADV
ejpam-2044	217	14	identity	identity	NOUN
ejpam-2044	217	15	(	(	PUNCT
ejpam-2044	217	16	36	36	NUM
ejpam-2044	217	17	)	)	PUNCT
ejpam-2044	217	18	yields	yield	NOUN
ejpam-2044	217	19	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	217	20	t	t	PROPN
ejpam-2044	217	21	1	1	NUM
ejpam-2044	217	22	]	]	PUNCT
ejpam-2044	217	23	=	=	PUNCT
ejpam-2044	217	24	t.	t.	NOUN
ejpam-2044	217	25	(	(	PUNCT
ejpam-2044	217	26	37	37	NUM
ejpam-2044	217	27	)	)	PUNCT
ejpam-2044	217	28	taking	take	VERB
ejpam-2044	217	29	partial	partial	ADJ
ejpam-2044	217	30	derivative	derivative	NOUN
ejpam-2044	217	31	with	with	ADP
ejpam-2044	217	32	respect	respect	NOUN
ejpam-2044	217	33	to	to	ADP
ejpam-2044	217	34	p	p	NOUN
ejpam-2044	217	35	from	from	ADP
ejpam-2044	217	36	both	both	DET
ejpam-2044	217	37	sides	side	NOUN
ejpam-2044	217	38	of	of	ADP
ejpam-2044	217	39	the	the	DET
ejpam-2044	217	40	equation	equation	NOUN
ejpam-2044	217	41	(	(	PUNCT
ejpam-2044	217	42	35	35	NUM
ejpam-2044	217	43	)	)	PUNCT
ejpam-2044	217	44	,	,	PUNCT
ejpam-2044	217	45	obtain	obtain	VERB
ejpam-2044	217	46	0	0	NUM
ejpam-2044	218	1	=	=	NUM
ejpam-2044	218	2	u	u	NOUN
ejpam-2044	218	3	′(w	′(w	NOUN
ejpam-2044	218	4	+	+	NOUN
ejpam-2044	218	5	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	218	6	t	t	PROPN
ejpam-2044	218	7	p]−	p]−	PROPN
ejpam-2044	218	8	t	t	PROPN
ejpam-2044	218	9	)	)	PUNCT
ejpam-2044	218	10	·	·	PUNCT
ejpam-2044	218	11	∂	∂	NUM
ejpam-2044	219	1	∂	∂	NUM
ejpam-2044	219	2	p	p	NOUN
ejpam-2044	219	3	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	219	4	t	t	X
ejpam-2044	219	5	p	p	X
ejpam-2044	219	6	]	]	X
ejpam-2044	219	7	·	·	PUNCT
ejpam-2044	219	8	p+	p+	VERB
ejpam-2044	219	9	u(w	u(w	PROPN
ejpam-2044	219	10	+	+	PROPN
ejpam-2044	219	11	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	219	12	t	t	PROPN
ejpam-2044	219	13	p]−	p]−	PROPN
ejpam-2044	219	14	t	t	PROPN
ejpam-2044	219	15	)	)	PUNCT
ejpam-2044	220	1	+	+	PUNCT
ejpam-2044	220	2	u	u	NOUN
ejpam-2044	220	3	′(w	′(w	NOUN
ejpam-2044	220	4	+	+	PROPN
ejpam-2044	220	5	πi.e.u.[x	πi.e.u.[x	NOUN
ejpam-2044	220	6	t	t	NOUN
ejpam-2044	220	7	p	p	X
ejpam-2044	220	8	]	]	X
ejpam-2044	220	9	)	)	PUNCT
ejpam-2044	220	10	·	·	PUNCT
ejpam-2044	220	11	∂	∂	NUM
ejpam-2044	220	12	∂	∂	NUM
ejpam-2044	220	13	p	p	NOUN
ejpam-2044	220	14	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	220	15	t	t	X
ejpam-2044	220	16	p	p	X
ejpam-2044	220	17	]	]	X
ejpam-2044	220	18	·	·	PUNCT
ejpam-2044	220	19	(	(	PUNCT
ejpam-2044	220	20	1−	1−	NUM
ejpam-2044	220	21	p)−	p)−	PROPN
ejpam-2044	220	22	u(w	u(w	PROPN
ejpam-2044	220	23	+	+	PROPN
ejpam-2044	220	24	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	220	25	t	t	NOUN
ejpam-2044	220	26	p	p	X
ejpam-2044	220	27	]	]	X
ejpam-2044	220	28	)	)	PUNCT
ejpam-2044	220	29	.	.	PUNCT
ejpam-2044	221	1	(	(	PUNCT
ejpam-2044	221	2	38	38	NUM
ejpam-2044	221	3	)	)	PUNCT
ejpam-2044	221	4	substituting	substitute	VERB
ejpam-2044	221	5	p	p	NOUN
ejpam-2044	221	6	=	=	NOUN
ejpam-2044	221	7	1	1	NUM
ejpam-2044	221	8	into	into	ADP
ejpam-2044	221	9	the	the	DET
ejpam-2044	221	10	equation	equation	NOUN
ejpam-2044	221	11	(	(	PUNCT
ejpam-2044	221	12	38	38	NUM
ejpam-2044	221	13	)	)	PUNCT
ejpam-2044	221	14	,	,	PUNCT
ejpam-2044	221	15	and	and	CCONJ
ejpam-2044	221	16	using	use	VERB
ejpam-2044	221	17	identity	identity	NOUN
ejpam-2044	221	18	(	(	PUNCT
ejpam-2044	221	19	37	37	NUM
ejpam-2044	221	20	)	)	PUNCT
ejpam-2044	221	21	,	,	PUNCT
ejpam-2044	221	22	obtain	obtain	VERB
ejpam-2044	221	23	an	an	DET
ejpam-2044	221	24	equation	equation	NOUN
ejpam-2044	221	25	u	u	NOUN
ejpam-2044	221	26	′(w	′(w	NOUN
ejpam-2044	221	27	)	)	PUNCT
ejpam-2044	221	28	·	·	PUNCT
ejpam-2044	221	29	�	�	PROPN
ejpam-2044	221	30	∂	∂	NUM
ejpam-2044	221	31	∂	∂	NUM
ejpam-2044	221	32	p	p	NOUN
ejpam-2044	221	33	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	221	34	t	t	PROPN
ejpam-2044	221	35	p	p	X
ejpam-2044	221	36	]	]	X
ejpam-2044	221	37	�	�	PROPN
ejpam-2044	221	38	�	�	PROPN
ejpam-2044	221	39	�	�	PROPN
ejpam-2044	221	40	�	�	PROPN
ejpam-2044	221	41	p=1	p=1	PROPN
ejpam-2044	221	42	�	�	PROPN
ejpam-2044	221	43	=	=	PUNCT
ejpam-2044	221	44	u(w	u(w	PROPN
ejpam-2044	221	45	+	+	CCONJ
ejpam-2044	221	46	t)−	t)−	PROPN
ejpam-2044	221	47	u(w	u(w	PROPN
ejpam-2044	221	48	)	)	PUNCT
ejpam-2044	221	49	.	.	PUNCT
ejpam-2044	222	1	(	(	PUNCT
ejpam-2044	222	2	39	39	NUM
ejpam-2044	222	3	)	)	PUNCT
ejpam-2044	222	4	m.	m.	NOUN
ejpam-2044	222	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	222	6	,	,	PUNCT
ejpam-2044	222	7	v.	v.	ADP
ejpam-2044	222	8	drozdenko	drozdenko	PROPN
ejpam-2044	222	9	/	/	SYM
ejpam-2044	222	10	eur	eur	PROPN
ejpam-2044	222	11	.	.	PUNCT
ejpam-2044	223	1	j.	j.	PROPN
ejpam-2044	223	2	pure	pure	PROPN
ejpam-2044	223	3	appl	appl	PROPN
ejpam-2044	223	4	.	.	PROPN
ejpam-2044	223	5	math	math	PROPN
ejpam-2044	223	6	,	,	PUNCT
ejpam-2044	223	7	7	7	NUM
ejpam-2044	223	8	(	(	PUNCT
ejpam-2044	223	9	2014	2014	NUM
ejpam-2044	223	10	)	)	PUNCT
ejpam-2044	223	11	,	,	PUNCT
ejpam-2044	223	12	267	267	X
ejpam-2044	223	13	-	-	SYM
ejpam-2044	223	14	288	288	NUM
ejpam-2044	223	15	277	277	NUM
ejpam-2044	223	16	since	since	SCONJ
ejpam-2044	223	17	we	we	PRON
ejpam-2044	223	18	a	a	DET
ejpam-2044	223	19	searching	searching	NOUN
ejpam-2044	223	20	for	for	ADP
ejpam-2044	223	21	the	the	DET
ejpam-2044	223	22	conditions	condition	NOUN
ejpam-2044	223	23	when	when	SCONJ
ejpam-2044	223	24	the	the	DET
ejpam-2044	223	25	premium	premium	NOUN
ejpam-2044	223	26	calculation	calculation	NOUN
ejpam-2044	223	27	principle	principle	NOUN
ejpam-2044	223	28	will	will	AUX
ejpam-2044	223	29	be	be	AUX
ejpam-2044	223	30	scale	scale	NOUN
ejpam-2044	223	31	invariant	invariant	ADJ
ejpam-2044	223	32	,	,	PUNCT
ejpam-2044	223	33	then	then	ADV
ejpam-2044	223	34	for	for	ADP
ejpam-2044	223	35	any	any	DET
ejpam-2044	223	36	insurer	insurer	NOUN
ejpam-2044	223	37	’s	’s	PART
ejpam-2044	223	38	initial	initial	ADJ
ejpam-2044	223	39	capital	capital	NOUN
ejpam-2044	223	40	w	w	NOUN
ejpam-2044	223	41	,	,	PUNCT
ejpam-2044	223	42	and	and	CCONJ
ejpam-2044	223	43	any	any	DET
ejpam-2044	223	44	positive	positive	ADJ
ejpam-2044	223	45	constant	constant	ADJ
ejpam-2044	223	46	θ	θ	PROPN
ejpam-2044	223	47	,	,	PUNCT
ejpam-2044	223	48	insurer	insurer	NOUN
ejpam-2044	223	49	’s	’s	PART
ejpam-2044	223	50	equivalent	equivalent	ADJ
ejpam-2044	223	51	utility	utility	NOUN
ejpam-2044	223	52	equation	equation	NOUN
ejpam-2044	223	53	(	(	PUNCT
ejpam-2044	223	54	2	2	NUM
ejpam-2044	223	55	)	)	PUNCT
ejpam-2044	223	56	for	for	ADP
ejpam-2044	223	57	the	the	DET
ejpam-2044	223	58	risk	risk	NOUN
ejpam-2044	223	59	θx	θx	ADP
ejpam-2044	223	60	t	t	PROPN
ejpam-2044	223	61	p	p	NOUN
ejpam-2044	223	62	can	can	AUX
ejpam-2044	223	63	be	be	AUX
ejpam-2044	223	64	written	write	VERB
ejpam-2044	223	65	in	in	ADP
ejpam-2044	223	66	the	the	DET
ejpam-2044	223	67	following	following	ADJ
ejpam-2044	223	68	way	way	NOUN
ejpam-2044	223	69	u(w	u(w	PROPN
ejpam-2044	223	70	)	)	PUNCT
ejpam-2044	224	1	=	=	PUNCT
ejpam-2044	225	1	u(w	u(w	PROPN
ejpam-2044	225	2	+	+	PROPN
ejpam-2044	225	3	θπi.e.u.[x	θπi.e.u.[x	ADJ
ejpam-2044	225	4	t	t	PROPN
ejpam-2044	225	5	p]−θt	p]−θt	PROPN
ejpam-2044	225	6	)	)	PUNCT
ejpam-2044	225	7	·	·	PUNCT
ejpam-2044	225	8	p+	p+	VERB
ejpam-2044	225	9	u(w	u(w	PROPN
ejpam-2044	225	10	+	+	PROPN
ejpam-2044	225	11	θπi.e.u.[x	θπi.e.u.[x	ADJ
ejpam-2044	225	12	t	t	NOUN
ejpam-2044	225	13	p	p	X
ejpam-2044	225	14	]	]	X
ejpam-2044	225	15	)	)	PUNCT
ejpam-2044	225	16	·	·	PUNCT
ejpam-2044	226	1	(	(	PUNCT
ejpam-2044	226	2	1−	1−	NUM
ejpam-2044	226	3	p	p	NOUN
ejpam-2044	226	4	)	)	PUNCT
ejpam-2044	226	5	.	.	PUNCT
ejpam-2044	227	1	(	(	PUNCT
ejpam-2044	227	2	40	40	NUM
ejpam-2044	227	3	)	)	PUNCT
ejpam-2044	227	4	calculating	calculate	VERB
ejpam-2044	227	5	partial	partial	ADJ
ejpam-2044	227	6	derivatives	derivative	NOUN
ejpam-2044	227	7	with	with	ADP
ejpam-2044	227	8	respect	respect	NOUN
ejpam-2044	227	9	to	to	ADP
ejpam-2044	227	10	p	p	NOUN
ejpam-2044	227	11	from	from	ADP
ejpam-2044	227	12	both	both	DET
ejpam-2044	227	13	sides	side	NOUN
ejpam-2044	227	14	of	of	ADP
ejpam-2044	227	15	equation	equation	NOUN
ejpam-2044	227	16	(	(	PUNCT
ejpam-2044	227	17	40	40	NUM
ejpam-2044	227	18	)	)	PUNCT
ejpam-2044	227	19	,	,	PUNCT
ejpam-2044	227	20	obtain	obtain	VERB
ejpam-2044	227	21	0	0	NUM
ejpam-2044	227	22	=	=	NUM
ejpam-2044	227	23	u	u	NOUN
ejpam-2044	227	24	′(w	′(w	NOUN
ejpam-2044	227	25	+	+	ADJ
ejpam-2044	227	26	θπi.e.u.[x	θπi.e.u.[x	ADJ
ejpam-2044	227	27	t	t	PROPN
ejpam-2044	227	28	p]−θt	p]−θt	PROPN
ejpam-2044	227	29	)	)	PUNCT
ejpam-2044	227	30	·	·	PUNCT
ejpam-2044	227	31	θ	θ	X
ejpam-2044	227	32	·	·	PUNCT
ejpam-2044	227	33	∂	∂	NUM
ejpam-2044	227	34	∂	∂	NOUN
ejpam-2044	227	35	p	p	NOUN
ejpam-2044	227	36	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	227	37	t	t	X
ejpam-2044	227	38	p	p	X
ejpam-2044	227	39	]	]	X
ejpam-2044	227	40	·	·	PUNCT
ejpam-2044	227	41	p+	p+	VERB
ejpam-2044	227	42	u(w	u(w	PROPN
ejpam-2044	227	43	+	+	PROPN
ejpam-2044	227	44	θπi.e.u.[x	θπi.e.u.[x	ADJ
ejpam-2044	227	45	t	t	PROPN
ejpam-2044	227	46	p]−θt	p]−θt	PROPN
ejpam-2044	227	47	)	)	PUNCT
ejpam-2044	228	1	+	+	PUNCT
ejpam-2044	228	2	u	u	PRON
ejpam-2044	228	3	′(w	′(w	NOUN
ejpam-2044	228	4	+	+	ADJ
ejpam-2044	228	5	θπi.e.u.[x	θπi.e.u.[x	ADJ
ejpam-2044	228	6	t	t	NOUN
ejpam-2044	228	7	p	p	X
ejpam-2044	228	8	]	]	X
ejpam-2044	228	9	)	)	PUNCT
ejpam-2044	228	10	·	·	PUNCT
ejpam-2044	228	11	θ	θ	X
ejpam-2044	228	12	·	·	PUNCT
ejpam-2044	228	13	∂	∂	NUM
ejpam-2044	228	14	∂	∂	NOUN
ejpam-2044	228	15	p	p	NOUN
ejpam-2044	228	16	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	229	1	t	t	X
ejpam-2044	229	2	p	p	X
ejpam-2044	229	3	]	]	X
ejpam-2044	229	4	·	·	PUNCT
ejpam-2044	229	5	(	(	PUNCT
ejpam-2044	229	6	1−	1−	NUM
ejpam-2044	229	7	p)−	p)−	NOUN
ejpam-2044	229	8	u(w	u(w	PROPN
ejpam-2044	230	1	+	+	PROPN
ejpam-2044	230	2	θπi.e.u.[x	θπi.e.u.[x	ADJ
ejpam-2044	230	3	t	t	NOUN
ejpam-2044	230	4	p	p	X
ejpam-2044	230	5	]	]	X
ejpam-2044	230	6	)	)	PUNCT
ejpam-2044	230	7	.	.	PUNCT
ejpam-2044	231	1	(	(	PUNCT
ejpam-2044	231	2	41	41	NUM
ejpam-2044	231	3	)	)	PUNCT
ejpam-2044	231	4	substituting	substitute	VERB
ejpam-2044	231	5	p	p	NOUN
ejpam-2044	231	6	=	=	NOUN
ejpam-2044	231	7	1	1	NUM
ejpam-2044	231	8	into	into	ADP
ejpam-2044	231	9	the	the	DET
ejpam-2044	231	10	equation	equation	NOUN
ejpam-2044	231	11	(	(	PUNCT
ejpam-2044	231	12	41	41	NUM
ejpam-2044	231	13	)	)	PUNCT
ejpam-2044	231	14	,	,	PUNCT
ejpam-2044	231	15	and	and	CCONJ
ejpam-2044	231	16	using	use	VERB
ejpam-2044	231	17	identity	identity	NOUN
ejpam-2044	231	18	(	(	PUNCT
ejpam-2044	231	19	37	37	NUM
ejpam-2044	231	20	)	)	PUNCT
ejpam-2044	231	21	,	,	PUNCT
ejpam-2044	231	22	we	we	PRON
ejpam-2044	231	23	get	get	VERB
ejpam-2044	231	24	an	an	DET
ejpam-2044	231	25	equation	equation	NOUN
ejpam-2044	231	26	u	u	NOUN
ejpam-2044	231	27	′(w	′(w	NOUN
ejpam-2044	231	28	)	)	PUNCT
ejpam-2044	231	29	·	·	PUNCT
ejpam-2044	231	30	θ	θ	X
ejpam-2044	231	31	·	·	PUNCT
ejpam-2044	231	32	�	�	PROPN
ejpam-2044	231	33	∂	∂	NUM
ejpam-2044	231	34	∂	∂	NUM
ejpam-2044	232	1	p	p	NOUN
ejpam-2044	232	2	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	232	3	t	t	PROPN
ejpam-2044	232	4	p	p	X
ejpam-2044	232	5	]	]	X
ejpam-2044	232	6	�	�	PROPN
ejpam-2044	232	7	�	�	PROPN
ejpam-2044	232	8	�	�	PROPN
ejpam-2044	232	9	�	�	PROPN
ejpam-2044	232	10	p=1	p=1	PROPN
ejpam-2044	232	11	�	�	PROPN
ejpam-2044	232	12	=	=	PUNCT
ejpam-2044	232	13	u(w	u(w	PROPN
ejpam-2044	232	14	+	+	PROPN
ejpam-2044	232	15	θt)−	θt)−	PROPN
ejpam-2044	232	16	u(w	u(w	PROPN
ejpam-2044	232	17	)	)	PUNCT
ejpam-2044	232	18	.	.	PUNCT
ejpam-2044	233	1	(	(	PUNCT
ejpam-2044	233	2	42	42	NUM
ejpam-2044	233	3	)	)	PUNCT
ejpam-2044	233	4	since	since	SCONJ
ejpam-2044	233	5	θ	θ	PROPN
ejpam-2044	233	6	>	>	X
ejpam-2044	233	7	0	0	NUM
ejpam-2044	233	8	,	,	PUNCT
ejpam-2044	233	9	then	then	ADV
ejpam-2044	233	10	equation	equation	NOUN
ejpam-2044	233	11	(	(	PUNCT
ejpam-2044	233	12	42	42	NUM
ejpam-2044	233	13	)	)	PUNCT
ejpam-2044	233	14	can	can	AUX
ejpam-2044	233	15	be	be	AUX
ejpam-2044	233	16	rewritten	rewrite	VERB
ejpam-2044	233	17	as	as	ADP
ejpam-2044	233	18	u	u	PROPN
ejpam-2044	233	19	′(w	′(w	NOUN
ejpam-2044	233	20	)	)	PUNCT
ejpam-2044	233	21	·	·	PUNCT
ejpam-2044	233	22	�	�	PROPN
ejpam-2044	233	23	∂	∂	NUM
ejpam-2044	233	24	∂	∂	NUM
ejpam-2044	234	1	p	p	NOUN
ejpam-2044	234	2	πi.e.u.[x	πi.e.u.[x	PROPN
ejpam-2044	234	3	t	t	PROPN
ejpam-2044	234	4	p	p	X
ejpam-2044	234	5	]	]	X
ejpam-2044	234	6	�	�	PROPN
ejpam-2044	234	7	�	�	PROPN
ejpam-2044	234	8	�	�	PROPN
ejpam-2044	234	9	�	�	PROPN
ejpam-2044	234	10	p=1	p=1	PROPN
ejpam-2044	234	11	�	�	PROPN
ejpam-2044	234	12	=	=	PUNCT
ejpam-2044	234	13	u(w	u(w	PROPN
ejpam-2044	234	14	+	+	PROPN
ejpam-2044	234	15	θt)−	θt)−	PROPN
ejpam-2044	234	16	u(w	u(w	PROPN
ejpam-2044	234	17	)	)	PUNCT
ejpam-2044	234	18	θ	θ	PROPN
ejpam-2044	234	19	.	.	PUNCT
ejpam-2044	235	1	(	(	PUNCT
ejpam-2044	235	2	43	43	X
ejpam-2044	235	3	)	)	PUNCT
ejpam-2044	235	4	observe	observe	VERB
ejpam-2044	235	5	that	that	SCONJ
ejpam-2044	235	6	equations	equation	NOUN
ejpam-2044	235	7	(	(	PUNCT
ejpam-2044	235	8	39	39	NUM
ejpam-2044	235	9	)	)	PUNCT
ejpam-2044	235	10	and	and	CCONJ
ejpam-2044	235	11	(	(	PUNCT
ejpam-2044	235	12	43	43	NUM
ejpam-2044	235	13	)	)	PUNCT
ejpam-2044	235	14	have	have	VERB
ejpam-2044	235	15	equal	equal	ADJ
ejpam-2044	235	16	left	leave	VERB
ejpam-2044	235	17	-	-	PUNCT
ejpam-2044	235	18	hand	hand	NOUN
ejpam-2044	235	19	sides	side	NOUN
ejpam-2044	235	20	,	,	PUNCT
ejpam-2044	235	21	hence	hence	ADV
ejpam-2044	235	22	their	their	PRON
ejpam-2044	235	23	right	right	ADJ
ejpam-2044	235	24	-	-	PUNCT
ejpam-2044	235	25	hand	hand	NOUN
ejpam-2044	235	26	sides	side	NOUN
ejpam-2044	235	27	also	also	ADV
ejpam-2044	235	28	have	have	VERB
ejpam-2044	235	29	to	to	PART
ejpam-2044	235	30	be	be	AUX
ejpam-2044	235	31	equal	equal	ADJ
ejpam-2044	235	32	;	;	PUNCT
ejpam-2044	235	33	this	this	PRON
ejpam-2044	235	34	finally	finally	ADV
ejpam-2044	235	35	gives	give	VERB
ejpam-2044	235	36	us	we	PRON
ejpam-2044	235	37	an	an	DET
ejpam-2044	235	38	equation	equation	NOUN
ejpam-2044	235	39	which	which	DET
ejpam-2044	235	40	insurer	insurer	NOUN
ejpam-2044	235	41	’s	’s	PART
ejpam-2044	235	42	utility	utility	NOUN
ejpam-2044	235	43	function	function	NOUN
ejpam-2044	235	44	has	have	VERB
ejpam-2044	235	45	to	to	PART
ejpam-2044	235	46	satisfy	satisfy	VERB
ejpam-2044	235	47	for	for	SCONJ
ejpam-2044	235	48	the	the	DET
ejpam-2044	235	49	premium	premium	ADJ
ejpam-2044	235	50	calculation	calculation	NOUN
ejpam-2044	235	51	principle	principle	NOUN
ejpam-2044	235	52	to	to	PART
ejpam-2044	235	53	be	be	AUX
ejpam-2044	235	54	scale	scale	NOUN
ejpam-2044	235	55	invariant	invariant	ADJ
ejpam-2044	235	56	,	,	PUNCT
ejpam-2044	235	57	namely	namely	ADV
ejpam-2044	235	58	u(w	u(w	PROPN
ejpam-2044	235	59	+	+	CCONJ
ejpam-2044	236	1	t)−	t)−	PROPN
ejpam-2044	236	2	u(w	u(w	PROPN
ejpam-2044	236	3	)	)	PUNCT
ejpam-2044	237	1	=	=	PUNCT
ejpam-2044	238	1	u(w	u(w	PROPN
ejpam-2044	238	2	+	+	PROPN
ejpam-2044	238	3	θt)−	θt)−	PROPN
ejpam-2044	238	4	u(w	u(w	PROPN
ejpam-2044	238	5	)	)	PUNCT
ejpam-2044	238	6	θ	θ	PROPN
ejpam-2044	238	7	.	.	PUNCT
ejpam-2044	239	1	(	(	PUNCT
ejpam-2044	239	2	44	44	X
ejpam-2044	239	3	)	)	PUNCT
ejpam-2044	239	4	taking	take	VERB
ejpam-2044	239	5	partial	partial	ADJ
ejpam-2044	239	6	derivatives	derivative	NOUN
ejpam-2044	239	7	with	with	ADP
ejpam-2044	239	8	respect	respect	NOUN
ejpam-2044	239	9	to	to	ADP
ejpam-2044	239	10	parameter	parameter	PROPN
ejpam-2044	239	11	t	t	PROPN
ejpam-2044	239	12	from	from	ADP
ejpam-2044	239	13	both	both	DET
ejpam-2044	239	14	sides	side	NOUN
ejpam-2044	239	15	of	of	ADP
ejpam-2044	239	16	(	(	PUNCT
ejpam-2044	239	17	44	44	NUM
ejpam-2044	239	18	)	)	PUNCT
ejpam-2044	239	19	yields	yield	VERB
ejpam-2044	239	20	u	u	NOUN
ejpam-2044	239	21	′(w	′(w	NOUN
ejpam-2044	239	22	+	+	X
ejpam-2044	239	23	t	t	NOUN
ejpam-2044	239	24	)	)	PUNCT
ejpam-2044	239	25	=	=	SYM
ejpam-2044	239	26	u	u	NOUN
ejpam-2044	239	27	′(w	′(w	NOUN
ejpam-2044	239	28	+	+	NOUN
ejpam-2044	239	29	θt	θt	ADJ
ejpam-2044	239	30	)	)	PUNCT
ejpam-2044	239	31	.	.	PUNCT
ejpam-2044	240	1	(	(	PUNCT
ejpam-2044	240	2	45	45	NUM
ejpam-2044	240	3	)	)	PUNCT
ejpam-2044	240	4	by	by	ADP
ejpam-2044	240	5	fixing	fix	VERB
ejpam-2044	240	6	values	value	NOUN
ejpam-2044	240	7	of	of	ADP
ejpam-2044	240	8	the	the	DET
ejpam-2044	240	9	parameters	parameter	NOUN
ejpam-2044	240	10	w	w	PROPN
ejpam-2044	240	11	and	and	CCONJ
ejpam-2044	240	12	t	t	PROPN
ejpam-2044	240	13	,	,	PUNCT
ejpam-2044	240	14	and	and	CCONJ
ejpam-2044	240	15	changing	change	VERB
ejpam-2044	240	16	values	value	NOUN
ejpam-2044	240	17	of	of	ADP
ejpam-2044	240	18	the	the	DET
ejpam-2044	240	19	parameter	parameter	NOUN
ejpam-2044	240	20	θ	θ	PROPN
ejpam-2044	240	21	,	,	PUNCT
ejpam-2044	240	22	we	we	PRON
ejpam-2044	240	23	will	will	AUX
ejpam-2044	240	24	make	make	VERB
ejpam-2044	240	25	u	u	PRON
ejpam-2044	240	26	′(w	′(w	VERB
ejpam-2044	240	27	+	+	NOUN
ejpam-2044	240	28	θt	θt	ADJ
ejpam-2044	240	29	)	)	PUNCT
ejpam-2044	240	30	a	a	DET
ejpam-2044	240	31	function	function	NOUN
ejpam-2044	240	32	of	of	ADP
ejpam-2044	240	33	changing	change	VERB
ejpam-2044	240	34	variable	variable	NOUN
ejpam-2044	240	35	while	while	SCONJ
ejpam-2044	240	36	the	the	DET
ejpam-2044	240	37	value	value	NOUN
ejpam-2044	240	38	u	u	NOUN
ejpam-2044	240	39	′(w	′(w	NOUN
ejpam-2044	240	40	+	+	CCONJ
ejpam-2044	240	41	t	t	NOUN
ejpam-2044	240	42	)	)	PUNCT
ejpam-2044	240	43	will	will	AUX
ejpam-2044	240	44	be	be	AUX
ejpam-2044	240	45	a	a	DET
ejpam-2044	240	46	fixed	fix	VERB
ejpam-2044	240	47	constant	constant	ADJ
ejpam-2044	240	48	.	.	PUNCT
ejpam-2044	241	1	using	use	VERB
ejpam-2044	241	2	this	this	DET
ejpam-2044	241	3	technique	technique	NOUN
ejpam-2044	241	4	and	and	CCONJ
ejpam-2044	241	5	taking	take	VERB
ejpam-2044	241	6	into	into	ADP
ejpam-2044	241	7	account	account	NOUN
ejpam-2044	241	8	monotonicity	monotonicity	NOUN
ejpam-2044	241	9	of	of	ADP
ejpam-2044	241	10	function	function	NOUN
ejpam-2044	241	11	u	u	PROPN
ejpam-2044	241	12	(	(	PUNCT
ejpam-2044	241	13	·	·	PUNCT
ejpam-2044	241	14	)	)	PUNCT
ejpam-2044	241	15	and	and	CCONJ
ejpam-2044	241	16	continuity	continuity	NOUN
ejpam-2044	241	17	of	of	ADP
ejpam-2044	241	18	function	function	NOUN
ejpam-2044	241	19	u	u	PROPN
ejpam-2044	241	20	′	′	PROPN
ejpam-2044	241	21	(	(	PUNCT
ejpam-2044	241	22	·	·	PUNCT
ejpam-2044	241	23	)	)	PUNCT
ejpam-2044	241	24	,	,	PUNCT
ejpam-2044	241	25	since	since	SCONJ
ejpam-2044	241	26	u	u	NOUN
ejpam-2044	241	27	(	(	PUNCT
ejpam-2044	241	28	·	·	PUNCT
ejpam-2044	241	29	)	)	PUNCT
ejpam-2044	241	30	∈	∈	PROPN
ejpam-2044	241	31	c2(r	c2(r	PROPN
ejpam-2044	241	32	)	)	PUNCT
ejpam-2044	241	33	,	,	PUNCT
ejpam-2044	241	34	using	use	VERB
ejpam-2044	241	35	equation	equation	NOUN
ejpam-2044	241	36	(	(	PUNCT
ejpam-2044	241	37	45	45	NUM
ejpam-2044	241	38	)	)	PUNCT
ejpam-2044	241	39	we	we	PRON
ejpam-2044	241	40	conclude	conclude	VERB
ejpam-2044	241	41	that	that	SCONJ
ejpam-2044	241	42	u	u	PROPN
ejpam-2044	241	43	′(x	′(x	NOUN
ejpam-2044	241	44	)	)	PUNCT
ejpam-2044	241	45	=	=	SYM
ejpam-2044	241	46	a	a	DET
ejpam-2044	241	47	>	>	X
ejpam-2044	241	48	0	0	NUM
ejpam-2044	241	49	,	,	PUNCT
ejpam-2044	241	50	for	for	SCONJ
ejpam-2044	241	51	x	x	PROPN
ejpam-2044	241	52	∈	∈	PROPN
ejpam-2044	241	53	r.	r.	NOUN
ejpam-2044	241	54	integration	integration	NOUN
ejpam-2044	241	55	yields	yield	VERB
ejpam-2044	241	56	u(x	u(x	NOUN
ejpam-2044	241	57	)	)	PUNCT
ejpam-2044	242	1	=	=	SYM
ejpam-2044	242	2	ax	ax	NOUN
ejpam-2044	242	3	+	+	CCONJ
ejpam-2044	242	4	b	b	NOUN
ejpam-2044	242	5	,	,	PUNCT
ejpam-2044	242	6	for	for	ADP
ejpam-2044	242	7	x	x	PROPN
ejpam-2044	242	8	∈	∈	PROPN
ejpam-2044	242	9	r	r	NOUN
ejpam-2044	242	10	,	,	PUNCT
ejpam-2044	242	11	and	and	CCONJ
ejpam-2044	242	12	constant	constant	ADJ
ejpam-2044	242	13	a	a	DET
ejpam-2044	242	14	>	>	X
ejpam-2044	242	15	0	0	X
ejpam-2044	242	16	.	.	PUNCT
ejpam-2044	243	1	let	let	VERB
ejpam-2044	243	2	us	we	PRON
ejpam-2044	243	3	give	give	VERB
ejpam-2044	243	4	also	also	ADV
ejpam-2044	243	5	a	a	DET
ejpam-2044	243	6	geometrical	geometrical	ADJ
ejpam-2044	243	7	interpretation	interpretation	NOUN
ejpam-2044	243	8	showing	show	VERB
ejpam-2044	243	9	that	that	SCONJ
ejpam-2044	243	10	non	non	ADJ
ejpam-2044	243	11	-	-	ADJ
ejpam-2044	243	12	linear	linear	ADJ
ejpam-2044	243	13	insurer	insurer	NOUN
ejpam-2044	243	14	’s	’s	PART
ejpam-2044	243	15	utility	utility	NOUN
ejpam-2044	243	16	functions	function	NOUN
ejpam-2044	243	17	will	will	AUX
ejpam-2044	243	18	not	not	PART
ejpam-2044	243	19	satisfy	satisfy	VERB
ejpam-2044	243	20	equation	equation	NOUN
ejpam-2044	243	21	(	(	PUNCT
ejpam-2044	243	22	44	44	NUM
ejpam-2044	243	23	)	)	PUNCT
ejpam-2044	243	24	.	.	PUNCT
ejpam-2044	244	1	let	let	VERB
ejpam-2044	244	2	us	we	PRON
ejpam-2044	244	3	consider	consider	VERB
ejpam-2044	244	4	two	two	NUM
ejpam-2044	244	5	triangles	triangle	NOUN
ejpam-2044	244	6	:	:	PUNCT
ejpam-2044	244	7	the	the	DET
ejpam-2044	244	8	first	first	ADJ
ejpam-2044	244	9	one	one	NOUN
ejpam-2044	244	10	will	will	AUX
ejpam-2044	244	11	be	be	AUX
ejpam-2044	244	12	formed	form	VERB
ejpam-2044	244	13	by	by	ADP
ejpam-2044	244	14	the	the	DET
ejpam-2044	244	15	points	point	NOUN
ejpam-2044	244	16	(	(	PUNCT
ejpam-2044	244	17	w	w	NOUN
ejpam-2044	244	18	,	,	PUNCT
ejpam-2044	244	19	u(w	u(w	PROPN
ejpam-2044	244	20	)	)	PUNCT
ejpam-2044	244	21	)	)	PUNCT
ejpam-2044	244	22	,	,	PUNCT
ejpam-2044	244	23	(	(	PUNCT
ejpam-2044	244	24	w	w	PROPN
ejpam-2044	244	25	+	+	PROPN
ejpam-2044	244	26	t	t	PROPN
ejpam-2044	244	27	,	,	PUNCT
ejpam-2044	244	28	u(w	u(w	PROPN
ejpam-2044	244	29	)	)	PUNCT
ejpam-2044	244	30	)	)	PUNCT
ejpam-2044	244	31	,	,	PUNCT
ejpam-2044	244	32	(	(	PUNCT
ejpam-2044	244	33	w	w	PROPN
ejpam-2044	244	34	+	+	PROPN
ejpam-2044	244	35	t	t	PROPN
ejpam-2044	244	36	,	,	PUNCT
ejpam-2044	244	37	u(w	u(w	PROPN
ejpam-2044	244	38	+	+	NUM
ejpam-2044	244	39	t	t	PROPN
ejpam-2044	244	40	)	)	PUNCT
ejpam-2044	244	41	)	)	PUNCT
ejpam-2044	244	42	and	and	CCONJ
ejpam-2044	244	43	the	the	DET
ejpam-2044	244	44	second	second	ADJ
ejpam-2044	244	45	one	one	NOUN
ejpam-2044	244	46	will	will	AUX
ejpam-2044	244	47	be	be	AUX
ejpam-2044	244	48	formed	form	VERB
ejpam-2044	244	49	m.	m.	NOUN
ejpam-2044	244	50	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	244	51	,	,	PUNCT
ejpam-2044	244	52	v.	v.	ADP
ejpam-2044	244	53	drozdenko	drozdenko	PROPN
ejpam-2044	244	54	/	/	SYM
ejpam-2044	244	55	eur	eur	PROPN
ejpam-2044	244	56	.	.	PUNCT
ejpam-2044	245	1	j.	j.	PROPN
ejpam-2044	245	2	pure	pure	PROPN
ejpam-2044	245	3	appl	appl	PROPN
ejpam-2044	245	4	.	.	PROPN
ejpam-2044	245	5	math	math	PROPN
ejpam-2044	245	6	,	,	PUNCT
ejpam-2044	245	7	7	7	NUM
ejpam-2044	245	8	(	(	PUNCT
ejpam-2044	245	9	2014	2014	NUM
ejpam-2044	245	10	)	)	PUNCT
ejpam-2044	245	11	,	,	PUNCT
ejpam-2044	245	12	267	267	NUM
ejpam-2044	245	13	-	-	SYM
ejpam-2044	245	14	288	288	NUM
ejpam-2044	245	15	278	278	NUM
ejpam-2044	245	16	by	by	ADP
ejpam-2044	245	17	the	the	DET
ejpam-2044	245	18	points	point	NOUN
ejpam-2044	245	19	(	(	PUNCT
ejpam-2044	245	20	w	w	NOUN
ejpam-2044	245	21	,	,	PUNCT
ejpam-2044	245	22	u(w	u(w	PROPN
ejpam-2044	245	23	)	)	PUNCT
ejpam-2044	245	24	)	)	PUNCT
ejpam-2044	245	25	,	,	PUNCT
ejpam-2044	245	26	(	(	PUNCT
ejpam-2044	245	27	w	w	ADP
ejpam-2044	245	28	+	+	NOUN
ejpam-2044	245	29	θt	θt	ADJ
ejpam-2044	245	30	,	,	PUNCT
ejpam-2044	245	31	u(w	u(w	PROPN
ejpam-2044	245	32	)	)	PUNCT
ejpam-2044	245	33	)	)	PUNCT
ejpam-2044	245	34	,	,	PUNCT
ejpam-2044	245	35	(	(	PUNCT
ejpam-2044	245	36	w	w	ADP
ejpam-2044	245	37	+	+	NOUN
ejpam-2044	245	38	θt	θt	ADJ
ejpam-2044	245	39	,	,	PUNCT
ejpam-2044	245	40	u(w	u(w	PROPN
ejpam-2044	245	41	+	+	PROPN
ejpam-2044	245	42	θt	θt	NOUN
ejpam-2044	245	43	)	)	PUNCT
ejpam-2044	245	44	)	)	PUNCT
ejpam-2044	245	45	.	.	PUNCT
ejpam-2044	246	1	observe	observe	VERB
ejpam-2044	246	2	that	that	SCONJ
ejpam-2044	246	3	both	both	DET
ejpam-2044	246	4	triangles	triangle	NOUN
ejpam-2044	246	5	are	be	AUX
ejpam-2044	246	6	right	right	ADJ
ejpam-2044	246	7	-	-	PUNCT
ejpam-2044	246	8	angled	angle	VERB
ejpam-2044	246	9	triangles	triangle	NOUN
ejpam-2044	246	10	,	,	PUNCT
ejpam-2044	246	11	they	they	PRON
ejpam-2044	246	12	have	have	VERB
ejpam-2044	246	13	a	a	DET
ejpam-2044	246	14	common	common	ADJ
ejpam-2044	246	15	vertex	vertex	NOUN
ejpam-2044	246	16	at	at	ADP
ejpam-2044	246	17	the	the	DET
ejpam-2044	246	18	point	point	NOUN
ejpam-2044	246	19	(	(	PUNCT
ejpam-2044	246	20	w	w	PROPN
ejpam-2044	246	21	,	,	PUNCT
ejpam-2044	246	22	u(w	u(w	PROPN
ejpam-2044	246	23	)	)	PUNCT
ejpam-2044	246	24	)	)	PUNCT
ejpam-2044	246	25	,	,	PUNCT
ejpam-2044	246	26	and	and	CCONJ
ejpam-2044	246	27	,	,	PUNCT
ejpam-2044	246	28	moreover	moreover	ADV
ejpam-2044	246	29	,	,	PUNCT
ejpam-2044	246	30	the	the	DET
ejpam-2044	246	31	points	point	NOUN
ejpam-2044	246	32	(	(	PUNCT
ejpam-2044	246	33	w	w	NOUN
ejpam-2044	246	34	,	,	PUNCT
ejpam-2044	246	35	u(w	u(w	PROPN
ejpam-2044	246	36	)	)	PUNCT
ejpam-2044	246	37	)	)	PUNCT
ejpam-2044	246	38	,	,	PUNCT
ejpam-2044	246	39	(	(	PUNCT
ejpam-2044	246	40	w	w	PROPN
ejpam-2044	246	41	+	+	PROPN
ejpam-2044	246	42	t	t	PROPN
ejpam-2044	246	43	,	,	PUNCT
ejpam-2044	246	44	u(w	u(w	PROPN
ejpam-2044	246	45	)	)	PUNCT
ejpam-2044	246	46	)	)	PUNCT
ejpam-2044	246	47	,	,	PUNCT
ejpam-2044	246	48	and	and	CCONJ
ejpam-2044	246	49	(	(	PUNCT
ejpam-2044	246	50	w	w	PROPN
ejpam-2044	246	51	+	+	NOUN
ejpam-2044	246	52	θt	θt	ADJ
ejpam-2044	246	53	,	,	PUNCT
ejpam-2044	246	54	u(w	u(w	PROPN
ejpam-2044	246	55	)	)	PUNCT
ejpam-2044	246	56	)	)	PUNCT
ejpam-2044	246	57	lie	lie	VERB
ejpam-2044	246	58	on	on	ADP
ejpam-2044	246	59	the	the	DET
ejpam-2044	246	60	same	same	ADJ
ejpam-2044	246	61	straight	straight	ADJ
ejpam-2044	246	62	line	line	NOUN
ejpam-2044	246	63	.	.	PUNCT
ejpam-2044	247	1	with	with	ADP
ejpam-2044	247	2	out	out	ADP
ejpam-2044	247	3	of	of	ADP
ejpam-2044	247	4	loss	loss	NOUN
ejpam-2044	247	5	of	of	ADP
ejpam-2044	247	6	generality	generality	NOUN
ejpam-2044	247	7	equation	equation	NOUN
ejpam-2044	247	8	(	(	PUNCT
ejpam-2044	247	9	44	44	NUM
ejpam-2044	247	10	)	)	PUNCT
ejpam-2044	247	11	can	can	AUX
ejpam-2044	247	12	be	be	AUX
ejpam-2044	247	13	rewritten	rewrite	VERB
ejpam-2044	247	14	in	in	ADP
ejpam-2044	247	15	the	the	DET
ejpam-2044	247	16	following	following	ADJ
ejpam-2044	247	17	way	way	NOUN
ejpam-2044	247	18	u(w	u(w	PROPN
ejpam-2044	247	19	+	+	CCONJ
ejpam-2044	247	20	t)−	t)−	PROPN
ejpam-2044	247	21	u(w	u(w	PROPN
ejpam-2044	247	22	)	)	PUNCT
ejpam-2044	247	23	(	(	PUNCT
ejpam-2044	248	1	w	w	PROPN
ejpam-2044	248	2	+	+	NUM
ejpam-2044	248	3	t)−w	t)−w	PROPN
ejpam-2044	248	4	=	=	SYM
ejpam-2044	248	5	u(w	u(w	PROPN
ejpam-2044	248	6	+	+	PROPN
ejpam-2044	248	7	θt)−	θt)−	PROPN
ejpam-2044	248	8	u(w	u(w	PROPN
ejpam-2044	248	9	)	)	PUNCT
ejpam-2044	248	10	(	(	PUNCT
ejpam-2044	248	11	w	w	PROPN
ejpam-2044	248	12	+	+	NOUN
ejpam-2044	248	13	θt)−w	θt)−w	PROPN
ejpam-2044	248	14	.	.	PUNCT
ejpam-2044	249	1	(	(	PUNCT
ejpam-2044	249	2	46	46	NUM
ejpam-2044	249	3	)	)	PUNCT
ejpam-2044	249	4	geometrically	geometrically	ADV
ejpam-2044	249	5	,	,	PUNCT
ejpam-2044	249	6	equation	equation	NOUN
ejpam-2044	249	7	(	(	PUNCT
ejpam-2044	249	8	46	46	NUM
ejpam-2044	249	9	)	)	PUNCT
ejpam-2044	249	10	can	can	AUX
ejpam-2044	249	11	be	be	AUX
ejpam-2044	249	12	interpreted	interpret	VERB
ejpam-2044	249	13	as	as	SCONJ
ejpam-2044	249	14	follows	follow	VERB
ejpam-2044	249	15	:	:	PUNCT
ejpam-2044	249	16	ratio	ratio	NOUN
ejpam-2044	249	17	of	of	ADP
ejpam-2044	249	18	the	the	DET
ejpam-2044	249	19	catheti	catheti	NOUN
ejpam-2044	249	20	in	in	ADP
ejpam-2044	249	21	one	one	NUM
ejpam-2044	249	22	of	of	ADP
ejpam-2044	249	23	the	the	DET
ejpam-2044	249	24	triangles	triangle	NOUN
ejpam-2044	249	25	is	be	AUX
ejpam-2044	249	26	equal	equal	ADJ
ejpam-2044	249	27	to	to	ADP
ejpam-2044	249	28	ratio	ratio	NOUN
ejpam-2044	249	29	of	of	ADP
ejpam-2044	249	30	the	the	DET
ejpam-2044	249	31	catheti	catheti	NOUN
ejpam-2044	249	32	in	in	ADP
ejpam-2044	249	33	the	the	DET
ejpam-2044	249	34	other	other	ADJ
ejpam-2044	249	35	triangle	triangle	NOUN
ejpam-2044	249	36	,	,	PUNCT
ejpam-2044	249	37	hence	hence	ADV
ejpam-2044	249	38	our	our	PRON
ejpam-2044	249	39	two	two	NUM
ejpam-2044	249	40	considered	consider	VERB
ejpam-2044	249	41	triangles	triangle	NOUN
ejpam-2044	249	42	are	be	AUX
ejpam-2044	249	43	similar	similar	ADJ
ejpam-2044	249	44	triangles	triangle	NOUN
ejpam-2044	249	45	.	.	PUNCT
ejpam-2044	250	1	due	due	ADP
ejpam-2044	250	2	to	to	ADP
ejpam-2044	250	3	the	the	DET
ejpam-2044	250	4	common	common	ADJ
ejpam-2044	250	5	vertex	vertex	NOUN
ejpam-2044	250	6	,	,	PUNCT
ejpam-2044	250	7	catheti	catheti	ADJ
ejpam-2044	250	8	which	which	PRON
ejpam-2044	250	9	lie	lie	VERB
ejpam-2044	250	10	on	on	ADP
ejpam-2044	250	11	a	a	DET
ejpam-2044	250	12	common	common	ADJ
ejpam-2044	250	13	straight	straight	ADJ
ejpam-2044	250	14	line	line	NOUN
ejpam-2044	250	15	,	,	PUNCT
ejpam-2044	250	16	and	and	CCONJ
ejpam-2044	250	17	the	the	DET
ejpam-2044	250	18	vertexes	vertex	NOUN
ejpam-2044	250	19	which	which	PRON
ejpam-2044	250	20	lie	lie	VERB
ejpam-2044	250	21	on	on	ADP
ejpam-2044	250	22	the	the	DET
ejpam-2044	250	23	same	same	ADJ
ejpam-2044	250	24	half	half	NOUN
ejpam-2044	250	25	plane	plane	NOUN
ejpam-2044	250	26	with	with	ADP
ejpam-2044	250	27	respect	respect	NOUN
ejpam-2044	250	28	to	to	ADP
ejpam-2044	250	29	the	the	DET
ejpam-2044	250	30	mentioned	mention	VERB
ejpam-2044	250	31	line	line	NOUN
ejpam-2044	250	32	,	,	PUNCT
ejpam-2044	250	33	we	we	PRON
ejpam-2044	250	34	conclude	conclude	VERB
ejpam-2044	250	35	that	that	SCONJ
ejpam-2044	250	36	the	the	DET
ejpam-2044	250	37	hypotenuses	hypotenuse	NOUN
ejpam-2044	250	38	will	will	AUX
ejpam-2044	250	39	also	also	ADV
ejpam-2044	250	40	lie	lie	VERB
ejpam-2044	250	41	on	on	ADP
ejpam-2044	250	42	a	a	DET
ejpam-2044	250	43	common	common	ADJ
ejpam-2044	250	44	straight	straight	ADJ
ejpam-2044	250	45	line	line	NOUN
ejpam-2044	250	46	;	;	PUNCT
ejpam-2044	250	47	in	in	ADP
ejpam-2044	250	48	other	other	ADJ
ejpam-2044	250	49	words	word	NOUN
ejpam-2044	250	50	,	,	PUNCT
ejpam-2044	250	51	the	the	DET
ejpam-2044	250	52	points	point	NOUN
ejpam-2044	250	53	(	(	PUNCT
ejpam-2044	250	54	w	w	NOUN
ejpam-2044	250	55	+	+	NOUN
ejpam-2044	250	56	θt	θt	ADJ
ejpam-2044	250	57	,	,	PUNCT
ejpam-2044	250	58	u(w	u(w	PROPN
ejpam-2044	250	59	+	+	PROPN
ejpam-2044	250	60	θt	θt	NOUN
ejpam-2044	250	61	)	)	PUNCT
ejpam-2044	250	62	)	)	PUNCT
ejpam-2044	250	63	,	,	PUNCT
ejpam-2044	250	64	for	for	ADP
ejpam-2044	250	65	any	any	DET
ejpam-2044	250	66	initial	initial	ADJ
ejpam-2044	250	67	capital	capital	NOUN
ejpam-2044	250	68	w	w	NOUN
ejpam-2044	250	69	,	,	PUNCT
ejpam-2044	250	70	all	all	DET
ejpam-2044	250	71	non	non	ADJ
ejpam-2044	250	72	-	-	ADJ
ejpam-2044	250	73	zero	zero	NUM
ejpam-2044	250	74	t	t	NOUN
ejpam-2044	250	75	,	,	PUNCT
ejpam-2044	250	76	and	and	CCONJ
ejpam-2044	250	77	all	all	PRON
ejpam-2044	250	78	θ	θ	PROPN
ejpam-2044	250	79	>	>	X
ejpam-2044	250	80	0	0	NUM
ejpam-2044	250	81	,	,	PUNCT
ejpam-2044	250	82	will	will	AUX
ejpam-2044	250	83	form	form	VERB
ejpam-2044	250	84	a	a	DET
ejpam-2044	250	85	straight	straight	ADJ
ejpam-2044	250	86	line	line	NOUN
ejpam-2044	250	87	.	.	PUNCT
ejpam-2044	251	1	so	so	ADV
ejpam-2044	251	2	,	,	PUNCT
ejpam-2044	251	3	we	we	PRON
ejpam-2044	251	4	can	can	AUX
ejpam-2044	251	5	conclude	conclude	VERB
ejpam-2044	251	6	that	that	DET
ejpam-2044	251	7	insurer	insurer	NOUN
ejpam-2044	251	8	’s	’s	PART
ejpam-2044	251	9	utility	utility	NOUN
ejpam-2044	251	10	function	function	NOUN
ejpam-2044	251	11	u(x	u(x	NOUN
ejpam-2044	251	12	)	)	PUNCT
ejpam-2044	251	13	is	be	AUX
ejpam-2044	251	14	a	a	DET
ejpam-2044	251	15	linear	linear	ADJ
ejpam-2044	251	16	function	function	NOUN
ejpam-2044	251	17	,	,	PUNCT
ejpam-2044	251	18	i.e.	i.e.	X
ejpam-2044	251	19	,	,	PUNCT
ejpam-2044	251	20	a	a	DET
ejpam-2044	251	21	function	function	NOUN
ejpam-2044	251	22	of	of	ADP
ejpam-2044	251	23	the	the	DET
ejpam-2044	251	24	form	form	NOUN
ejpam-2044	251	25	u(x	u(x	VERB
ejpam-2044	251	26	)	)	PUNCT
ejpam-2044	252	1	=	=	SYM
ejpam-2044	252	2	ax	ax	NOUN
ejpam-2044	252	3	+	+	PROPN
ejpam-2044	252	4	b.	b.	PROPN
ejpam-2044	252	5	initial	initial	ADJ
ejpam-2044	252	6	assumption	assumption	NOUN
ejpam-2044	252	7	of	of	ADP
ejpam-2044	252	8	positivity	positivity	NOUN
ejpam-2044	252	9	of	of	ADP
ejpam-2044	252	10	first	first	ADJ
ejpam-2044	252	11	derivative	derivative	NOUN
ejpam-2044	252	12	of	of	ADP
ejpam-2044	252	13	the	the	DET
ejpam-2044	252	14	function	function	NOUN
ejpam-2044	252	15	u(x	u(x	NOUN
ejpam-2044	252	16	)	)	PUNCT
ejpam-2044	252	17	gives	give	VERB
ejpam-2044	252	18	us	we	PRON
ejpam-2044	252	19	additional	additional	ADJ
ejpam-2044	252	20	restriction	restriction	NOUN
ejpam-2044	252	21	on	on	ADP
ejpam-2044	252	22	the	the	DET
ejpam-2044	252	23	parameter	parameter	NOUN
ejpam-2044	252	24	a	a	DET
ejpam-2044	252	25	:	:	PUNCT
ejpam-2044	252	26	parameter	parameter	NOUN
ejpam-2044	252	27	a	a	PRON
ejpam-2044	252	28	must	must	AUX
ejpam-2044	252	29	be	be	AUX
ejpam-2044	252	30	a	a	DET
ejpam-2044	252	31	strictly	strictly	ADV
ejpam-2044	252	32	positive	positive	ADJ
ejpam-2044	252	33	constant	constant	ADJ
ejpam-2044	252	34	.	.	PUNCT
ejpam-2044	253	1	this	this	PRON
ejpam-2044	253	2	completes	complete	VERB
ejpam-2044	253	3	the	the	DET
ejpam-2044	253	4	proof	proof	NOUN
ejpam-2044	253	5	of	of	ADP
ejpam-2044	253	6	theorem	theorem	NOUN
ejpam-2044	253	7	3	3	NUM
ejpam-2044	253	8	.	.	PUNCT
ejpam-2044	253	9	since	since	SCONJ
ejpam-2044	253	10	initial	initial	ADJ
ejpam-2044	253	11	capital	capital	NOUN
ejpam-2044	253	12	used	use	VERB
ejpam-2044	253	13	in	in	ADP
ejpam-2044	253	14	the	the	DET
ejpam-2044	253	15	proof	proof	NOUN
ejpam-2044	253	16	of	of	ADP
ejpam-2044	253	17	theorem	theorem	ADJ
ejpam-2044	253	18	3	3	NUM
ejpam-2044	253	19	was	be	AUX
ejpam-2044	253	20	chosen	choose	VERB
ejpam-2044	253	21	arbitrary	arbitrary	ADJ
ejpam-2044	253	22	and	and	CCONJ
ejpam-2044	253	23	no	no	DET
ejpam-2044	253	24	additional	additional	ADJ
ejpam-2044	253	25	restrictions	restriction	NOUN
ejpam-2044	253	26	on	on	ADP
ejpam-2044	253	27	insurer	insurer	NOUN
ejpam-2044	253	28	’s	’s	PART
ejpam-2044	253	29	initial	initial	ADJ
ejpam-2044	253	30	capital	capital	NOUN
ejpam-2044	253	31	were	be	AUX
ejpam-2044	253	32	involved	involve	VERB
ejpam-2044	253	33	,	,	PUNCT
ejpam-2044	253	34	then	then	ADV
ejpam-2044	253	35	we	we	PRON
ejpam-2044	253	36	can	can	AUX
ejpam-2044	253	37	formulate	formulate	VERB
ejpam-2044	253	38	the	the	DET
ejpam-2044	253	39	following	follow	VERB
ejpam-2044	253	40	corollary	corollary	NOUN
ejpam-2044	253	41	to	to	ADP
ejpam-2044	253	42	theorem	theorem	ADJ
ejpam-2044	253	43	3	3	NUM
ejpam-2044	253	44	.	.	PUNCT
ejpam-2044	253	45	corollary	corollary	ADJ
ejpam-2044	253	46	1	1	NUM
ejpam-2044	253	47	.	.	PUNCT
ejpam-2044	253	48	insurer	insurer	NOUN
ejpam-2044	253	49	zero	zero	NUM
ejpam-2044	253	50	utility	utility	NOUN
ejpam-2044	253	51	premium	premium	NOUN
ejpam-2044	253	52	calculation	calculation	NOUN
ejpam-2044	253	53	principle	principle	NOUN
ejpam-2044	253	54	possesses	possess	VERB
ejpam-2044	253	55	scale	scale	NOUN
ejpam-2044	253	56	invariance	invariance	NOUN
ejpam-2044	253	57	property	property	NOUN
ejpam-2044	253	58	if	if	SCONJ
ejpam-2044	253	59	and	and	CCONJ
ejpam-2044	253	60	only	only	ADV
ejpam-2044	253	61	if	if	SCONJ
ejpam-2044	253	62	u(x	u(x	NOUN
ejpam-2044	253	63	)	)	PUNCT
ejpam-2044	253	64	=	=	SYM
ejpam-2044	253	65	ax	ax	NOUN
ejpam-2044	253	66	+	+	CCONJ
ejpam-2044	253	67	b	b	NOUN
ejpam-2044	253	68	,	,	PUNCT
ejpam-2044	253	69	for	for	ADP
ejpam-2044	253	70	a	a	DET
ejpam-2044	253	71	>	>	X
ejpam-2044	253	72	0	0	NUM
ejpam-2044	253	73	,	,	PUNCT
ejpam-2044	253	74	i.e.	i.e.	X
ejpam-2044	253	75	,	,	PUNCT
ejpam-2044	253	76	only	only	ADV
ejpam-2044	253	77	in	in	ADP
ejpam-2044	253	78	the	the	DET
ejpam-2044	253	79	case	case	NOUN
ejpam-2044	253	80	when	when	SCONJ
ejpam-2044	253	81	it	it	PRON
ejpam-2044	253	82	coincides	coincide	VERB
ejpam-2044	253	83	with	with	ADP
ejpam-2044	253	84	net	net	ADJ
ejpam-2044	253	85	premium	premium	NOUN
ejpam-2044	253	86	principle	principle	NOUN
ejpam-2044	253	87	.	.	PUNCT
ejpam-2044	254	1	observe	observe	VERB
ejpam-2044	254	2	that	that	DET
ejpam-2044	254	3	analog	analog	NOUN
ejpam-2044	254	4	of	of	ADP
ejpam-2044	254	5	theorems	theorem	NOUN
ejpam-2044	254	6	2	2	NUM
ejpam-2044	254	7	and	and	CCONJ
ejpam-2044	254	8	5	5	NUM
ejpam-2044	254	9	does	do	AUX
ejpam-2044	254	10	not	not	PART
ejpam-2044	254	11	exist	exist	VERB
ejpam-2044	254	12	for	for	ADP
ejpam-2044	254	13	insurer	insurer	NOUN
ejpam-2044	254	14	equivalent	equivalent	ADJ
ejpam-2044	254	15	/	/	SYM
ejpam-2044	254	16	zero	zero	NUM
ejpam-2044	254	17	utility	utility	NOUN
ejpam-2044	254	18	premium	premium	NOUN
ejpam-2044	254	19	calculation	calculation	NOUN
ejpam-2044	254	20	principle	principle	NOUN
ejpam-2044	254	21	.	.	PUNCT
ejpam-2044	255	1	4	4	X
ejpam-2044	255	2	.	.	X
ejpam-2044	255	3	customer	customer	NOUN
ejpam-2044	255	4	equivalent	equivalent	ADJ
ejpam-2044	255	5	utility	utility	NOUN
ejpam-2044	255	6	premium	premium	NOUN
ejpam-2044	255	7	principle	principle	NOUN
ejpam-2044	255	8	the	the	DET
ejpam-2044	255	9	following	follow	VERB
ejpam-2044	255	10	theorem	theorem	NOUN
ejpam-2044	255	11	describes	describe	VERB
ejpam-2044	255	12	conditions	condition	NOUN
ejpam-2044	255	13	under	under	ADP
ejpam-2044	255	14	which	which	DET
ejpam-2044	255	15	scale	scale	NOUN
ejpam-2044	255	16	invariance	invariance	NOUN
ejpam-2044	255	17	property	property	NOUN
ejpam-2044	255	18	will	will	AUX
ejpam-2044	255	19	be	be	AUX
ejpam-2044	255	20	satisfied	satisfy	VERB
ejpam-2044	255	21	by	by	ADP
ejpam-2044	255	22	customer	customer	NOUN
ejpam-2044	255	23	equivalent	equivalent	ADJ
ejpam-2044	255	24	utility	utility	NOUN
ejpam-2044	255	25	premium	premium	NOUN
ejpam-2044	255	26	calculation	calculation	NOUN
ejpam-2044	255	27	principle	principle	NOUN
ejpam-2044	255	28	.	.	PUNCT
ejpam-2044	256	1	theorem	theorem	ADJ
ejpam-2044	256	2	4	4	NUM
ejpam-2044	256	3	.	.	PUNCT
ejpam-2044	256	4	customer	customer	NOUN
ejpam-2044	256	5	equivalent	equivalent	ADJ
ejpam-2044	256	6	utility	utility	NOUN
ejpam-2044	256	7	premium	premium	NOUN
ejpam-2044	256	8	calculation	calculation	NOUN
ejpam-2044	256	9	principle	principle	NOUN
ejpam-2044	256	10	possesses	possess	VERB
ejpam-2044	256	11	scale	scale	NOUN
ejpam-2044	256	12	invariance	invariance	NOUN
ejpam-2044	256	13	property	property	NOUN
ejpam-2044	257	1	if	if	SCONJ
ejpam-2044	257	2	and	and	CCONJ
ejpam-2044	257	3	only	only	ADV
ejpam-2044	257	4	if	if	SCONJ
ejpam-2044	257	5	u(x	u(x	NOUN
ejpam-2044	257	6	)	)	PUNCT
ejpam-2044	257	7	=	=	SYM
ejpam-2044	257	8	ax	ax	NOUN
ejpam-2044	257	9	+	+	CCONJ
ejpam-2044	257	10	b	b	NOUN
ejpam-2044	257	11	,	,	PUNCT
ejpam-2044	257	12	for	for	ADP
ejpam-2044	257	13	a	a	DET
ejpam-2044	257	14	>	>	X
ejpam-2044	257	15	0	0	NUM
ejpam-2044	257	16	,	,	PUNCT
ejpam-2044	257	17	i.e.	i.e.	X
ejpam-2044	257	18	,	,	PUNCT
ejpam-2044	257	19	only	only	ADV
ejpam-2044	257	20	in	in	ADP
ejpam-2044	257	21	the	the	DET
ejpam-2044	257	22	case	case	NOUN
ejpam-2044	257	23	when	when	SCONJ
ejpam-2044	257	24	it	it	PRON
ejpam-2044	257	25	coincides	coincide	VERB
ejpam-2044	257	26	with	with	ADP
ejpam-2044	257	27	net	net	ADJ
ejpam-2044	257	28	premium	premium	ADJ
ejpam-2044	257	29	principle	principle	NOUN
ejpam-2044	257	30	.	.	PUNCT
ejpam-2044	258	1	proof	proof	NOUN
ejpam-2044	258	2	.	.	PUNCT
ejpam-2044	259	1	we	we	PRON
ejpam-2044	259	2	begin	begin	VERB
ejpam-2044	259	3	again	again	ADV
ejpam-2044	259	4	from	from	ADP
ejpam-2044	259	5	the	the	DET
ejpam-2044	259	6	sufficiency	sufficiency	NOUN
ejpam-2044	259	7	.	.	PUNCT
ejpam-2044	260	1	from	from	ADP
ejpam-2044	260	2	the	the	DET
ejpam-2044	260	3	definition	definition	NOUN
ejpam-2044	260	4	equation	equation	NOUN
ejpam-2044	260	5	(	(	PUNCT
ejpam-2044	260	6	4	4	NUM
ejpam-2044	260	7	)	)	PUNCT
ejpam-2044	260	8	,	,	PUNCT
ejpam-2044	260	9	for	for	ADP
ejpam-2044	260	10	u(x	u(x	NOUN
ejpam-2044	260	11	)	)	PUNCT
ejpam-2044	260	12	=	=	SYM
ejpam-2044	260	13	ax	ax	NOUN
ejpam-2044	260	14	+	+	CCONJ
ejpam-2044	260	15	b	b	NOUN
ejpam-2044	260	16	with	with	ADP
ejpam-2044	260	17	a	a	DET
ejpam-2044	260	18	>	>	X
ejpam-2044	260	19	0	0	NUM
ejpam-2044	260	20	,	,	PUNCT
ejpam-2044	260	21	and	and	CCONJ
ejpam-2044	260	22	any	any	DET
ejpam-2044	260	23	initial	initial	ADJ
ejpam-2044	260	24	capital	capital	NOUN
ejpam-2044	260	25	ω	ω	PROPN
ejpam-2044	260	26	,	,	PUNCT
ejpam-2044	260	27	it	it	PRON
ejpam-2044	260	28	follows	follow	VERB
ejpam-2044	260	29	aω−	aω−	PUNCT
ejpam-2044	260	30	aπc.e.u.[x	aπc.e.u.[x	PROPN
ejpam-2044	260	31	]	]	PUNCT
ejpam-2044	260	32	+	+	PUNCT
ejpam-2044	260	33	b	b	X
ejpam-2044	260	34	=	=	SYM
ejpam-2044	260	35	e[aω−	e[aω−	NOUN
ejpam-2044	260	36	ax	ax	NOUN
ejpam-2044	260	37	+	+	CCONJ
ejpam-2044	260	38	b	b	X
ejpam-2044	260	39	]	]	X
ejpam-2044	260	40	=	=	SYM
ejpam-2044	260	41	aω−	aω−	PUNCT
ejpam-2044	261	1	ae[x	ae[x	X
ejpam-2044	261	2	]	]	PUNCT
ejpam-2044	261	3	+	+	NUM
ejpam-2044	261	4	b	b	X
ejpam-2044	261	5	,	,	PUNCT
ejpam-2044	261	6	hence	hence	ADV
ejpam-2044	261	7	πc.e.u.[x	πc.e.u.[x	VERB
ejpam-2044	261	8	]	]	PUNCT
ejpam-2044	261	9	=	=	PUNCT
ejpam-2044	261	10	e[x	e[x	NOUN
ejpam-2044	261	11	]	]	X
ejpam-2044	261	12	=	=	PUNCT
ejpam-2044	261	13	πnet[x	πnet[x	X
ejpam-2044	261	14	]	]	PUNCT
ejpam-2044	261	15	.	.	PUNCT
ejpam-2044	262	1	m.	m.	PROPN
ejpam-2044	262	2	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	262	3	,	,	PUNCT
ejpam-2044	262	4	v.	v.	ADP
ejpam-2044	262	5	drozdenko	drozdenko	PROPN
ejpam-2044	262	6	/	/	SYM
ejpam-2044	262	7	eur	eur	PROPN
ejpam-2044	262	8	.	.	PUNCT
ejpam-2044	263	1	j.	j.	PROPN
ejpam-2044	263	2	pure	pure	PROPN
ejpam-2044	263	3	appl	appl	PROPN
ejpam-2044	263	4	.	.	PROPN
ejpam-2044	263	5	math	math	PROPN
ejpam-2044	263	6	,	,	PUNCT
ejpam-2044	263	7	7	7	NUM
ejpam-2044	263	8	(	(	PUNCT
ejpam-2044	263	9	2014	2014	NUM
ejpam-2044	263	10	)	)	PUNCT
ejpam-2044	263	11	,	,	PUNCT
ejpam-2044	263	12	267	267	X
ejpam-2044	263	13	-	-	SYM
ejpam-2044	263	14	288	288	NUM
ejpam-2044	263	15	279	279	NUM
ejpam-2044	263	16	on	on	ADP
ejpam-2044	263	17	the	the	DET
ejpam-2044	263	18	other	other	ADJ
ejpam-2044	263	19	hand	hand	NOUN
ejpam-2044	263	20	,	,	PUNCT
ejpam-2044	263	21	from	from	ADP
ejpam-2044	263	22	the	the	DET
ejpam-2044	263	23	equation	equation	NOUN
ejpam-2044	263	24	(	(	PUNCT
ejpam-2044	263	25	4	4	NUM
ejpam-2044	263	26	)	)	PUNCT
ejpam-2044	263	27	,	,	PUNCT
ejpam-2044	263	28	for	for	ADP
ejpam-2044	263	29	any	any	DET
ejpam-2044	263	30	θ	θ	PROPN
ejpam-2044	263	31	>	>	X
ejpam-2044	263	32	0	0	PROPN
ejpam-2044	263	33	,	,	PUNCT
ejpam-2044	263	34	any	any	DET
ejpam-2044	263	35	initial	initial	ADJ
ejpam-2044	263	36	capital	capital	NOUN
ejpam-2044	263	37	ω	ω	PROPN
ejpam-2044	263	38	,	,	PUNCT
ejpam-2044	263	39	and	and	CCONJ
ejpam-2044	263	40	the	the	DET
ejpam-2044	263	41	same	same	ADJ
ejpam-2044	263	42	utility	utility	NOUN
ejpam-2044	263	43	function	function	NOUN
ejpam-2044	264	1	,	,	PUNCT
ejpam-2044	264	2	it	it	PRON
ejpam-2044	264	3	follows	follow	VERB
ejpam-2044	264	4	aω−	aω−	PUNCT
ejpam-2044	264	5	aπc.e.u.[θx	aπc.e.u.[θx	PROPN
ejpam-2044	264	6	]	]	PUNCT
ejpam-2044	265	1	+	+	PUNCT
ejpam-2044	265	2	b	b	X
ejpam-2044	265	3	=	=	PUNCT
ejpam-2044	265	4	e[aω−	e[aω−	NOUN
ejpam-2044	265	5	aθx	aθx	ADP
ejpam-2044	265	6	+	+	NOUN
ejpam-2044	265	7	b	b	NOUN
ejpam-2044	265	8	]	]	X
ejpam-2044	265	9	=	=	SYM
ejpam-2044	265	10	aω−	aω−	PUNCT
ejpam-2044	265	11	aθe[x	aθe[x	X
ejpam-2044	265	12	]	]	X
ejpam-2044	266	1	+	+	CCONJ
ejpam-2044	266	2	b	b	X
ejpam-2044	266	3	,	,	PUNCT
ejpam-2044	266	4	thus	thus	ADV
ejpam-2044	266	5	πc.e.u.[θx	πc.e.u.[θx	NOUN
ejpam-2044	266	6	]	]	PUNCT
ejpam-2044	266	7	=	=	PUNCT
ejpam-2044	266	8	θe[x	θe[x	NOUN
ejpam-2044	266	9	]	]	PUNCT
ejpam-2044	267	1	=	=	PUNCT
ejpam-2044	268	1	θπc.e.u.[x	θπc.e.u.[x	NOUN
ejpam-2044	268	2	]	]	PUNCT
ejpam-2044	268	3	,	,	PUNCT
ejpam-2044	268	4	and	and	CCONJ
ejpam-2044	268	5	we	we	PRON
ejpam-2044	268	6	see	see	VERB
ejpam-2044	268	7	that	that	DET
ejpam-2044	268	8	scale	scale	NOUN
ejpam-2044	268	9	invariance	invariance	NOUN
ejpam-2044	268	10	property	property	NOUN
ejpam-2044	268	11	holds	hold	VERB
ejpam-2044	268	12	in	in	ADP
ejpam-2044	268	13	this	this	DET
ejpam-2044	268	14	particular	particular	ADJ
ejpam-2044	268	15	case	case	NOUN
ejpam-2044	268	16	.	.	PUNCT
ejpam-2044	269	1	the	the	DET
ejpam-2044	269	2	proof	proof	NOUN
ejpam-2044	269	3	of	of	ADP
ejpam-2044	269	4	the	the	DET
ejpam-2044	269	5	sufficiency	sufficiency	NOUN
ejpam-2044	269	6	was	be	AUX
ejpam-2044	269	7	finished	finish	VERB
ejpam-2044	269	8	,	,	PUNCT
ejpam-2044	269	9	so	so	SCONJ
ejpam-2044	269	10	we	we	PRON
ejpam-2044	269	11	can	can	AUX
ejpam-2044	269	12	start	start	VERB
ejpam-2044	269	13	to	to	PART
ejpam-2044	269	14	prove	prove	VERB
ejpam-2044	269	15	the	the	DET
ejpam-2044	269	16	necessity	necessity	NOUN
ejpam-2044	269	17	.	.	PUNCT
ejpam-2044	270	1	to	to	PART
ejpam-2044	270	2	show	show	VERB
ejpam-2044	270	3	that	that	SCONJ
ejpam-2044	270	4	customer	customer	NOUN
ejpam-2044	270	5	equivalent	equivalent	ADJ
ejpam-2044	270	6	utility	utility	NOUN
ejpam-2044	270	7	premium	premium	NOUN
ejpam-2044	270	8	calculation	calculation	NOUN
ejpam-2044	270	9	principle	principle	NOUN
ejpam-2044	270	10	with	with	ADP
ejpam-2044	270	11	non	non	ADJ
ejpam-2044	270	12	-	-	ADJ
ejpam-2044	270	13	linear	linear	ADJ
ejpam-2044	270	14	customer	customer	NOUN
ejpam-2044	270	15	utility	utility	NOUN
ejpam-2044	270	16	function	function	NOUN
ejpam-2044	270	17	u(x	u(x	NOUN
ejpam-2044	270	18	)	)	PUNCT
ejpam-2044	270	19	will	will	AUX
ejpam-2044	270	20	not	not	PART
ejpam-2044	270	21	possess	possess	VERB
ejpam-2044	270	22	scale	scale	NOUN
ejpam-2044	270	23	invariance	invariance	NOUN
ejpam-2044	270	24	property	property	NOUN
ejpam-2044	270	25	,	,	PUNCT
ejpam-2044	270	26	we	we	PRON
ejpam-2044	270	27	will	will	AUX
ejpam-2044	270	28	choose	choose	VERB
ejpam-2044	270	29	a	a	DET
ejpam-2044	270	30	risk	risk	NOUN
ejpam-2044	270	31	x	x	PUNCT
ejpam-2044	270	32	which	which	PRON
ejpam-2044	270	33	takes	take	VERB
ejpam-2044	270	34	only	only	ADV
ejpam-2044	270	35	two	two	NUM
ejpam-2044	270	36	possible	possible	ADJ
ejpam-2044	270	37	values	value	NOUN
ejpam-2044	270	38	,	,	PUNCT
ejpam-2044	270	39	namely	namely	ADV
ejpam-2044	270	40	0	0	NUM
ejpam-2044	270	41	and	and	CCONJ
ejpam-2044	270	42	t	t	NOUN
ejpam-2044	270	43	with	with	ADP
ejpam-2044	270	44	probabilities	probability	NOUN
ejpam-2044	270	45	1	1	NUM
ejpam-2044	270	46	−	−	NOUN
ejpam-2044	270	47	p	p	NOUN
ejpam-2044	270	48	and	and	CCONJ
ejpam-2044	270	49	p	p	NOUN
ejpam-2044	270	50	respectively	respectively	ADV
ejpam-2044	270	51	.	.	PUNCT
ejpam-2044	271	1	the	the	DET
ejpam-2044	271	2	risk	risk	NOUN
ejpam-2044	271	3	x	x	X
ejpam-2044	271	4	can	can	AUX
ejpam-2044	271	5	in	in	ADP
ejpam-2044	271	6	this	this	DET
ejpam-2044	271	7	case	case	NOUN
ejpam-2044	271	8	be	be	AUX
ejpam-2044	271	9	considered	consider	VERB
ejpam-2044	271	10	as	as	ADP
ejpam-2044	271	11	a	a	DET
ejpam-2044	271	12	random	random	ADJ
ejpam-2044	271	13	function	function	NOUN
ejpam-2044	271	14	of	of	ADP
ejpam-2044	271	15	two	two	NUM
ejpam-2044	271	16	parameters	parameter	NOUN
ejpam-2044	271	17	,	,	PUNCT
ejpam-2044	271	18	namely	namely	ADV
ejpam-2044	271	19	p	p	NOUN
ejpam-2044	271	20	and	and	CCONJ
ejpam-2044	271	21	t	t	PROPN
ejpam-2044	271	22	,	,	PUNCT
ejpam-2044	271	23	and	and	CCONJ
ejpam-2044	271	24	,	,	PUNCT
ejpam-2044	271	25	therefore	therefore	ADV
ejpam-2044	271	26	,	,	PUNCT
ejpam-2044	271	27	within	within	ADP
ejpam-2044	271	28	the	the	DET
ejpam-2044	271	29	proof	proof	NOUN
ejpam-2044	271	30	of	of	ADP
ejpam-2044	271	31	theorem	theorem	NOUN
ejpam-2044	271	32	4	4	NUM
ejpam-2044	271	33	it	it	PRON
ejpam-2044	271	34	will	will	AUX
ejpam-2044	271	35	be	be	AUX
ejpam-2044	271	36	denoted	denote	VERB
ejpam-2044	271	37	as	as	ADP
ejpam-2044	271	38	x	x	PROPN
ejpam-2044	271	39	t	t	PROPN
ejpam-2044	271	40	p.	p.	NOUN
ejpam-2044	271	41	for	for	ADP
ejpam-2044	271	42	any	any	DET
ejpam-2044	271	43	customer	customer	NOUN
ejpam-2044	271	44	’s	’s	PART
ejpam-2044	271	45	initial	initial	ADJ
ejpam-2044	271	46	capital	capital	NOUN
ejpam-2044	271	47	ω	ω	PROPN
ejpam-2044	271	48	,	,	PUNCT
ejpam-2044	271	49	customer	customer	NOUN
ejpam-2044	271	50	’s	’s	PART
ejpam-2044	271	51	equivalent	equivalent	ADJ
ejpam-2044	271	52	utility	utility	NOUN
ejpam-2044	271	53	equation	equation	NOUN
ejpam-2044	271	54	(	(	PUNCT
ejpam-2044	271	55	4	4	NUM
ejpam-2044	271	56	)	)	PUNCT
ejpam-2044	271	57	for	for	ADP
ejpam-2044	271	58	the	the	DET
ejpam-2044	271	59	risk	risk	NOUN
ejpam-2044	271	60	x	x	X
ejpam-2044	271	61	t	t	NOUN
ejpam-2044	271	62	p	p	NOUN
ejpam-2044	271	63	will	will	AUX
ejpam-2044	271	64	take	take	VERB
ejpam-2044	271	65	the	the	DET
ejpam-2044	271	66	following	follow	VERB
ejpam-2044	271	67	form	form	NOUN
ejpam-2044	271	68	u(ω−πc.e.u.[x	u(ω−πc.e.u.[x	PROPN
ejpam-2044	271	69	t	t	PROPN
ejpam-2044	271	70	p	p	X
ejpam-2044	271	71	]	]	X
ejpam-2044	271	72	)	)	PUNCT
ejpam-2044	272	1	=	=	SYM
ejpam-2044	272	2	u(ω−	u(ω−	PROPN
ejpam-2044	272	3	t	t	PROPN
ejpam-2044	272	4	)	)	PUNCT
ejpam-2044	272	5	·	·	PUNCT
ejpam-2044	273	1	p+	p+	X
ejpam-2044	273	2	u(ω	u(ω	PROPN
ejpam-2044	273	3	)	)	PUNCT
ejpam-2044	273	4	·	·	PUNCT
ejpam-2044	274	1	(	(	PUNCT
ejpam-2044	274	2	1−	1−	NUM
ejpam-2044	274	3	p	p	NOUN
ejpam-2044	274	4	)	)	PUNCT
ejpam-2044	274	5	.	.	PUNCT
ejpam-2044	275	1	(	(	PUNCT
ejpam-2044	275	2	47	47	NUM
ejpam-2044	275	3	)	)	PUNCT
ejpam-2044	275	4	substituting	substitute	VERB
ejpam-2044	275	5	p	p	NOUN
ejpam-2044	275	6	=	=	NOUN
ejpam-2044	275	7	0	0	NUM
ejpam-2044	275	8	into	into	ADP
ejpam-2044	275	9	the	the	DET
ejpam-2044	275	10	equation	equation	NOUN
ejpam-2044	275	11	(	(	PUNCT
ejpam-2044	275	12	47	47	NUM
ejpam-2044	275	13	)	)	PUNCT
ejpam-2044	275	14	,	,	PUNCT
ejpam-2044	275	15	obtain	obtain	VERB
ejpam-2044	275	16	u(ω−πc.e.u.[x	u(ω−πc.e.u.[x	ADJ
ejpam-2044	275	17	t	t	PROPN
ejpam-2044	275	18	0	0	NUM
ejpam-2044	275	19	]	]	PUNCT
ejpam-2044	275	20	)	)	PUNCT
ejpam-2044	276	1	=	=	SYM
ejpam-2044	276	2	u(ω	u(ω	PROPN
ejpam-2044	276	3	)	)	PUNCT
ejpam-2044	276	4	.	.	PUNCT
ejpam-2044	277	1	(	(	PUNCT
ejpam-2044	277	2	48	48	NUM
ejpam-2044	277	3	)	)	PUNCT
ejpam-2044	277	4	since	since	SCONJ
ejpam-2044	277	5	u(x	u(x	NOUN
ejpam-2044	277	6	)	)	PUNCT
ejpam-2044	277	7	is	be	AUX
ejpam-2044	277	8	a	a	DET
ejpam-2044	277	9	strictly	strictly	ADV
ejpam-2044	277	10	increasing	increase	VERB
ejpam-2044	277	11	function	function	NOUN
ejpam-2044	277	12	,	,	PUNCT
ejpam-2044	277	13	then	then	ADV
ejpam-2044	277	14	the	the	DET
ejpam-2044	277	15	equation	equation	NOUN
ejpam-2044	277	16	(	(	PUNCT
ejpam-2044	277	17	48	48	NUM
ejpam-2044	277	18	)	)	PUNCT
ejpam-2044	277	19	yields	yield	NOUN
ejpam-2044	277	20	πc.e.u.[x	πc.e.u.[x	VERB
ejpam-2044	277	21	t	t	NOUN
ejpam-2044	277	22	0	0	NUM
ejpam-2044	277	23	]	]	X
ejpam-2044	278	1	=	=	SYM
ejpam-2044	278	2	0	0	X
ejpam-2044	278	3	.	.	PUNCT
ejpam-2044	279	1	(	(	PUNCT
ejpam-2044	279	2	49	49	NUM
ejpam-2044	279	3	)	)	PUNCT
ejpam-2044	279	4	let	let	VERB
ejpam-2044	279	5	us	we	PRON
ejpam-2044	279	6	now	now	ADV
ejpam-2044	279	7	take	take	VERB
ejpam-2044	279	8	partial	partial	ADJ
ejpam-2044	279	9	derivatives	derivative	NOUN
ejpam-2044	279	10	with	with	ADP
ejpam-2044	279	11	respect	respect	NOUN
ejpam-2044	279	12	to	to	ADP
ejpam-2044	279	13	p	p	NOUN
ejpam-2044	279	14	from	from	ADP
ejpam-2044	279	15	both	both	DET
ejpam-2044	279	16	sides	side	NOUN
ejpam-2044	279	17	of	of	ADP
ejpam-2044	279	18	the	the	DET
ejpam-2044	279	19	equation	equation	NOUN
ejpam-2044	279	20	(	(	PUNCT
ejpam-2044	279	21	47	47	NUM
ejpam-2044	279	22	)	)	PUNCT
ejpam-2044	280	1	−u′(ω−πc.e.u.[x	−u′(ω−πc.e.u.[x	PROPN
ejpam-2044	280	2	t	t	NOUN
ejpam-2044	281	1	p	p	X
ejpam-2044	281	2	]	]	X
ejpam-2044	281	3	)	)	PUNCT
ejpam-2044	281	4	·	·	PUNCT
ejpam-2044	281	5	∂	∂	NUM
ejpam-2044	281	6	∂	∂	NUM
ejpam-2044	281	7	p	p	NOUN
ejpam-2044	281	8	πc.e.u.[x	πc.e.u.[x	PUNCT
ejpam-2044	281	9	t	t	NOUN
ejpam-2044	282	1	p	p	X
ejpam-2044	282	2	]	]	X
ejpam-2044	282	3	=	=	PUNCT
ejpam-2044	282	4	u(ω−	u(ω−	X
ejpam-2044	282	5	t)−	t)−	PROPN
ejpam-2044	282	6	u(ω	u(ω	PROPN
ejpam-2044	282	7	)	)	PUNCT
ejpam-2044	282	8	.	.	PUNCT
ejpam-2044	283	1	(	(	PUNCT
ejpam-2044	283	2	50	50	X
ejpam-2044	283	3	)	)	PUNCT
ejpam-2044	283	4	substituting	substitute	VERB
ejpam-2044	283	5	p	p	NOUN
ejpam-2044	283	6	=	=	NOUN
ejpam-2044	283	7	0	0	NUM
ejpam-2044	283	8	into	into	ADP
ejpam-2044	283	9	the	the	DET
ejpam-2044	283	10	equation	equation	NOUN
ejpam-2044	283	11	(	(	PUNCT
ejpam-2044	283	12	50	50	NUM
ejpam-2044	283	13	)	)	PUNCT
ejpam-2044	283	14	and	and	CCONJ
ejpam-2044	283	15	using	use	VERB
ejpam-2044	283	16	identity	identity	NOUN
ejpam-2044	283	17	(	(	PUNCT
ejpam-2044	283	18	49	49	NUM
ejpam-2044	283	19	)	)	PUNCT
ejpam-2044	283	20	,	,	PUNCT
ejpam-2044	283	21	we	we	PRON
ejpam-2044	283	22	get	get	VERB
ejpam-2044	283	23	−u′(ω	−u′(ω	PROPN
ejpam-2044	283	24	)	)	PUNCT
ejpam-2044	284	1	·	·	PUNCT
ejpam-2044	284	2	�	�	PROPN
ejpam-2044	284	3	∂	∂	NUM
ejpam-2044	284	4	∂	∂	NUM
ejpam-2044	284	5	p	p	NOUN
ejpam-2044	284	6	πc.e.u.[x	πc.e.u.[x	PUNCT
ejpam-2044	284	7	t	t	PROPN
ejpam-2044	284	8	p	p	X
ejpam-2044	284	9	]	]	X
ejpam-2044	284	10	�	�	PROPN
ejpam-2044	284	11	�	�	PROPN
ejpam-2044	284	12	�	�	PROPN
ejpam-2044	284	13	�	�	PROPN
ejpam-2044	284	14	p=0	p=0	PROPN
ejpam-2044	284	15	�	�	PROPN
ejpam-2044	284	16	=	=	PUNCT
ejpam-2044	284	17	u(ω−	u(ω−	X
ejpam-2044	284	18	t)−	t)−	PROPN
ejpam-2044	284	19	u(ω	u(ω	PROPN
ejpam-2044	284	20	)	)	PUNCT
ejpam-2044	284	21	.	.	PUNCT
ejpam-2044	285	1	(	(	PUNCT
ejpam-2044	285	2	51	51	NUM
ejpam-2044	285	3	)	)	PUNCT
ejpam-2044	285	4	since	since	SCONJ
ejpam-2044	285	5	we	we	PRON
ejpam-2044	285	6	are	be	AUX
ejpam-2044	285	7	searching	search	VERB
ejpam-2044	285	8	for	for	ADP
ejpam-2044	285	9	the	the	DET
ejpam-2044	285	10	conditions	condition	NOUN
ejpam-2044	285	11	when	when	SCONJ
ejpam-2044	285	12	the	the	DET
ejpam-2044	285	13	premium	premium	NOUN
ejpam-2044	285	14	calculation	calculation	NOUN
ejpam-2044	285	15	principle	principle	NOUN
ejpam-2044	285	16	will	will	AUX
ejpam-2044	285	17	be	be	AUX
ejpam-2044	285	18	scale	scale	NOUN
ejpam-2044	285	19	invariant	invariant	ADJ
ejpam-2044	285	20	,	,	PUNCT
ejpam-2044	285	21	then	then	ADV
ejpam-2044	285	22	for	for	ADP
ejpam-2044	285	23	any	any	DET
ejpam-2044	285	24	customer	customer	NOUN
ejpam-2044	285	25	’s	’s	PART
ejpam-2044	285	26	initial	initial	ADJ
ejpam-2044	285	27	capitalω	capitalω	NOUN
ejpam-2044	285	28	and	and	CCONJ
ejpam-2044	285	29	any	any	DET
ejpam-2044	285	30	positive	positive	ADJ
ejpam-2044	285	31	constantθ	constantθ	NOUN
ejpam-2044	285	32	,	,	PUNCT
ejpam-2044	285	33	customer	customer	NOUN
ejpam-2044	285	34	’s	’s	PART
ejpam-2044	285	35	equivalent	equivalent	ADJ
ejpam-2044	285	36	utility	utility	NOUN
ejpam-2044	285	37	equation	equation	NOUN
ejpam-2044	285	38	(	(	PUNCT
ejpam-2044	285	39	4	4	NUM
ejpam-2044	285	40	)	)	PUNCT
ejpam-2044	285	41	for	for	ADP
ejpam-2044	285	42	the	the	DET
ejpam-2044	285	43	risk	risk	NOUN
ejpam-2044	285	44	θx	θx	ADP
ejpam-2044	285	45	t	t	PROPN
ejpam-2044	285	46	p	p	NOUN
ejpam-2044	285	47	can	can	AUX
ejpam-2044	285	48	be	be	AUX
ejpam-2044	285	49	written	write	VERB
ejpam-2044	285	50	in	in	ADP
ejpam-2044	285	51	the	the	DET
ejpam-2044	285	52	following	following	ADJ
ejpam-2044	285	53	way	way	NOUN
ejpam-2044	285	54	u(ω−θπc.e.u.[x	u(ω−θπc.e.u.[x	PROPN
ejpam-2044	285	55	t	t	NOUN
ejpam-2044	285	56	p	p	X
ejpam-2044	285	57	]	]	X
ejpam-2044	285	58	)	)	PUNCT
ejpam-2044	285	59	=	=	SYM
ejpam-2044	285	60	u(ω−θt	u(ω−θt	PROPN
ejpam-2044	285	61	)	)	PUNCT
ejpam-2044	285	62	·	·	PUNCT
ejpam-2044	286	1	p+	p+	X
ejpam-2044	286	2	u(ω	u(ω	PROPN
ejpam-2044	286	3	)	)	PUNCT
ejpam-2044	286	4	·	·	PUNCT
ejpam-2044	287	1	(	(	PUNCT
ejpam-2044	287	2	1−	1−	NUM
ejpam-2044	287	3	p	p	NOUN
ejpam-2044	287	4	)	)	PUNCT
ejpam-2044	287	5	.	.	PUNCT
ejpam-2044	288	1	(	(	PUNCT
ejpam-2044	288	2	52	52	NUM
ejpam-2044	288	3	)	)	PUNCT
ejpam-2044	288	4	we	we	PRON
ejpam-2044	288	5	are	be	AUX
ejpam-2044	288	6	now	now	ADV
ejpam-2044	288	7	taking	take	VERB
ejpam-2044	288	8	partial	partial	ADJ
ejpam-2044	288	9	derivative	derivative	NOUN
ejpam-2044	288	10	with	with	ADP
ejpam-2044	288	11	respect	respect	NOUN
ejpam-2044	288	12	to	to	ADP
ejpam-2044	288	13	p	p	NOUN
ejpam-2044	288	14	from	from	ADP
ejpam-2044	288	15	both	both	DET
ejpam-2044	288	16	sides	side	NOUN
ejpam-2044	288	17	of	of	ADP
ejpam-2044	288	18	the	the	DET
ejpam-2044	288	19	equation	equation	NOUN
ejpam-2044	288	20	(	(	PUNCT
ejpam-2044	288	21	52	52	NUM
ejpam-2044	288	22	)	)	PUNCT
ejpam-2044	288	23	−u′(ω−πc.e.u.[x	−u′(ω−πc.e.u.[x	NOUN
ejpam-2044	288	24	t	t	NOUN
ejpam-2044	289	1	p	p	X
ejpam-2044	289	2	]	]	X
ejpam-2044	289	3	)	)	PUNCT
ejpam-2044	289	4	·	·	PUNCT
ejpam-2044	289	5	θ	θ	X
ejpam-2044	289	6	·	·	PUNCT
ejpam-2044	289	7	∂	∂	NUM
ejpam-2044	289	8	∂	∂	NOUN
ejpam-2044	289	9	p	p	NOUN
ejpam-2044	289	10	πc.e.u.[x	πc.e.u.[x	PUNCT
ejpam-2044	289	11	t	t	NOUN
ejpam-2044	289	12	p	p	X
ejpam-2044	289	13	]	]	X
ejpam-2044	289	14	=	=	PUNCT
ejpam-2044	289	15	u(ω−θt)−	u(ω−θt)−	PROPN
ejpam-2044	289	16	u(ω	u(ω	PROPN
ejpam-2044	289	17	)	)	PUNCT
ejpam-2044	289	18	.	.	PUNCT
ejpam-2044	290	1	(	(	PUNCT
ejpam-2044	290	2	53	53	NUM
ejpam-2044	290	3	)	)	PUNCT
ejpam-2044	290	4	m.	m.	NOUN
ejpam-2044	290	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	290	6	,	,	PUNCT
ejpam-2044	290	7	v.	v.	ADP
ejpam-2044	290	8	drozdenko	drozdenko	PROPN
ejpam-2044	290	9	/	/	SYM
ejpam-2044	290	10	eur	eur	PROPN
ejpam-2044	290	11	.	.	PUNCT
ejpam-2044	291	1	j.	j.	PROPN
ejpam-2044	291	2	pure	pure	PROPN
ejpam-2044	291	3	appl	appl	PROPN
ejpam-2044	291	4	.	.	PROPN
ejpam-2044	291	5	math	math	PROPN
ejpam-2044	291	6	,	,	PUNCT
ejpam-2044	291	7	7	7	NUM
ejpam-2044	291	8	(	(	PUNCT
ejpam-2044	291	9	2014	2014	NUM
ejpam-2044	291	10	)	)	PUNCT
ejpam-2044	291	11	,	,	PUNCT
ejpam-2044	291	12	267	267	NUM
ejpam-2044	291	13	-	-	SYM
ejpam-2044	291	14	288	288	NUM
ejpam-2044	291	15	280	280	NUM
ejpam-2044	291	16	substituting	substitute	VERB
ejpam-2044	291	17	p	p	NOUN
ejpam-2044	291	18	=	=	NOUN
ejpam-2044	291	19	0	0	NUM
ejpam-2044	291	20	into	into	ADP
ejpam-2044	291	21	the	the	DET
ejpam-2044	291	22	equation	equation	NOUN
ejpam-2044	291	23	(	(	PUNCT
ejpam-2044	291	24	53	53	NUM
ejpam-2044	291	25	)	)	PUNCT
ejpam-2044	291	26	,	,	PUNCT
ejpam-2044	291	27	and	and	CCONJ
ejpam-2044	291	28	using	use	VERB
ejpam-2044	291	29	identity	identity	NOUN
ejpam-2044	291	30	(	(	PUNCT
ejpam-2044	291	31	49	49	NUM
ejpam-2044	291	32	)	)	PUNCT
ejpam-2044	291	33	,	,	PUNCT
ejpam-2044	291	34	we	we	PRON
ejpam-2044	291	35	get	get	VERB
ejpam-2044	291	36	−u′(ω	−u′(ω	PROPN
ejpam-2044	291	37	)	)	PUNCT
ejpam-2044	291	38	·	·	PUNCT
ejpam-2044	291	39	θ	θ	X
ejpam-2044	291	40	·	·	PUNCT
ejpam-2044	291	41	�	�	PROPN
ejpam-2044	291	42	∂	∂	NUM
ejpam-2044	291	43	∂	∂	NUM
ejpam-2044	291	44	p	p	NOUN
ejpam-2044	291	45	πc.e.u.[x	πc.e.u.[x	PUNCT
ejpam-2044	291	46	t	t	PROPN
ejpam-2044	291	47	p	p	X
ejpam-2044	291	48	]	]	X
ejpam-2044	291	49	�	�	PROPN
ejpam-2044	291	50	�	�	PROPN
ejpam-2044	291	51	�	�	PROPN
ejpam-2044	291	52	�	�	PROPN
ejpam-2044	291	53	p=0	p=0	PROPN
ejpam-2044	291	54	�	�	PROPN
ejpam-2044	292	1	=	=	SYM
ejpam-2044	292	2	u(ω−θt)−	u(ω−θt)−	PROPN
ejpam-2044	292	3	u(ω	u(ω	PROPN
ejpam-2044	292	4	)	)	PUNCT
ejpam-2044	292	5	.	.	PUNCT
ejpam-2044	293	1	(	(	PUNCT
ejpam-2044	293	2	54	54	NUM
ejpam-2044	293	3	)	)	PUNCT
ejpam-2044	293	4	since	since	SCONJ
ejpam-2044	293	5	θ	θ	PROPN
ejpam-2044	293	6	>	>	X
ejpam-2044	293	7	0	0	NUM
ejpam-2044	293	8	,	,	PUNCT
ejpam-2044	293	9	then	then	ADV
ejpam-2044	293	10	the	the	DET
ejpam-2044	293	11	equation	equation	NOUN
ejpam-2044	293	12	(	(	PUNCT
ejpam-2044	293	13	54	54	NUM
ejpam-2044	293	14	)	)	PUNCT
ejpam-2044	293	15	can	can	AUX
ejpam-2044	293	16	be	be	AUX
ejpam-2044	293	17	rewritten	rewrite	VERB
ejpam-2044	293	18	as	as	SCONJ
ejpam-2044	293	19	follows	follow	VERB
ejpam-2044	293	20	−u′(ω	−u′(ω	PROPN
ejpam-2044	293	21	)	)	PUNCT
ejpam-2044	293	22	·	·	PUNCT
ejpam-2044	293	23	�	�	PROPN
ejpam-2044	293	24	∂	∂	NUM
ejpam-2044	293	25	∂	∂	NUM
ejpam-2044	293	26	p	p	NOUN
ejpam-2044	293	27	πc.e.u.[x	πc.e.u.[x	PUNCT
ejpam-2044	293	28	t	t	PROPN
ejpam-2044	293	29	p	p	X
ejpam-2044	293	30	]	]	X
ejpam-2044	293	31	�	�	PROPN
ejpam-2044	293	32	�	�	PROPN
ejpam-2044	293	33	�	�	PROPN
ejpam-2044	293	34	�	�	PROPN
ejpam-2044	293	35	p=0	p=0	PROPN
ejpam-2044	293	36	�	�	PROPN
ejpam-2044	294	1	=	=	SYM
ejpam-2044	294	2	u(ω−θt)−	u(ω−θt)−	PROPN
ejpam-2044	294	3	u(ω	u(ω	PROPN
ejpam-2044	294	4	)	)	PUNCT
ejpam-2044	294	5	θ	θ	PROPN
ejpam-2044	294	6	.	.	PUNCT
ejpam-2044	295	1	(	(	PUNCT
ejpam-2044	295	2	55	55	X
ejpam-2044	295	3	)	)	PUNCT
ejpam-2044	295	4	observe	observe	VERB
ejpam-2044	295	5	that	that	SCONJ
ejpam-2044	295	6	equations	equation	NOUN
ejpam-2044	295	7	(	(	PUNCT
ejpam-2044	295	8	51	51	NUM
ejpam-2044	295	9	)	)	PUNCT
ejpam-2044	295	10	and	and	CCONJ
ejpam-2044	295	11	(	(	PUNCT
ejpam-2044	295	12	55	55	NUM
ejpam-2044	295	13	)	)	PUNCT
ejpam-2044	295	14	have	have	VERB
ejpam-2044	295	15	equal	equal	ADJ
ejpam-2044	295	16	left	leave	VERB
ejpam-2044	295	17	-	-	PUNCT
ejpam-2044	295	18	hand	hand	NOUN
ejpam-2044	295	19	sides	side	NOUN
ejpam-2044	295	20	,	,	PUNCT
ejpam-2044	295	21	this	this	PRON
ejpam-2044	295	22	means	mean	VERB
ejpam-2044	295	23	that	that	SCONJ
ejpam-2044	295	24	their	their	PRON
ejpam-2044	295	25	right	right	ADJ
ejpam-2044	295	26	-	-	PUNCT
ejpam-2044	295	27	hand	hand	NOUN
ejpam-2044	295	28	sides	side	NOUN
ejpam-2044	295	29	also	also	ADV
ejpam-2044	295	30	have	have	VERB
ejpam-2044	295	31	to	to	PART
ejpam-2044	295	32	be	be	AUX
ejpam-2044	295	33	equal	equal	ADJ
ejpam-2044	295	34	,	,	PUNCT
ejpam-2044	295	35	and	and	CCONJ
ejpam-2044	295	36	we	we	PRON
ejpam-2044	295	37	finally	finally	ADV
ejpam-2044	295	38	get	get	VERB
ejpam-2044	295	39	an	an	DET
ejpam-2044	295	40	equation	equation	NOUN
ejpam-2044	295	41	which	which	DET
ejpam-2044	295	42	customer	customer	NOUN
ejpam-2044	295	43	’s	’s	PART
ejpam-2044	295	44	utility	utility	NOUN
ejpam-2044	295	45	function	function	NOUN
ejpam-2044	295	46	u(x	u(x	NOUN
ejpam-2044	295	47	)	)	PUNCT
ejpam-2044	295	48	has	have	VERB
ejpam-2044	295	49	to	to	PART
ejpam-2044	295	50	satisfy	satisfy	VERB
ejpam-2044	295	51	for	for	SCONJ
ejpam-2044	295	52	the	the	DET
ejpam-2044	295	53	premium	premium	ADJ
ejpam-2044	295	54	calculation	calculation	NOUN
ejpam-2044	295	55	principle	principle	NOUN
ejpam-2044	295	56	to	to	PART
ejpam-2044	295	57	be	be	AUX
ejpam-2044	295	58	scale	scale	NOUN
ejpam-2044	295	59	invariant	invariant	ADJ
ejpam-2044	295	60	,	,	PUNCT
ejpam-2044	295	61	namely	namely	ADV
ejpam-2044	295	62	u(ω−	u(ω−	VERB
ejpam-2044	295	63	t)−	t)−	PROPN
ejpam-2044	295	64	u(ω	u(ω	PROPN
ejpam-2044	295	65	)	)	PUNCT
ejpam-2044	296	1	=	=	SYM
ejpam-2044	296	2	u(ω−θt)−	u(ω−θt)−	PROPN
ejpam-2044	296	3	u(ω	u(ω	PROPN
ejpam-2044	296	4	)	)	PUNCT
ejpam-2044	296	5	θ	θ	PROPN
ejpam-2044	296	6	.	.	PUNCT
ejpam-2044	297	1	(	(	PUNCT
ejpam-2044	297	2	56	56	X
ejpam-2044	297	3	)	)	PUNCT
ejpam-2044	297	4	taking	take	VERB
ejpam-2044	297	5	partial	partial	ADJ
ejpam-2044	297	6	derivatives	derivative	NOUN
ejpam-2044	297	7	with	with	ADP
ejpam-2044	297	8	respect	respect	NOUN
ejpam-2044	297	9	to	to	ADP
ejpam-2044	297	10	the	the	DET
ejpam-2044	297	11	parameter	parameter	NOUN
ejpam-2044	297	12	t	t	PROPN
ejpam-2044	297	13	from	from	ADP
ejpam-2044	297	14	both	both	DET
ejpam-2044	297	15	sides	side	NOUN
ejpam-2044	297	16	of	of	ADP
ejpam-2044	297	17	(	(	PUNCT
ejpam-2044	297	18	56	56	NUM
ejpam-2044	297	19	)	)	PUNCT
ejpam-2044	297	20	,	,	PUNCT
ejpam-2044	297	21	we	we	PRON
ejpam-2044	297	22	get	get	VERB
ejpam-2044	297	23	u′(ω−	u′(ω−	ADJ
ejpam-2044	297	24	t	t	PROPN
ejpam-2044	297	25	)	)	PUNCT
ejpam-2044	297	26	=	=	SYM
ejpam-2044	297	27	u′(ω−θt	u′(ω−θt	PROPN
ejpam-2044	297	28	)	)	PUNCT
ejpam-2044	297	29	.	.	PUNCT
ejpam-2044	298	1	(	(	PUNCT
ejpam-2044	298	2	57	57	NUM
ejpam-2044	298	3	)	)	PUNCT
ejpam-2044	298	4	by	by	ADP
ejpam-2044	298	5	fixing	fix	VERB
ejpam-2044	298	6	values	value	NOUN
ejpam-2044	298	7	of	of	ADP
ejpam-2044	298	8	the	the	DET
ejpam-2044	298	9	parameters	parameter	NOUN
ejpam-2044	298	10	ω	ω	PROPN
ejpam-2044	298	11	and	and	CCONJ
ejpam-2044	298	12	t	t	PROPN
ejpam-2044	298	13	,	,	PUNCT
ejpam-2044	298	14	and	and	CCONJ
ejpam-2044	298	15	changing	change	VERB
ejpam-2044	298	16	values	value	NOUN
ejpam-2044	298	17	of	of	ADP
ejpam-2044	298	18	the	the	DET
ejpam-2044	298	19	parameter	parameter	NOUN
ejpam-2044	298	20	θ	θ	PROPN
ejpam-2044	298	21	,	,	PUNCT
ejpam-2044	298	22	we	we	PRON
ejpam-2044	298	23	will	will	AUX
ejpam-2044	298	24	make	make	VERB
ejpam-2044	298	25	u′(ω	u′(ω	PRON
ejpam-2044	298	26	−	−	VERB
ejpam-2044	298	27	θt	θt	ADJ
ejpam-2044	298	28	)	)	PUNCT
ejpam-2044	298	29	a	a	DET
ejpam-2044	298	30	function	function	NOUN
ejpam-2044	298	31	of	of	ADP
ejpam-2044	298	32	changing	change	VERB
ejpam-2044	298	33	variable	variable	NOUN
ejpam-2044	298	34	while	while	SCONJ
ejpam-2044	298	35	the	the	DET
ejpam-2044	298	36	value	value	NOUN
ejpam-2044	298	37	u′(ω	u′(ω	PROPN
ejpam-2044	298	38	−	−	PROPN
ejpam-2044	298	39	t	t	PROPN
ejpam-2044	298	40	)	)	PUNCT
ejpam-2044	298	41	will	will	AUX
ejpam-2044	298	42	be	be	AUX
ejpam-2044	298	43	a	a	DET
ejpam-2044	298	44	fixed	fix	VERB
ejpam-2044	298	45	constant	constant	ADJ
ejpam-2044	298	46	.	.	PUNCT
ejpam-2044	299	1	using	use	VERB
ejpam-2044	299	2	this	this	DET
ejpam-2044	299	3	technique	technique	NOUN
ejpam-2044	299	4	and	and	CCONJ
ejpam-2044	299	5	taking	take	VERB
ejpam-2044	299	6	into	into	ADP
ejpam-2044	299	7	account	account	NOUN
ejpam-2044	299	8	monotonicity	monotonicity	NOUN
ejpam-2044	299	9	of	of	ADP
ejpam-2044	299	10	function	function	NOUN
ejpam-2044	299	11	u	u	PROPN
ejpam-2044	299	12	(	(	PUNCT
ejpam-2044	299	13	·	·	PUNCT
ejpam-2044	299	14	)	)	PUNCT
ejpam-2044	299	15	and	and	CCONJ
ejpam-2044	299	16	continuity	continuity	NOUN
ejpam-2044	299	17	of	of	ADP
ejpam-2044	299	18	function	function	NOUN
ejpam-2044	299	19	u′	u′	PROPN
ejpam-2044	299	20	(	(	PUNCT
ejpam-2044	299	21	·	·	PUNCT
ejpam-2044	299	22	)	)	PUNCT
ejpam-2044	299	23	,	,	PUNCT
ejpam-2044	299	24	since	since	SCONJ
ejpam-2044	299	25	u	u	NOUN
ejpam-2044	299	26	(	(	PUNCT
ejpam-2044	299	27	·	·	PUNCT
ejpam-2044	299	28	)	)	PUNCT
ejpam-2044	299	29	∈	∈	PROPN
ejpam-2044	299	30	c2(r	c2(r	PROPN
ejpam-2044	299	31	)	)	PUNCT
ejpam-2044	299	32	,	,	PUNCT
ejpam-2044	299	33	using	use	VERB
ejpam-2044	299	34	the	the	DET
ejpam-2044	299	35	equation	equation	NOUN
ejpam-2044	299	36	(	(	PUNCT
ejpam-2044	299	37	57	57	NUM
ejpam-2044	299	38	)	)	PUNCT
ejpam-2044	299	39	we	we	PRON
ejpam-2044	299	40	may	may	AUX
ejpam-2044	299	41	conclude	conclude	VERB
ejpam-2044	299	42	that	that	PRON
ejpam-2044	299	43	u′(x	u′(x	ADP
ejpam-2044	299	44	)	)	PUNCT
ejpam-2044	299	45	=	=	SYM
ejpam-2044	299	46	a	a	DET
ejpam-2044	299	47	>	>	X
ejpam-2044	299	48	0	0	NUM
ejpam-2044	299	49	,	,	PUNCT
ejpam-2044	299	50	for	for	SCONJ
ejpam-2044	299	51	x	x	PROPN
ejpam-2044	299	52	∈	∈	PROPN
ejpam-2044	299	53	r.	r.	NOUN
ejpam-2044	299	54	integration	integration	NOUN
ejpam-2044	299	55	yields	yield	VERB
ejpam-2044	299	56	u(x	u(x	NOUN
ejpam-2044	299	57	)	)	PUNCT
ejpam-2044	300	1	=	=	SYM
ejpam-2044	300	2	ax	ax	NOUN
ejpam-2044	300	3	+	+	CCONJ
ejpam-2044	300	4	b	b	NOUN
ejpam-2044	300	5	,	,	PUNCT
ejpam-2044	300	6	for	for	ADP
ejpam-2044	300	7	x	x	PROPN
ejpam-2044	300	8	∈	∈	PROPN
ejpam-2044	300	9	r	r	NOUN
ejpam-2044	300	10	,	,	PUNCT
ejpam-2044	300	11	and	and	CCONJ
ejpam-2044	300	12	constant	constant	ADJ
ejpam-2044	300	13	a	a	DET
ejpam-2044	300	14	>	>	X
ejpam-2044	300	15	0	0	X
ejpam-2044	300	16	.	.	PUNCT
ejpam-2044	301	1	let	let	VERB
ejpam-2044	301	2	us	we	PRON
ejpam-2044	301	3	give	give	VERB
ejpam-2044	301	4	also	also	ADV
ejpam-2044	301	5	a	a	DET
ejpam-2044	301	6	geometrical	geometrical	ADJ
ejpam-2044	301	7	interpretation	interpretation	NOUN
ejpam-2044	301	8	showing	show	VERB
ejpam-2044	301	9	that	that	SCONJ
ejpam-2044	301	10	non	non	ADJ
ejpam-2044	301	11	-	-	ADJ
ejpam-2044	301	12	linear	linear	ADJ
ejpam-2044	301	13	customer	customer	NOUN
ejpam-2044	301	14	utility	utility	NOUN
ejpam-2044	301	15	functions	function	NOUN
ejpam-2044	301	16	will	will	AUX
ejpam-2044	301	17	not	not	PART
ejpam-2044	301	18	satisfy	satisfy	VERB
ejpam-2044	301	19	equation	equation	NOUN
ejpam-2044	301	20	(	(	PUNCT
ejpam-2044	301	21	56	56	NUM
ejpam-2044	301	22	)	)	PUNCT
ejpam-2044	301	23	.	.	PUNCT
ejpam-2044	302	1	let	let	VERB
ejpam-2044	302	2	us	we	PRON
ejpam-2044	302	3	consider	consider	VERB
ejpam-2044	302	4	two	two	NUM
ejpam-2044	302	5	triangles	triangle	NOUN
ejpam-2044	302	6	:	:	PUNCT
ejpam-2044	302	7	the	the	DET
ejpam-2044	302	8	first	first	ADJ
ejpam-2044	302	9	one	one	NOUN
ejpam-2044	302	10	will	will	AUX
ejpam-2044	302	11	be	be	AUX
ejpam-2044	302	12	formed	form	VERB
ejpam-2044	302	13	by	by	ADP
ejpam-2044	302	14	the	the	DET
ejpam-2044	302	15	points	point	NOUN
ejpam-2044	302	16	(	(	PUNCT
ejpam-2044	302	17	ω−	ω−	PROPN
ejpam-2044	302	18	t	t	PROPN
ejpam-2044	302	19	,	,	PUNCT
ejpam-2044	302	20	u(ω−	u(ω−	PROPN
ejpam-2044	302	21	t	t	PROPN
ejpam-2044	302	22	)	)	PUNCT
ejpam-2044	302	23	)	)	PUNCT
ejpam-2044	302	24	,	,	PUNCT
ejpam-2044	302	25	(	(	PUNCT
ejpam-2044	302	26	ω	ω	NOUN
ejpam-2044	302	27	,	,	PUNCT
ejpam-2044	302	28	u(ω−	u(ω−	PROPN
ejpam-2044	302	29	t	t	PROPN
ejpam-2044	302	30	)	)	PUNCT
ejpam-2044	302	31	)	)	PUNCT
ejpam-2044	302	32	,	,	PUNCT
ejpam-2044	302	33	(	(	PUNCT
ejpam-2044	302	34	ω	ω	NOUN
ejpam-2044	302	35	,	,	PUNCT
ejpam-2044	302	36	u(ω	u(ω	PROPN
ejpam-2044	302	37	)	)	PUNCT
ejpam-2044	302	38	)	)	PUNCT
ejpam-2044	302	39	and	and	CCONJ
ejpam-2044	302	40	the	the	DET
ejpam-2044	302	41	second	second	ADJ
ejpam-2044	302	42	one	one	NOUN
ejpam-2044	302	43	will	will	AUX
ejpam-2044	302	44	be	be	AUX
ejpam-2044	302	45	formed	form	VERB
ejpam-2044	302	46	by	by	ADP
ejpam-2044	302	47	the	the	DET
ejpam-2044	302	48	points	point	NOUN
ejpam-2044	302	49	(	(	PUNCT
ejpam-2044	302	50	ω−θt	ω−θt	ADJ
ejpam-2044	302	51	,	,	PUNCT
ejpam-2044	302	52	u(ω−θt	u(ω−θt	NOUN
ejpam-2044	302	53	)	)	PUNCT
ejpam-2044	302	54	)	)	PUNCT
ejpam-2044	302	55	,	,	PUNCT
ejpam-2044	302	56	(	(	PUNCT
ejpam-2044	302	57	ω	ω	NOUN
ejpam-2044	302	58	,	,	PUNCT
ejpam-2044	302	59	u(ω−θt	u(ω−θt	PROPN
ejpam-2044	302	60	)	)	PUNCT
ejpam-2044	302	61	)	)	PUNCT
ejpam-2044	302	62	,	,	PUNCT
ejpam-2044	302	63	(	(	PUNCT
ejpam-2044	302	64	ω	ω	NOUN
ejpam-2044	302	65	,	,	PUNCT
ejpam-2044	302	66	u(ω	u(ω	PROPN
ejpam-2044	302	67	)	)	PUNCT
ejpam-2044	302	68	)	)	PUNCT
ejpam-2044	302	69	.	.	PUNCT
ejpam-2044	303	1	observe	observe	VERB
ejpam-2044	303	2	that	that	SCONJ
ejpam-2044	303	3	both	both	DET
ejpam-2044	303	4	triangles	triangle	NOUN
ejpam-2044	303	5	are	be	AUX
ejpam-2044	303	6	right	right	ADJ
ejpam-2044	303	7	-	-	PUNCT
ejpam-2044	303	8	angled	angle	VERB
ejpam-2044	303	9	triangles	triangle	NOUN
ejpam-2044	303	10	,	,	PUNCT
ejpam-2044	303	11	they	they	PRON
ejpam-2044	303	12	have	have	VERB
ejpam-2044	303	13	a	a	DET
ejpam-2044	303	14	common	common	ADJ
ejpam-2044	303	15	vertex	vertex	NOUN
ejpam-2044	303	16	at	at	ADP
ejpam-2044	303	17	the	the	DET
ejpam-2044	303	18	point	point	NOUN
ejpam-2044	303	19	(	(	PUNCT
ejpam-2044	303	20	ω	ω	NOUN
ejpam-2044	303	21	,	,	PUNCT
ejpam-2044	303	22	u(ω	u(ω	PROPN
ejpam-2044	303	23	)	)	PUNCT
ejpam-2044	303	24	)	)	PUNCT
ejpam-2044	303	25	,	,	PUNCT
ejpam-2044	303	26	and	and	CCONJ
ejpam-2044	303	27	,	,	PUNCT
ejpam-2044	303	28	moreover	moreover	ADV
ejpam-2044	303	29	,	,	PUNCT
ejpam-2044	303	30	the	the	DET
ejpam-2044	303	31	points	point	NOUN
ejpam-2044	303	32	(	(	PUNCT
ejpam-2044	303	33	ω	ω	NOUN
ejpam-2044	303	34	,	,	PUNCT
ejpam-2044	303	35	u(ω	u(ω	PROPN
ejpam-2044	303	36	)	)	PUNCT
ejpam-2044	303	37	)	)	PUNCT
ejpam-2044	303	38	,	,	PUNCT
ejpam-2044	303	39	(	(	PUNCT
ejpam-2044	303	40	ω	ω	NOUN
ejpam-2044	303	41	,	,	PUNCT
ejpam-2044	303	42	u(ω−	u(ω−	PROPN
ejpam-2044	303	43	t	t	PROPN
ejpam-2044	303	44	)	)	PUNCT
ejpam-2044	303	45	)	)	PUNCT
ejpam-2044	303	46	,	,	PUNCT
ejpam-2044	303	47	and	and	CCONJ
ejpam-2044	303	48	(	(	PUNCT
ejpam-2044	303	49	ω	ω	PROPN
ejpam-2044	303	50	,	,	PUNCT
ejpam-2044	303	51	u(ω−θt	u(ω−θt	PROPN
ejpam-2044	303	52	)	)	PUNCT
ejpam-2044	303	53	)	)	PUNCT
ejpam-2044	303	54	lie	lie	VERB
ejpam-2044	303	55	on	on	ADP
ejpam-2044	303	56	the	the	DET
ejpam-2044	303	57	same	same	ADJ
ejpam-2044	303	58	straight	straight	ADJ
ejpam-2044	303	59	line	line	NOUN
ejpam-2044	303	60	.	.	PUNCT
ejpam-2044	304	1	with	with	ADP
ejpam-2044	304	2	out	out	ADP
ejpam-2044	304	3	of	of	ADP
ejpam-2044	304	4	loss	loss	NOUN
ejpam-2044	304	5	of	of	ADP
ejpam-2044	304	6	generality	generality	NOUN
ejpam-2044	304	7	equation	equation	NOUN
ejpam-2044	304	8	(	(	PUNCT
ejpam-2044	304	9	56	56	NUM
ejpam-2044	304	10	)	)	PUNCT
ejpam-2044	304	11	can	can	AUX
ejpam-2044	304	12	be	be	AUX
ejpam-2044	304	13	rewritten	rewrite	VERB
ejpam-2044	304	14	in	in	ADP
ejpam-2044	304	15	the	the	DET
ejpam-2044	304	16	following	follow	VERB
ejpam-2044	304	17	way	way	NOUN
ejpam-2044	304	18	u(ω)−	u(ω)−	PROPN
ejpam-2044	304	19	u(ω−	u(ω−	PROPN
ejpam-2044	304	20	t	t	NOUN
ejpam-2044	304	21	)	)	PUNCT
ejpam-2044	304	22	ω−	ω−	VERB
ejpam-2044	304	23	(	(	PUNCT
ejpam-2044	304	24	ω−	ω−	PROPN
ejpam-2044	304	25	t	t	PROPN
ejpam-2044	304	26	)	)	PUNCT
ejpam-2044	304	27	=	=	SYM
ejpam-2044	305	1	u(ω)−	u(ω)−	PROPN
ejpam-2044	305	2	u(ω−θt	u(ω−θt	PROPN
ejpam-2044	305	3	)	)	PUNCT
ejpam-2044	306	1	ω−	ω−	VERB
ejpam-2044	306	2	(	(	PUNCT
ejpam-2044	306	3	ω−θt	ω−θt	NUM
ejpam-2044	306	4	)	)	PUNCT
ejpam-2044	306	5	.	.	PUNCT
ejpam-2044	307	1	(	(	PUNCT
ejpam-2044	307	2	58	58	NUM
ejpam-2044	307	3	)	)	PUNCT
ejpam-2044	307	4	geometrically	geometrically	ADV
ejpam-2044	307	5	,	,	PUNCT
ejpam-2044	307	6	equation	equation	NOUN
ejpam-2044	307	7	(	(	PUNCT
ejpam-2044	307	8	58	58	NUM
ejpam-2044	307	9	)	)	PUNCT
ejpam-2044	307	10	can	can	AUX
ejpam-2044	307	11	be	be	AUX
ejpam-2044	307	12	interpreted	interpret	VERB
ejpam-2044	307	13	as	as	SCONJ
ejpam-2044	307	14	follows	follow	VERB
ejpam-2044	307	15	:	:	PUNCT
ejpam-2044	307	16	ratio	ratio	NOUN
ejpam-2044	307	17	of	of	ADP
ejpam-2044	307	18	the	the	DET
ejpam-2044	307	19	catheti	catheti	NOUN
ejpam-2044	307	20	in	in	ADP
ejpam-2044	307	21	one	one	NUM
ejpam-2044	307	22	of	of	ADP
ejpam-2044	307	23	the	the	DET
ejpam-2044	307	24	triangles	triangle	NOUN
ejpam-2044	307	25	is	be	AUX
ejpam-2044	307	26	equal	equal	ADJ
ejpam-2044	307	27	to	to	ADP
ejpam-2044	307	28	ratio	ratio	NOUN
ejpam-2044	307	29	of	of	ADP
ejpam-2044	307	30	the	the	DET
ejpam-2044	307	31	catheti	catheti	NOUN
ejpam-2044	307	32	in	in	ADP
ejpam-2044	307	33	the	the	DET
ejpam-2044	307	34	other	other	ADJ
ejpam-2044	307	35	triangle	triangle	NOUN
ejpam-2044	307	36	,	,	PUNCT
ejpam-2044	307	37	and	and	CCONJ
ejpam-2044	307	38	hence	hence	ADV
ejpam-2044	307	39	our	our	PRON
ejpam-2044	307	40	two	two	NUM
ejpam-2044	307	41	considered	consider	VERB
ejpam-2044	307	42	triangles	triangle	NOUN
ejpam-2044	307	43	are	be	AUX
ejpam-2044	307	44	similar	similar	ADJ
ejpam-2044	307	45	triangles	triangle	NOUN
ejpam-2044	307	46	.	.	PUNCT
ejpam-2044	308	1	due	due	ADP
ejpam-2044	308	2	to	to	ADP
ejpam-2044	308	3	the	the	DET
ejpam-2044	308	4	common	common	ADJ
ejpam-2044	308	5	vertex	vertex	NOUN
ejpam-2044	308	6	,	,	PUNCT
ejpam-2044	308	7	catheti	catheti	ADJ
ejpam-2044	308	8	which	which	PRON
ejpam-2044	308	9	lie	lie	VERB
ejpam-2044	308	10	on	on	ADP
ejpam-2044	308	11	a	a	DET
ejpam-2044	308	12	common	common	ADJ
ejpam-2044	308	13	straight	straight	ADJ
ejpam-2044	308	14	line	line	NOUN
ejpam-2044	308	15	,	,	PUNCT
ejpam-2044	308	16	and	and	CCONJ
ejpam-2044	308	17	vertexes	vertex	NOUN
ejpam-2044	308	18	which	which	PRON
ejpam-2044	308	19	lie	lie	VERB
ejpam-2044	308	20	on	on	ADP
ejpam-2044	308	21	the	the	DET
ejpam-2044	308	22	same	same	ADJ
ejpam-2044	308	23	half	half	NOUN
ejpam-2044	308	24	plane	plane	NOUN
ejpam-2044	308	25	with	with	ADP
ejpam-2044	308	26	respect	respect	NOUN
ejpam-2044	308	27	to	to	ADP
ejpam-2044	308	28	the	the	DET
ejpam-2044	308	29	mentioned	mention	VERB
ejpam-2044	308	30	line	line	NOUN
ejpam-2044	308	31	,	,	PUNCT
ejpam-2044	308	32	we	we	PRON
ejpam-2044	308	33	conclude	conclude	VERB
ejpam-2044	308	34	that	that	SCONJ
ejpam-2044	308	35	hypotenuses	hypotenuse	NOUN
ejpam-2044	308	36	will	will	AUX
ejpam-2044	308	37	also	also	ADV
ejpam-2044	308	38	lie	lie	VERB
ejpam-2044	308	39	on	on	ADP
ejpam-2044	308	40	a	a	DET
ejpam-2044	308	41	common	common	ADJ
ejpam-2044	308	42	straight	straight	ADJ
ejpam-2044	308	43	line	line	NOUN
ejpam-2044	308	44	;	;	PUNCT
ejpam-2044	308	45	in	in	ADP
ejpam-2044	308	46	other	other	ADJ
ejpam-2044	308	47	words	word	NOUN
ejpam-2044	308	48	,	,	PUNCT
ejpam-2044	308	49	the	the	DET
ejpam-2044	308	50	m.	m.	NOUN
ejpam-2044	308	51	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	308	52	,	,	PUNCT
ejpam-2044	308	53	v.	v.	ADP
ejpam-2044	308	54	drozdenko	drozdenko	PROPN
ejpam-2044	308	55	/	/	SYM
ejpam-2044	308	56	eur	eur	PROPN
ejpam-2044	308	57	.	.	PUNCT
ejpam-2044	309	1	j.	j.	PROPN
ejpam-2044	309	2	pure	pure	PROPN
ejpam-2044	309	3	appl	appl	PROPN
ejpam-2044	309	4	.	.	PROPN
ejpam-2044	309	5	math	math	PROPN
ejpam-2044	309	6	,	,	PUNCT
ejpam-2044	309	7	7	7	NUM
ejpam-2044	309	8	(	(	PUNCT
ejpam-2044	309	9	2014	2014	NUM
ejpam-2044	309	10	)	)	PUNCT
ejpam-2044	309	11	,	,	PUNCT
ejpam-2044	309	12	267	267	X
ejpam-2044	309	13	-	-	SYM
ejpam-2044	309	14	288	288	NUM
ejpam-2044	309	15	281	281	NUM
ejpam-2044	309	16	points	point	NOUN
ejpam-2044	309	17	(	(	PUNCT
ejpam-2044	309	18	ω	ω	PROPN
ejpam-2044	309	19	−θt	−θt	PROPN
ejpam-2044	309	20	,	,	PUNCT
ejpam-2044	309	21	u(ω	u(ω	PROPN
ejpam-2044	309	22	−θt	−θt	PROPN
ejpam-2044	309	23	)	)	PUNCT
ejpam-2044	309	24	)	)	PUNCT
ejpam-2044	309	25	,	,	PUNCT
ejpam-2044	309	26	for	for	ADP
ejpam-2044	309	27	any	any	DET
ejpam-2044	309	28	initial	initial	ADJ
ejpam-2044	309	29	capital	capital	NOUN
ejpam-2044	309	30	ω	ω	PROPN
ejpam-2044	309	31	,	,	PUNCT
ejpam-2044	309	32	any	any	DET
ejpam-2044	309	33	non	non	ADJ
ejpam-2044	309	34	-	-	ADJ
ejpam-2044	309	35	zero	zero	NUM
ejpam-2044	309	36	t	t	NOUN
ejpam-2044	309	37	,	,	PUNCT
ejpam-2044	309	38	and	and	CCONJ
ejpam-2044	309	39	every	every	DET
ejpam-2044	309	40	θ	θ	X
ejpam-2044	309	41	>	>	X
ejpam-2044	309	42	0	0	NUM
ejpam-2044	309	43	,	,	PUNCT
ejpam-2044	309	44	will	will	AUX
ejpam-2044	309	45	form	form	VERB
ejpam-2044	309	46	a	a	DET
ejpam-2044	309	47	straight	straight	ADJ
ejpam-2044	309	48	line	line	NOUN
ejpam-2044	309	49	.	.	PUNCT
ejpam-2044	310	1	so	so	ADV
ejpam-2044	310	2	,	,	PUNCT
ejpam-2044	310	3	we	we	PRON
ejpam-2044	310	4	can	can	AUX
ejpam-2044	310	5	conclude	conclude	VERB
ejpam-2044	310	6	that	that	SCONJ
ejpam-2044	310	7	the	the	DET
ejpam-2044	310	8	customer	customer	NOUN
ejpam-2044	310	9	’s	’s	PART
ejpam-2044	310	10	utility	utility	NOUN
ejpam-2044	310	11	function	function	NOUN
ejpam-2044	310	12	u(x	u(x	NOUN
ejpam-2044	310	13	)	)	PUNCT
ejpam-2044	310	14	is	be	AUX
ejpam-2044	310	15	a	a	DET
ejpam-2044	310	16	linear	linear	ADJ
ejpam-2044	310	17	function	function	NOUN
ejpam-2044	310	18	,	,	PUNCT
ejpam-2044	310	19	i.e.	i.e.	X
ejpam-2044	310	20	,	,	PUNCT
ejpam-2044	310	21	a	a	DET
ejpam-2044	310	22	function	function	NOUN
ejpam-2044	310	23	of	of	ADP
ejpam-2044	310	24	the	the	DET
ejpam-2044	310	25	form	form	NOUN
ejpam-2044	310	26	u(x	u(x	VERB
ejpam-2044	310	27	)	)	PUNCT
ejpam-2044	311	1	=	=	SYM
ejpam-2044	311	2	ax	ax	NOUN
ejpam-2044	311	3	+	+	PROPN
ejpam-2044	311	4	b.	b.	PROPN
ejpam-2044	311	5	initial	initial	ADJ
ejpam-2044	311	6	assumption	assumption	NOUN
ejpam-2044	311	7	of	of	ADP
ejpam-2044	311	8	positivity	positivity	NOUN
ejpam-2044	311	9	of	of	ADP
ejpam-2044	311	10	first	first	ADJ
ejpam-2044	311	11	derivative	derivative	NOUN
ejpam-2044	311	12	of	of	ADP
ejpam-2044	311	13	the	the	DET
ejpam-2044	311	14	function	function	NOUN
ejpam-2044	311	15	u(x	u(x	NOUN
ejpam-2044	311	16	)	)	PUNCT
ejpam-2044	311	17	gives	give	VERB
ejpam-2044	311	18	us	we	PRON
ejpam-2044	311	19	additional	additional	ADJ
ejpam-2044	311	20	restriction	restriction	NOUN
ejpam-2044	311	21	on	on	ADP
ejpam-2044	311	22	the	the	DET
ejpam-2044	311	23	parameter	parameter	NOUN
ejpam-2044	311	24	a	a	DET
ejpam-2044	311	25	:	:	PUNCT
ejpam-2044	311	26	parameter	parameter	NOUN
ejpam-2044	311	27	a	a	PRON
ejpam-2044	311	28	must	must	AUX
ejpam-2044	311	29	be	be	AUX
ejpam-2044	311	30	a	a	DET
ejpam-2044	311	31	strictly	strictly	ADV
ejpam-2044	311	32	positive	positive	ADJ
ejpam-2044	311	33	constant	constant	ADJ
ejpam-2044	311	34	.	.	PUNCT
ejpam-2044	312	1	this	this	PRON
ejpam-2044	312	2	completes	complete	VERB
ejpam-2044	312	3	the	the	DET
ejpam-2044	312	4	proof	proof	NOUN
ejpam-2044	312	5	of	of	ADP
ejpam-2044	312	6	theorem	theorem	NOUN
ejpam-2044	312	7	4	4	NUM
ejpam-2044	312	8	.	.	PUNCT
ejpam-2044	312	9	since	since	SCONJ
ejpam-2044	312	10	initial	initial	ADJ
ejpam-2044	312	11	capital	capital	NOUN
ejpam-2044	312	12	used	use	VERB
ejpam-2044	312	13	in	in	ADP
ejpam-2044	312	14	the	the	DET
ejpam-2044	312	15	proof	proof	NOUN
ejpam-2044	312	16	of	of	ADP
ejpam-2044	312	17	theorem	theorem	ADJ
ejpam-2044	312	18	4	4	NUM
ejpam-2044	312	19	was	be	AUX
ejpam-2044	312	20	chosen	choose	VERB
ejpam-2044	312	21	arbitrary	arbitrary	ADJ
ejpam-2044	312	22	and	and	CCONJ
ejpam-2044	312	23	no	no	DET
ejpam-2044	312	24	restrictions	restriction	NOUN
ejpam-2044	312	25	on	on	ADP
ejpam-2044	312	26	customer	customer	NOUN
ejpam-2044	312	27	’s	’s	PART
ejpam-2044	312	28	initial	initial	ADJ
ejpam-2044	312	29	capital	capital	NOUN
ejpam-2044	312	30	were	be	AUX
ejpam-2044	312	31	imposed	impose	VERB
ejpam-2044	312	32	,	,	PUNCT
ejpam-2044	312	33	then	then	ADV
ejpam-2044	312	34	we	we	PRON
ejpam-2044	312	35	can	can	AUX
ejpam-2044	312	36	formulate	formulate	VERB
ejpam-2044	312	37	the	the	DET
ejpam-2044	312	38	following	follow	VERB
ejpam-2044	312	39	corollary	corollary	NOUN
ejpam-2044	312	40	to	to	ADP
ejpam-2044	312	41	theorem	theorem	ADJ
ejpam-2044	312	42	4	4	NUM
ejpam-2044	312	43	.	.	PUNCT
ejpam-2044	312	44	corollary	corollary	ADJ
ejpam-2044	312	45	2	2	NUM
ejpam-2044	312	46	.	.	PUNCT
ejpam-2044	312	47	customer	customer	NOUN
ejpam-2044	312	48	zero	zero	NUM
ejpam-2044	312	49	utility	utility	NOUN
ejpam-2044	312	50	premium	premium	NOUN
ejpam-2044	312	51	calculation	calculation	NOUN
ejpam-2044	312	52	principle	principle	NOUN
ejpam-2044	312	53	possesses	possess	VERB
ejpam-2044	312	54	scale	scale	NOUN
ejpam-2044	312	55	invariance	invariance	NOUN
ejpam-2044	312	56	property	property	NOUN
ejpam-2044	312	57	if	if	SCONJ
ejpam-2044	312	58	and	and	CCONJ
ejpam-2044	312	59	only	only	ADV
ejpam-2044	312	60	if	if	SCONJ
ejpam-2044	312	61	u(x	u(x	NOUN
ejpam-2044	312	62	)	)	PUNCT
ejpam-2044	312	63	=	=	SYM
ejpam-2044	312	64	ax+b	ax+b	PROPN
ejpam-2044	312	65	,	,	PUNCT
ejpam-2044	312	66	for	for	ADP
ejpam-2044	312	67	a	a	DET
ejpam-2044	312	68	>	>	X
ejpam-2044	312	69	0	0	NUM
ejpam-2044	312	70	,	,	PUNCT
ejpam-2044	312	71	i.e.	i.e.	X
ejpam-2044	312	72	,	,	PUNCT
ejpam-2044	312	73	only	only	ADV
ejpam-2044	312	74	in	in	ADP
ejpam-2044	312	75	the	the	DET
ejpam-2044	312	76	case	case	NOUN
ejpam-2044	312	77	when	when	SCONJ
ejpam-2044	312	78	it	it	PRON
ejpam-2044	312	79	coincides	coincide	VERB
ejpam-2044	312	80	with	with	ADP
ejpam-2044	312	81	net	net	ADJ
ejpam-2044	312	82	premium	premium	NOUN
ejpam-2044	312	83	principle	principle	NOUN
ejpam-2044	312	84	.	.	PUNCT
ejpam-2044	313	1	in	in	ADP
ejpam-2044	313	2	the	the	DET
ejpam-2044	313	3	case	case	NOUN
ejpam-2044	313	4	when	when	SCONJ
ejpam-2044	313	5	customer	customer	NOUN
ejpam-2044	313	6	zero	zero	NUM
ejpam-2044	313	7	utility	utility	NOUN
ejpam-2044	313	8	premium	premium	NOUN
ejpam-2044	313	9	calculation	calculation	NOUN
ejpam-2044	313	10	principle	principle	NOUN
ejpam-2044	313	11	is	be	AUX
ejpam-2044	313	12	applied	apply	VERB
ejpam-2044	313	13	to	to	ADP
ejpam-2044	313	14	a	a	DET
ejpam-2044	313	15	special	special	ADJ
ejpam-2044	313	16	class	class	NOUN
ejpam-2044	313	17	of	of	ADP
ejpam-2044	313	18	risks	risk	NOUN
ejpam-2044	313	19	,	,	PUNCT
ejpam-2044	313	20	it	it	PRON
ejpam-2044	313	21	is	be	AUX
ejpam-2044	313	22	enough	enough	ADJ
ejpam-2044	313	23	to	to	PART
ejpam-2044	313	24	define	define	VERB
ejpam-2044	313	25	the	the	DET
ejpam-2044	313	26	utility	utility	NOUN
ejpam-2044	313	27	function	function	NOUN
ejpam-2044	313	28	u(x	u(x	NOUN
ejpam-2044	313	29	)	)	PUNCT
ejpam-2044	313	30	on	on	ADP
ejpam-2044	313	31	a	a	DET
ejpam-2044	313	32	subset	subset	NOUN
ejpam-2044	313	33	a	a	DET
ejpam-2044	313	34	⊂	⊂	X
ejpam-2044	313	35	r	r	NOUN
ejpam-2044	313	36	preserving	preserve	VERB
ejpam-2044	313	37	monotonicity	monotonicity	NOUN
ejpam-2044	313	38	and	and	CCONJ
ejpam-2044	313	39	concavity	concavity	NOUN
ejpam-2044	313	40	properties	property	NOUN
ejpam-2044	313	41	,	,	PUNCT
ejpam-2044	313	42	i.e.	i.e.	X
ejpam-2044	313	43	,	,	PUNCT
ejpam-2044	313	44	u(x	u(x	NOUN
ejpam-2044	313	45	)	)	PUNCT
ejpam-2044	313	46	must	must	AUX
ejpam-2044	313	47	be	be	AUX
ejpam-2044	313	48	such	such	ADJ
ejpam-2044	313	49	that	that	PRON
ejpam-2044	313	50	u′(x	u′(x	X
ejpam-2044	313	51	)	)	PUNCT
ejpam-2044	313	52	>	>	X
ejpam-2044	313	53	0	0	PUNCT
ejpam-2044	314	1	and	and	CCONJ
ejpam-2044	314	2	u′′(x	u′′(x	NOUN
ejpam-2044	314	3	)	)	PUNCT
ejpam-2044	314	4	≤	≤	NOUN
ejpam-2044	314	5	0	0	NUM
ejpam-2044	315	1	for	for	ADP
ejpam-2044	315	2	all	all	DET
ejpam-2044	315	3	x	x	SYM
ejpam-2044	315	4	∈	∈	PROPN
ejpam-2044	315	5	a	a	PRON
ejpam-2044	315	6	,	,	PUNCT
ejpam-2044	315	7	and	and	CCONJ
ejpam-2044	315	8	,	,	PUNCT
ejpam-2044	315	9	moreover	moreover	ADV
ejpam-2044	315	10	,	,	PUNCT
ejpam-2044	315	11	equation	equation	NOUN
ejpam-2044	315	12	(	(	PUNCT
ejpam-2044	315	13	5	5	NUM
ejpam-2044	315	14	)	)	PUNCT
ejpam-2044	315	15	must	must	AUX
ejpam-2044	315	16	preserve	preserve	VERB
ejpam-2044	315	17	its	its	PRON
ejpam-2044	315	18	correct	correct	ADJ
ejpam-2044	315	19	mathematical	mathematical	ADJ
ejpam-2044	315	20	meaning	meaning	NOUN
ejpam-2044	315	21	for	for	ADP
ejpam-2044	315	22	all	all	DET
ejpam-2044	315	23	risks	risk	NOUN
ejpam-2044	315	24	from	from	ADP
ejpam-2044	315	25	the	the	DET
ejpam-2044	315	26	mentioned	mention	VERB
ejpam-2044	315	27	class	class	NOUN
ejpam-2044	315	28	.	.	PUNCT
ejpam-2044	316	1	it	it	PRON
ejpam-2044	316	2	is	be	AUX
ejpam-2044	316	3	interesting	interesting	ADJ
ejpam-2044	316	4	to	to	PART
ejpam-2044	316	5	see	see	VERB
ejpam-2044	316	6	that	that	SCONJ
ejpam-2044	316	7	in	in	ADP
ejpam-2044	316	8	the	the	DET
ejpam-2044	316	9	case	case	NOUN
ejpam-2044	316	10	of	of	ADP
ejpam-2044	316	11	subjecting	subject	VERB
ejpam-2044	316	12	of	of	ADP
ejpam-2044	316	13	customer	customer	NOUN
ejpam-2044	316	14	zero	zero	NUM
ejpam-2044	316	15	utility	utility	NOUN
ejpam-2044	316	16	premium	premium	NOUN
ejpam-2044	316	17	calculation	calculation	NOUN
ejpam-2044	316	18	principle	principle	NOUN
ejpam-2044	316	19	to	to	ADP
ejpam-2044	316	20	pricing	pricing	NOUN
ejpam-2044	316	21	of	of	ADP
ejpam-2044	316	22	only	only	ADV
ejpam-2044	316	23	strictly	strictly	ADV
ejpam-2044	316	24	positive	positive	ADJ
ejpam-2044	316	25	risks	risk	NOUN
ejpam-2044	316	26	the	the	DET
ejpam-2044	316	27	class	class	NOUN
ejpam-2044	316	28	of	of	ADP
ejpam-2044	316	29	the	the	DET
ejpam-2044	316	30	functions	function	NOUN
ejpam-2044	316	31	u(x	u(x	VERB
ejpam-2044	316	32	)	)	PUNCT
ejpam-2044	316	33	producing	produce	VERB
ejpam-2044	316	34	scale	scale	NOUN
ejpam-2044	316	35	invariant	invariant	ADJ
ejpam-2044	316	36	premiums	premium	NOUN
ejpam-2044	316	37	is	be	AUX
ejpam-2044	316	38	larger	large	ADJ
ejpam-2044	316	39	than	than	ADP
ejpam-2044	316	40	in	in	ADP
ejpam-2044	316	41	the	the	DET
ejpam-2044	316	42	general	general	ADJ
ejpam-2044	316	43	case	case	NOUN
ejpam-2044	316	44	.	.	PUNCT
ejpam-2044	317	1	we	we	PRON
ejpam-2044	317	2	believe	believe	VERB
ejpam-2044	317	3	that	that	SCONJ
ejpam-2044	317	4	this	this	DET
ejpam-2044	317	5	observation	observation	NOUN
ejpam-2044	317	6	deserves	deserve	VERB
ejpam-2044	317	7	to	to	PART
ejpam-2044	317	8	be	be	AUX
ejpam-2044	317	9	formulated	formulate	VERB
ejpam-2044	317	10	in	in	ADP
ejpam-2044	317	11	a	a	DET
ejpam-2044	317	12	form	form	NOUN
ejpam-2044	317	13	of	of	ADP
ejpam-2044	317	14	theorem	theorem	NOUN
ejpam-2044	317	15	.	.	PUNCT
ejpam-2044	318	1	the	the	DET
ejpam-2044	318	2	following	follow	VERB
ejpam-2044	318	3	theorem	theorem	NOUN
ejpam-2044	318	4	is	be	AUX
ejpam-2044	318	5	valid	valid	ADJ
ejpam-2044	318	6	only	only	ADV
ejpam-2044	318	7	for	for	ADP
ejpam-2044	318	8	customer	customer	NOUN
ejpam-2044	318	9	zero	zero	NUM
ejpam-2044	318	10	utility	utility	NOUN
ejpam-2044	318	11	principle	principle	NOUN
ejpam-2044	318	12	and	and	CCONJ
ejpam-2044	318	13	not	not	PART
ejpam-2044	318	14	for	for	ADP
ejpam-2044	318	15	customer	customer	NOUN
ejpam-2044	318	16	equivalent	equivalent	ADJ
ejpam-2044	318	17	utility	utility	NOUN
ejpam-2044	318	18	principle	principle	NOUN
ejpam-2044	318	19	.	.	PUNCT
ejpam-2044	319	1	theorem	theorem	ADJ
ejpam-2044	319	2	5	5	NUM
ejpam-2044	319	3	.	.	PUNCT
ejpam-2044	319	4	customer	customer	NOUN
ejpam-2044	319	5	zero	zero	NUM
ejpam-2044	319	6	utility	utility	NOUN
ejpam-2044	319	7	premium	premium	NOUN
ejpam-2044	319	8	calculation	calculation	NOUN
ejpam-2044	319	9	principle	principle	NOUN
ejpam-2044	319	10	subjected	subject	VERB
ejpam-2044	319	11	to	to	ADP
ejpam-2044	319	12	consideration	consideration	NOUN
ejpam-2044	319	13	of	of	ADP
ejpam-2044	319	14	only	only	ADV
ejpam-2044	319	15	strictly	strictly	ADV
ejpam-2044	319	16	positive	positive	ADJ
ejpam-2044	319	17	risks	risk	NOUN
ejpam-2044	319	18	possesses	possess	VERB
ejpam-2044	319	19	scale	scale	NOUN
ejpam-2044	319	20	invariance	invariance	NOUN
ejpam-2044	319	21	property	property	NOUN
ejpam-2044	319	22	if	if	SCONJ
ejpam-2044	319	23	and	and	CCONJ
ejpam-2044	319	24	only	only	ADV
ejpam-2044	319	25	if	if	SCONJ
ejpam-2044	319	26	u(x	u(x	NOUN
ejpam-2044	319	27	)	)	PUNCT
ejpam-2044	319	28	=	=	PUNCT
ejpam-2044	320	1	−a(−x)κ	−a(−x)κ	PUNCT
ejpam-2044	321	1	+	+	NUM
ejpam-2044	321	2	b	b	NOUN
ejpam-2044	321	3	,	,	PUNCT
ejpam-2044	321	4	for	for	ADP
ejpam-2044	321	5	a	a	DET
ejpam-2044	321	6	>	>	X
ejpam-2044	321	7	0	0	PUNCT
ejpam-2044	321	8	and	and	CCONJ
ejpam-2044	321	9	κ≥	κ≥	PROPN
ejpam-2044	321	10	1	1	NUM
ejpam-2044	321	11	,	,	PUNCT
ejpam-2044	321	12	defined	define	VERB
ejpam-2044	321	13	for	for	ADP
ejpam-2044	321	14	x	x	PROPN
ejpam-2044	321	15	∈	∈	PROPN
ejpam-2044	321	16	(	(	PUNCT
ejpam-2044	321	17	−∞	−∞	NOUN
ejpam-2044	321	18	,	,	PUNCT
ejpam-2044	321	19	0	0	NUM
ejpam-2044	321	20	)	)	PUNCT
ejpam-2044	321	21	.	.	PUNCT
ejpam-2044	322	1	observe	observe	VERB
ejpam-2044	322	2	that	that	SCONJ
ejpam-2044	322	3	for	for	SCONJ
ejpam-2044	322	4	the	the	DET
ejpam-2044	322	5	function	function	NOUN
ejpam-2044	322	6	u(x	u(x	VERB
ejpam-2044	322	7	)	)	PUNCT
ejpam-2044	323	1	=	=	SYM
ejpam-2044	323	2	−a(−x)κ+b	−a(−x)κ+b	PROPN
ejpam-2044	323	3	with	with	ADP
ejpam-2044	323	4	a	a	DET
ejpam-2044	323	5	>	>	X
ejpam-2044	323	6	0	0	NUM
ejpam-2044	323	7	and	and	CCONJ
ejpam-2044	323	8	κ	κ	X
ejpam-2044	323	9	>	>	X
ejpam-2044	323	10	1	1	NUM
ejpam-2044	323	11	condition	condition	NOUN
ejpam-2044	323	12	u′(x	u′(x	NOUN
ejpam-2044	323	13	)	)	PUNCT
ejpam-2044	323	14	>	>	X
ejpam-2044	323	15	0	0	NUM
ejpam-2044	323	16	violates	violate	VERB
ejpam-2044	323	17	at	at	ADP
ejpam-2044	323	18	the	the	DET
ejpam-2044	323	19	point	point	NOUN
ejpam-2044	323	20	x	x	PUNCT
ejpam-2044	323	21	=	=	SYM
ejpam-2044	323	22	0	0	NUM
ejpam-2044	323	23	,	,	PUNCT
ejpam-2044	323	24	therefore	therefore	ADV
ejpam-2044	323	25	,	,	PUNCT
ejpam-2044	323	26	statement	statement	NOUN
ejpam-2044	323	27	of	of	ADP
ejpam-2044	323	28	theorem	theorem	NOUN
ejpam-2044	323	29	5	5	NUM
ejpam-2044	323	30	does	do	AUX
ejpam-2044	323	31	not	not	PART
ejpam-2044	323	32	contradict	contradict	VERB
ejpam-2044	323	33	statement	statement	NOUN
ejpam-2044	323	34	of	of	ADP
ejpam-2044	323	35	theorem	theorem	ADJ
ejpam-2044	323	36	4	4	NUM
ejpam-2044	323	37	.	.	PUNCT
ejpam-2044	324	1	proof	proof	NOUN
ejpam-2044	324	2	.	.	PUNCT
ejpam-2044	325	1	since	since	SCONJ
ejpam-2044	325	2	in	in	ADP
ejpam-2044	325	3	the	the	DET
ejpam-2044	325	4	case	case	NOUN
ejpam-2044	325	5	of	of	ADP
ejpam-2044	325	6	strictly	strictly	ADV
ejpam-2044	325	7	positive	positive	ADJ
ejpam-2044	325	8	risk	risk	NOUN
ejpam-2044	325	9	x	x	VERB
ejpam-2044	325	10	we	we	PRON
ejpam-2044	325	11	get	get	VERB
ejpam-2044	325	12	e[x	e[x	NOUN
ejpam-2044	325	13	]	]	PUNCT
ejpam-2044	325	14	>	>	X
ejpam-2044	325	15	0	0	NUM
ejpam-2044	325	16	,	,	PUNCT
ejpam-2044	325	17	then	then	ADV
ejpam-2044	325	18	,	,	PUNCT
ejpam-2044	325	19	combining	combine	VERB
ejpam-2044	325	20	jensen	jensen	PROPN
ejpam-2044	325	21	inequality	inequality	PROPN
ejpam-2044	325	22	u(−e[x	u(−e[x	PROPN
ejpam-2044	325	23	]	]	PUNCT
ejpam-2044	325	24	)	)	PUNCT
ejpam-2044	325	25	≥	≥	PROPN
ejpam-2044	325	26	e[u(−x	e[u(−x	NOUN
ejpam-2044	325	27	)	)	PUNCT
ejpam-2044	325	28	]	]	PUNCT
ejpam-2044	325	29	with	with	ADP
ejpam-2044	325	30	definition	definition	NOUN
ejpam-2044	325	31	equation	equation	NOUN
ejpam-2044	325	32	(	(	PUNCT
ejpam-2044	325	33	5	5	NUM
ejpam-2044	325	34	)	)	PUNCT
ejpam-2044	325	35	,	,	PUNCT
ejpam-2044	325	36	we	we	PRON
ejpam-2044	325	37	see	see	VERB
ejpam-2044	325	38	that	that	DET
ejpam-2044	325	39	customer	customer	NOUN
ejpam-2044	325	40	zero	zero	NUM
ejpam-2044	325	41	utility	utility	NOUN
ejpam-2044	325	42	premium	premium	NOUN
ejpam-2044	325	43	calculation	calculation	NOUN
ejpam-2044	325	44	principle	principle	NOUN
ejpam-2044	325	45	will	will	AUX
ejpam-2044	325	46	be	be	AUX
ejpam-2044	325	47	well	well	ADV
ejpam-2044	325	48	-	-	PUNCT
ejpam-2044	325	49	defined	define	VERB
ejpam-2044	325	50	if	if	SCONJ
ejpam-2044	325	51	the	the	DET
ejpam-2044	325	52	function	function	NOUN
ejpam-2044	325	53	u(x	u(x	VERB
ejpam-2044	325	54	)	)	PUNCT
ejpam-2044	325	55	will	will	AUX
ejpam-2044	325	56	be	be	AUX
ejpam-2044	325	57	defined	define	VERB
ejpam-2044	325	58	just	just	ADV
ejpam-2044	325	59	for	for	SCONJ
ejpam-2044	325	60	x	x	PROPN
ejpam-2044	325	61	∈	∈	PROPN
ejpam-2044	325	62	(	(	PUNCT
ejpam-2044	325	63	−∞	−∞	NOUN
ejpam-2044	325	64	,	,	PUNCT
ejpam-2044	325	65	0	0	NUM
ejpam-2044	325	66	)	)	PUNCT
ejpam-2044	325	67	with	with	ADP
ejpam-2044	325	68	preservation	preservation	NOUN
ejpam-2044	325	69	of	of	ADP
ejpam-2044	325	70	monotonicity	monotonicity	NOUN
ejpam-2044	325	71	and	and	CCONJ
ejpam-2044	325	72	concavity	concavity	NOUN
ejpam-2044	325	73	assumptions	assumption	NOUN
ejpam-2044	325	74	,	,	PUNCT
ejpam-2044	325	75	i.e.	i.e.	X
ejpam-2044	325	76	,	,	PUNCT
ejpam-2044	325	77	the	the	DET
ejpam-2044	325	78	function	function	NOUN
ejpam-2044	325	79	u(x)must	u(x)must	AUX
ejpam-2044	325	80	be	be	AUX
ejpam-2044	325	81	defined	define	VERB
ejpam-2044	325	82	on	on	ADP
ejpam-2044	325	83	(	(	PUNCT
ejpam-2044	325	84	−∞	−∞	NOUN
ejpam-2044	325	85	,	,	PUNCT
ejpam-2044	325	86	0	0	NUM
ejpam-2044	325	87	)	)	PUNCT
ejpam-2044	325	88	such	such	ADJ
ejpam-2044	325	89	that	that	PRON
ejpam-2044	325	90	u′(x	u′(x	X
ejpam-2044	325	91	)	)	PUNCT
ejpam-2044	325	92	>	>	X
ejpam-2044	325	93	0	0	PUNCT
ejpam-2044	326	1	and	and	CCONJ
ejpam-2044	326	2	u′′(x)≤	u′′(x)≤	PROPN
ejpam-2044	326	3	0	0	NUM
ejpam-2044	326	4	for	for	ADP
ejpam-2044	326	5	all	all	DET
ejpam-2044	326	6	x	x	SYM
ejpam-2044	326	7	∈	∈	PROPN
ejpam-2044	326	8	(	(	PUNCT
ejpam-2044	326	9	−∞	−∞	NOUN
ejpam-2044	326	10	,	,	PUNCT
ejpam-2044	326	11	0	0	NUM
ejpam-2044	326	12	)	)	PUNCT
ejpam-2044	326	13	.	.	PUNCT
ejpam-2044	327	1	let	let	VERB
ejpam-2044	327	2	us	we	PRON
ejpam-2044	327	3	at	at	ADP
ejpam-2044	327	4	the	the	DET
ejpam-2044	327	5	beginning	beginning	NOUN
ejpam-2044	327	6	prove	prove	VERB
ejpam-2044	327	7	the	the	DET
ejpam-2044	327	8	sufficiency	sufficiency	NOUN
ejpam-2044	327	9	of	of	ADP
ejpam-2044	327	10	the	the	DET
ejpam-2044	327	11	statement	statement	NOUN
ejpam-2044	327	12	.	.	PUNCT
ejpam-2044	328	1	indeed	indeed	ADV
ejpam-2044	328	2	in	in	ADP
ejpam-2044	328	3	the	the	DET
ejpam-2044	328	4	case	case	NOUN
ejpam-2044	328	5	of	of	ADP
ejpam-2044	328	6	u(x	u(x	NOUN
ejpam-2044	328	7	)	)	PUNCT
ejpam-2044	328	8	=	=	PUNCT
ejpam-2044	329	1	−a(−x)κ	−a(−x)κ	PUNCT
ejpam-2044	330	1	+	+	NUM
ejpam-2044	330	2	b	b	NOUN
ejpam-2044	330	3	,	,	PUNCT
ejpam-2044	330	4	with	with	ADP
ejpam-2044	330	5	a	a	DET
ejpam-2044	330	6	>	>	X
ejpam-2044	330	7	0	0	NUM
ejpam-2044	330	8	and	and	CCONJ
ejpam-2044	330	9	κ	κ	X
ejpam-2044	330	10	≥	≥	NOUN
ejpam-2044	330	11	1	1	NUM
ejpam-2044	330	12	,	,	PUNCT
ejpam-2044	330	13	for	for	ADP
ejpam-2044	330	14	any	any	DET
ejpam-2044	330	15	strictly	strictly	ADV
ejpam-2044	330	16	positive	positive	ADJ
ejpam-2044	330	17	risk	risk	NOUN
ejpam-2044	330	18	x	x	X
ejpam-2044	330	19	equation	equation	NOUN
ejpam-2044	330	20	(	(	PUNCT
ejpam-2044	330	21	5	5	X
ejpam-2044	330	22	)	)	PUNCT
ejpam-2044	330	23	will	will	AUX
ejpam-2044	330	24	have	have	VERB
ejpam-2044	330	25	the	the	DET
ejpam-2044	330	26	following	follow	VERB
ejpam-2044	330	27	form	form	NOUN
ejpam-2044	330	28	−a(πc.z.u.[x	−a(πc.z.u.[x	PROPN
ejpam-2044	330	29	]	]	PUNCT
ejpam-2044	330	30	)	)	PUNCT
ejpam-2044	330	31	κ	κ	PROPN
ejpam-2044	331	1	+	+	CCONJ
ejpam-2044	331	2	b	b	NOUN
ejpam-2044	331	3	=	=	SYM
ejpam-2044	331	4	e[−ax	e[−ax	NOUN
ejpam-2044	331	5	κ	κ	NOUN
ejpam-2044	331	6	+	+	NOUN
ejpam-2044	331	7	b	b	X
ejpam-2044	331	8	]	]	X
ejpam-2044	331	9	=	=	PUNCT
ejpam-2044	331	10	−ae[x	−ae[x	PROPN
ejpam-2044	331	11	κ	κ	X
ejpam-2044	331	12	]	]	X
ejpam-2044	331	13	+	+	CCONJ
ejpam-2044	331	14	b	b	NUM
ejpam-2044	331	15	,	,	PUNCT
ejpam-2044	331	16	m.	m.	NOUN
ejpam-2044	331	17	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	331	18	,	,	PUNCT
ejpam-2044	331	19	v.	v.	ADP
ejpam-2044	331	20	drozdenko	drozdenko	PROPN
ejpam-2044	331	21	/	/	SYM
ejpam-2044	331	22	eur	eur	PROPN
ejpam-2044	331	23	.	.	PUNCT
ejpam-2044	332	1	j.	j.	PROPN
ejpam-2044	332	2	pure	pure	PROPN
ejpam-2044	332	3	appl	appl	PROPN
ejpam-2044	332	4	.	.	PROPN
ejpam-2044	332	5	math	math	PROPN
ejpam-2044	332	6	,	,	PUNCT
ejpam-2044	332	7	7	7	NUM
ejpam-2044	332	8	(	(	PUNCT
ejpam-2044	332	9	2014	2014	NUM
ejpam-2044	332	10	)	)	PUNCT
ejpam-2044	332	11	,	,	PUNCT
ejpam-2044	332	12	267	267	X
ejpam-2044	332	13	-	-	SYM
ejpam-2044	332	14	288	288	NUM
ejpam-2044	332	15	282	282	NUM
ejpam-2044	332	16	therefore	therefore	ADV
ejpam-2044	332	17	,	,	PUNCT
ejpam-2044	332	18	in	in	ADP
ejpam-2044	332	19	the	the	DET
ejpam-2044	332	20	considered	consider	VERB
ejpam-2044	332	21	case	case	NOUN
ejpam-2044	332	22	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	332	23	]	]	PUNCT
ejpam-2044	333	1	=	=	SYM
ejpam-2044	334	1	(	(	PUNCT
ejpam-2044	334	2	e[x	e[x	NUM
ejpam-2044	334	3	κ])1	κ])1	PROPN
ejpam-2044	334	4	/	/	SYM
ejpam-2044	334	5	κ	κ	NOUN
ejpam-2044	334	6	.	.	NOUN
ejpam-2044	335	1	on	on	ADP
ejpam-2044	335	2	the	the	DET
ejpam-2044	335	3	other	other	ADJ
ejpam-2044	335	4	hand	hand	NOUN
ejpam-2044	335	5	,	,	PUNCT
ejpam-2044	335	6	for	for	ADP
ejpam-2044	335	7	the	the	DET
ejpam-2044	335	8	same	same	ADJ
ejpam-2044	335	9	function	function	NOUN
ejpam-2044	335	10	u(x	u(x	NOUN
ejpam-2044	335	11	)	)	PUNCT
ejpam-2044	335	12	,	,	PUNCT
ejpam-2044	335	13	the	the	DET
ejpam-2044	335	14	same	same	ADJ
ejpam-2044	335	15	risk	risk	NOUN
ejpam-2044	335	16	x	x	X
ejpam-2044	335	17	,	,	PUNCT
ejpam-2044	335	18	and	and	CCONJ
ejpam-2044	335	19	any	any	DET
ejpam-2044	335	20	θ	θ	PROPN
ejpam-2044	335	21	>	>	PUNCT
ejpam-2044	335	22	0	0	NUM
ejpam-2044	335	23	,	,	PUNCT
ejpam-2044	335	24	from	from	ADP
ejpam-2044	335	25	the	the	DET
ejpam-2044	335	26	equation	equation	NOUN
ejpam-2044	335	27	(	(	PUNCT
ejpam-2044	335	28	5	5	X
ejpam-2044	335	29	)	)	PUNCT
ejpam-2044	335	30	it	it	PRON
ejpam-2044	335	31	follows	follow	VERB
ejpam-2044	335	32	−a(πc.z.u.[θx	−a(πc.z.u.[θx	NOUN
ejpam-2044	335	33	]	]	PUNCT
ejpam-2044	335	34	)	)	PUNCT
ejpam-2044	335	35	κ	κ	PROPN
ejpam-2044	335	36	+	+	PROPN
ejpam-2044	335	37	b	b	X
ejpam-2044	335	38	=	=	SYM
ejpam-2044	335	39	e[−a(θx	e[−a(θx	PROPN
ejpam-2044	335	40	)	)	PUNCT
ejpam-2044	335	41	κ	κ	PROPN
ejpam-2044	336	1	+	+	NOUN
ejpam-2044	336	2	b	b	X
ejpam-2044	336	3	]	]	X
ejpam-2044	336	4	=	=	SYM
ejpam-2044	336	5	−aθκe[x	−aθκe[x	NOUN
ejpam-2044	336	6	κ	κ	X
ejpam-2044	336	7	]	]	X
ejpam-2044	337	1	+	+	CCONJ
ejpam-2044	337	2	b	b	X
ejpam-2044	337	3	so	so	ADV
ejpam-2044	337	4	,	,	PUNCT
ejpam-2044	337	5	here	here	ADV
ejpam-2044	337	6	we	we	PRON
ejpam-2044	337	7	get	get	VERB
ejpam-2044	337	8	πc.z.u.[θx	πc.z.u.[θx	NOUN
ejpam-2044	337	9	]	]	PUNCT
ejpam-2044	337	10	=	=	PUNCT
ejpam-2044	337	11	θ(e[x	θ(e[x	X
ejpam-2044	337	12	κ])1	κ])1	PROPN
ejpam-2044	337	13	/	/	SYM
ejpam-2044	337	14	κ	κ	X
ejpam-2044	337	15	=	=	SYM
ejpam-2044	337	16	θπc.z.u.[x	θπc.z.u.[x	PROPN
ejpam-2044	337	17	]	]	PUNCT
ejpam-2044	337	18	,	,	PUNCT
ejpam-2044	337	19	and	and	CCONJ
ejpam-2044	337	20	as	as	SCONJ
ejpam-2044	337	21	we	we	PRON
ejpam-2044	337	22	see	see	VERB
ejpam-2044	337	23	,	,	PUNCT
ejpam-2044	337	24	customer	customer	NOUN
ejpam-2044	337	25	zero	zero	NUM
ejpam-2044	337	26	utility	utility	NOUN
ejpam-2044	337	27	premium	premium	NOUN
ejpam-2044	337	28	calculation	calculation	NOUN
ejpam-2044	337	29	principle	principle	NOUN
ejpam-2044	337	30	subjected	subject	VERB
ejpam-2044	337	31	to	to	ADP
ejpam-2044	337	32	consideration	consideration	NOUN
ejpam-2044	337	33	of	of	ADP
ejpam-2044	337	34	only	only	ADV
ejpam-2044	337	35	strictly	strictly	ADV
ejpam-2044	337	36	positive	positive	ADJ
ejpam-2044	337	37	risks	risk	NOUN
ejpam-2044	337	38	possesses	possess	VERB
ejpam-2044	337	39	scale	scale	NOUN
ejpam-2044	337	40	invariance	invariance	NOUN
ejpam-2044	337	41	property	property	NOUN
ejpam-2044	337	42	in	in	ADP
ejpam-2044	337	43	the	the	DET
ejpam-2044	337	44	case	case	NOUN
ejpam-2044	337	45	of	of	ADP
ejpam-2044	337	46	u(x	u(x	NOUN
ejpam-2044	337	47	)	)	PUNCT
ejpam-2044	337	48	=	=	PUNCT
ejpam-2044	338	1	−a(−x)κ	−a(−x)κ	PUNCT
ejpam-2044	339	1	+	+	NUM
ejpam-2044	339	2	b	b	NOUN
ejpam-2044	339	3	,	,	PUNCT
ejpam-2044	339	4	for	for	ADP
ejpam-2044	339	5	a	a	DET
ejpam-2044	339	6	>	>	X
ejpam-2044	339	7	0	0	PUNCT
ejpam-2044	339	8	and	and	CCONJ
ejpam-2044	339	9	κ≥	κ≥	PROPN
ejpam-2044	339	10	1	1	NUM
ejpam-2044	339	11	,	,	PUNCT
ejpam-2044	339	12	defined	define	VERB
ejpam-2044	339	13	for	for	ADP
ejpam-2044	339	14	x	x	PROPN
ejpam-2044	339	15	∈	∈	PROPN
ejpam-2044	339	16	(	(	PUNCT
ejpam-2044	339	17	−∞	−∞	NOUN
ejpam-2044	339	18	,	,	PUNCT
ejpam-2044	339	19	0	0	NUM
ejpam-2044	339	20	)	)	PUNCT
ejpam-2044	339	21	.	.	PUNCT
ejpam-2044	340	1	let	let	VERB
ejpam-2044	340	2	us	we	PRON
ejpam-2044	340	3	now	now	ADV
ejpam-2044	340	4	switch	switch	VERB
ejpam-2044	340	5	to	to	ADP
ejpam-2044	340	6	the	the	DET
ejpam-2044	340	7	statement	statement	NOUN
ejpam-2044	340	8	of	of	ADP
ejpam-2044	340	9	the	the	DET
ejpam-2044	340	10	necessity	necessity	NOUN
ejpam-2044	340	11	.	.	PUNCT
ejpam-2044	341	1	in	in	ADP
ejpam-2044	341	2	order	order	NOUN
ejpam-2044	341	3	to	to	PART
ejpam-2044	341	4	show	show	VERB
ejpam-2044	341	5	that	that	SCONJ
ejpam-2044	341	6	customer	customer	NOUN
ejpam-2044	341	7	zero	zero	NUM
ejpam-2044	341	8	utility	utility	NOUN
ejpam-2044	341	9	premium	premium	NOUN
ejpam-2044	341	10	calculation	calculation	NOUN
ejpam-2044	341	11	principle	principle	NOUN
ejpam-2044	341	12	subjected	subject	VERB
ejpam-2044	341	13	to	to	ADP
ejpam-2044	341	14	consideration	consideration	NOUN
ejpam-2044	341	15	of	of	ADP
ejpam-2044	341	16	only	only	ADV
ejpam-2044	341	17	strictly	strictly	ADV
ejpam-2044	341	18	positive	positive	ADJ
ejpam-2044	341	19	risks	risk	NOUN
ejpam-2044	341	20	with	with	ADP
ejpam-2044	341	21	all	all	DET
ejpam-2044	341	22	other	other	ADJ
ejpam-2044	341	23	types	type	NOUN
ejpam-2044	341	24	of	of	ADP
ejpam-2044	341	25	function	function	NOUN
ejpam-2044	341	26	u(x)will	u(x)will	NOUN
ejpam-2044	341	27	not	not	PART
ejpam-2044	341	28	possess	possess	VERB
ejpam-2044	341	29	scale	scale	NOUN
ejpam-2044	341	30	invariance	invariance	NOUN
ejpam-2044	341	31	property	property	NOUN
ejpam-2044	341	32	,	,	PUNCT
ejpam-2044	341	33	we	we	PRON
ejpam-2044	341	34	will	will	AUX
ejpam-2044	341	35	consider	consider	VERB
ejpam-2044	341	36	a	a	DET
ejpam-2044	341	37	risk	risk	NOUN
ejpam-2044	341	38	x	x	ADP
ejpam-2044	341	39	taking	take	VERB
ejpam-2044	341	40	values	value	NOUN
ejpam-2044	341	41	ε	ε	X
ejpam-2044	341	42	>	>	PUNCT
ejpam-2044	341	43	0	0	PUNCT
ejpam-2044	341	44	and	and	CCONJ
ejpam-2044	341	45	1	1	NUM
ejpam-2044	341	46	with	with	ADP
ejpam-2044	341	47	probabilities	probability	NOUN
ejpam-2044	341	48	p	p	NOUN
ejpam-2044	341	49	and	and	CCONJ
ejpam-2044	341	50	1−	1−	NUM
ejpam-2044	341	51	p	p	NOUN
ejpam-2044	341	52	respectively	respectively	ADV
ejpam-2044	341	53	.	.	PUNCT
ejpam-2044	342	1	being	be	AUX
ejpam-2044	342	2	a	a	DET
ejpam-2044	342	3	random	random	ADJ
ejpam-2044	342	4	function	function	NOUN
ejpam-2044	342	5	of	of	ADP
ejpam-2044	342	6	the	the	DET
ejpam-2044	342	7	parameters	parameter	NOUN
ejpam-2044	342	8	ε	ε	PROPN
ejpam-2044	342	9	and	and	CCONJ
ejpam-2044	342	10	p	p	X
ejpam-2044	342	11	,	,	PUNCT
ejpam-2044	342	12	the	the	DET
ejpam-2044	342	13	risk	risk	NOUN
ejpam-2044	342	14	x	x	PUNCT
ejpam-2044	342	15	within	within	ADP
ejpam-2044	342	16	the	the	DET
ejpam-2044	342	17	proof	proof	NOUN
ejpam-2044	342	18	of	of	ADP
ejpam-2044	342	19	theorem	theorem	NOUN
ejpam-2044	342	20	5	5	NUM
ejpam-2044	342	21	will	will	AUX
ejpam-2044	342	22	be	be	AUX
ejpam-2044	342	23	denoted	denote	VERB
ejpam-2044	342	24	as	as	ADP
ejpam-2044	342	25	x	x	PROPN
ejpam-2044	342	26	εp	εp	NOUN
ejpam-2044	342	27	.	.	NOUN
ejpam-2044	342	28	for	for	ADP
ejpam-2044	342	29	the	the	DET
ejpam-2044	342	30	described	describe	VERB
ejpam-2044	342	31	risk	risk	NOUN
ejpam-2044	342	32	x	x	PUNCT
ejpam-2044	342	33	εp	εp	ADP
ejpam-2044	342	34	definition	definition	NOUN
ejpam-2044	342	35	equation	equation	NOUN
ejpam-2044	342	36	(	(	PUNCT
ejpam-2044	342	37	5	5	X
ejpam-2044	342	38	)	)	PUNCT
ejpam-2044	342	39	will	will	AUX
ejpam-2044	342	40	have	have	VERB
ejpam-2044	342	41	the	the	DET
ejpam-2044	342	42	following	follow	VERB
ejpam-2044	342	43	form	form	NOUN
ejpam-2044	342	44	u(−πc.z.u.[x	u(−πc.z.u.[x	PROPN
ejpam-2044	342	45	ε	ε	PROPN
ejpam-2044	342	46	p	p	X
ejpam-2044	342	47	]	]	X
ejpam-2044	342	48	)	)	PUNCT
ejpam-2044	342	49	=	=	SYM
ejpam-2044	342	50	u(−ε	u(−ε	NOUN
ejpam-2044	342	51	)	)	PUNCT
ejpam-2044	342	52	·	·	PUNCT
ejpam-2044	342	53	p+	p+	PROPN
ejpam-2044	342	54	u(−1	u(−1	PROPN
ejpam-2044	342	55	)	)	PUNCT
ejpam-2044	342	56	·	·	PUNCT
ejpam-2044	343	1	(	(	PUNCT
ejpam-2044	343	2	1−	1−	NUM
ejpam-2044	343	3	p	p	NOUN
ejpam-2044	343	4	)	)	PUNCT
ejpam-2044	343	5	.	.	PUNCT
ejpam-2044	344	1	(	(	PUNCT
ejpam-2044	344	2	59	59	NUM
ejpam-2044	344	3	)	)	PUNCT
ejpam-2044	344	4	from	from	ADP
ejpam-2044	344	5	the	the	DET
ejpam-2044	344	6	equation	equation	NOUN
ejpam-2044	344	7	(	(	PUNCT
ejpam-2044	344	8	59	59	NUM
ejpam-2044	344	9	)	)	PUNCT
ejpam-2044	344	10	it	it	PRON
ejpam-2044	344	11	follows	follow	VERB
ejpam-2044	344	12	u(−πc.z.u.[x	u(−πc.z.u.[x	PROPN
ejpam-2044	344	13	ε	ε	PROPN
ejpam-2044	344	14	0	0	NUM
ejpam-2044	344	15	]	]	PUNCT
ejpam-2044	344	16	)	)	PUNCT
ejpam-2044	345	1	=	=	SYM
ejpam-2044	345	2	u(−1	u(−1	PROPN
ejpam-2044	345	3	)	)	PUNCT
ejpam-2044	345	4	,	,	PUNCT
ejpam-2044	345	5	moreover	moreover	ADV
ejpam-2044	345	6	,	,	PUNCT
ejpam-2044	345	7	since	since	SCONJ
ejpam-2044	345	8	u(x	u(x	NOUN
ejpam-2044	345	9	)	)	PUNCT
ejpam-2044	345	10	is	be	AUX
ejpam-2044	345	11	a	a	DET
ejpam-2044	345	12	strictly	strictly	ADV
ejpam-2044	345	13	increasing	increase	VERB
ejpam-2044	345	14	function	function	NOUN
ejpam-2044	345	15	,	,	PUNCT
ejpam-2044	345	16	then	then	ADV
ejpam-2044	345	17	πc.z.u.[x	πc.z.u.[x	CCONJ
ejpam-2044	345	18	ε	ε	PROPN
ejpam-2044	345	19	0	0	NUM
ejpam-2044	345	20	]	]	X
ejpam-2044	345	21	=	=	SYM
ejpam-2044	345	22	1	1	X
ejpam-2044	345	23	.	.	PUNCT
ejpam-2044	345	24	(	(	PUNCT
ejpam-2044	345	25	60	60	NUM
ejpam-2044	345	26	)	)	PUNCT
ejpam-2044	345	27	calculating	calculate	VERB
ejpam-2044	345	28	partial	partial	ADJ
ejpam-2044	345	29	derivatives	derivative	NOUN
ejpam-2044	345	30	with	with	ADP
ejpam-2044	345	31	respect	respect	NOUN
ejpam-2044	345	32	to	to	ADP
ejpam-2044	345	33	the	the	DET
ejpam-2044	345	34	parameter	parameter	NOUN
ejpam-2044	345	35	p	p	NOUN
ejpam-2044	345	36	from	from	ADP
ejpam-2044	345	37	both	both	DET
ejpam-2044	345	38	sides	side	NOUN
ejpam-2044	345	39	of	of	ADP
ejpam-2044	345	40	the	the	DET
ejpam-2044	345	41	equation	equation	NOUN
ejpam-2044	345	42	(	(	PUNCT
ejpam-2044	345	43	59	59	NUM
ejpam-2044	345	44	)	)	PUNCT
ejpam-2044	345	45	,	,	PUNCT
ejpam-2044	345	46	obtain	obtain	VERB
ejpam-2044	345	47	−u′(−πc.z.u.[x	−u′(−πc.z.u.[x	ADJ
ejpam-2044	345	48	ε	ε	PROPN
ejpam-2044	345	49	p	p	X
ejpam-2044	345	50	]	]	X
ejpam-2044	345	51	)	)	PUNCT
ejpam-2044	345	52	·	·	PUNCT
ejpam-2044	345	53	∂	∂	NUM
ejpam-2044	346	1	∂	∂	NOUN
ejpam-2044	346	2	p	p	NOUN
ejpam-2044	346	3	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	346	4	ε	ε	PROPN
ejpam-2044	346	5	p	p	X
ejpam-2044	346	6	]	]	X
ejpam-2044	346	7	=	=	SYM
ejpam-2044	346	8	u(−ε)−	u(−ε)−	PROPN
ejpam-2044	346	9	u(−1	u(−1	PROPN
ejpam-2044	346	10	)	)	PUNCT
ejpam-2044	346	11	.	.	PUNCT
ejpam-2044	347	1	(	(	PUNCT
ejpam-2044	347	2	61	61	NUM
ejpam-2044	347	3	)	)	PUNCT
ejpam-2044	347	4	substituting	substitute	VERB
ejpam-2044	347	5	p	p	NOUN
ejpam-2044	347	6	=	=	NOUN
ejpam-2044	347	7	0	0	NUM
ejpam-2044	347	8	into	into	ADP
ejpam-2044	347	9	the	the	DET
ejpam-2044	347	10	equation	equation	NOUN
ejpam-2044	347	11	(	(	PUNCT
ejpam-2044	347	12	61	61	NUM
ejpam-2044	347	13	)	)	PUNCT
ejpam-2044	347	14	,	,	PUNCT
ejpam-2044	347	15	obtain	obtain	VERB
ejpam-2044	347	16	−u′(−πc.z.u.[x	−u′(−πc.z.u.[x	ADJ
ejpam-2044	347	17	ε	ε	PROPN
ejpam-2044	347	18	0	0	NUM
ejpam-2044	347	19	]	]	PUNCT
ejpam-2044	347	20	)	)	PUNCT
ejpam-2044	347	21	·	·	PUNCT
ejpam-2044	347	22	∂	∂	NUM
ejpam-2044	348	1	∂	∂	NOUN
ejpam-2044	348	2	p	p	NOUN
ejpam-2044	348	3	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	348	4	ε	ε	PROPN
ejpam-2044	348	5	p	p	X
ejpam-2044	348	6	]	]	X
ejpam-2044	348	7	�	�	PROPN
ejpam-2044	348	8	�	�	PROPN
ejpam-2044	348	9	�	�	PROPN
ejpam-2044	348	10	�	�	PROPN
ejpam-2044	348	11	p=0	p=0	PROPN
ejpam-2044	348	12	=	=	PUNCT
ejpam-2044	348	13	u(−ε)−	u(−ε)−	PROPN
ejpam-2044	348	14	u(−1	u(−1	PROPN
ejpam-2044	348	15	)	)	PUNCT
ejpam-2044	348	16	.	.	PUNCT
ejpam-2044	349	1	(	(	PUNCT
ejpam-2044	349	2	62	62	X
ejpam-2044	349	3	)	)	PUNCT
ejpam-2044	349	4	using	use	VERB
ejpam-2044	349	5	(	(	PUNCT
ejpam-2044	349	6	60	60	NUM
ejpam-2044	349	7	)	)	PUNCT
ejpam-2044	349	8	,	,	PUNCT
ejpam-2044	349	9	equation	equation	NOUN
ejpam-2044	349	10	(	(	PUNCT
ejpam-2044	349	11	62	62	NUM
ejpam-2044	349	12	)	)	PUNCT
ejpam-2044	349	13	can	can	AUX
ejpam-2044	349	14	be	be	AUX
ejpam-2044	349	15	rewritten	rewrite	VERB
ejpam-2044	349	16	in	in	ADP
ejpam-2044	349	17	the	the	DET
ejpam-2044	349	18	following	following	ADJ
ejpam-2044	349	19	way	way	NOUN
ejpam-2044	349	20	−u′(−1	−u′(−1	PROPN
ejpam-2044	349	21	)	)	PUNCT
ejpam-2044	349	22	·	·	PUNCT
ejpam-2044	350	1	∂	∂	NUM
ejpam-2044	351	1	∂	∂	NOUN
ejpam-2044	351	2	p	p	NOUN
ejpam-2044	351	3	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	351	4	ε	ε	PROPN
ejpam-2044	351	5	p	p	X
ejpam-2044	351	6	]	]	X
ejpam-2044	351	7	�	�	PROPN
ejpam-2044	351	8	�	�	PROPN
ejpam-2044	351	9	�	�	PROPN
ejpam-2044	351	10	�	�	PROPN
ejpam-2044	351	11	p=0	p=0	PROPN
ejpam-2044	351	12	=	=	PUNCT
ejpam-2044	351	13	u(−ε)−	u(−ε)−	PROPN
ejpam-2044	351	14	u(−1	u(−1	PROPN
ejpam-2044	351	15	)	)	PUNCT
ejpam-2044	351	16	.	.	PUNCT
ejpam-2044	352	1	(	(	PUNCT
ejpam-2044	352	2	63	63	NUM
ejpam-2044	352	3	)	)	PUNCT
ejpam-2044	352	4	m.	m.	NOUN
ejpam-2044	352	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	352	6	,	,	PUNCT
ejpam-2044	352	7	v.	v.	ADP
ejpam-2044	352	8	drozdenko	drozdenko	PROPN
ejpam-2044	352	9	/	/	SYM
ejpam-2044	352	10	eur	eur	PROPN
ejpam-2044	352	11	.	.	PUNCT
ejpam-2044	353	1	j.	j.	PROPN
ejpam-2044	353	2	pure	pure	PROPN
ejpam-2044	353	3	appl	appl	PROPN
ejpam-2044	353	4	.	.	PROPN
ejpam-2044	353	5	math	math	PROPN
ejpam-2044	353	6	,	,	PUNCT
ejpam-2044	353	7	7	7	NUM
ejpam-2044	353	8	(	(	PUNCT
ejpam-2044	353	9	2014	2014	NUM
ejpam-2044	353	10	)	)	PUNCT
ejpam-2044	353	11	,	,	PUNCT
ejpam-2044	353	12	267	267	X
ejpam-2044	353	13	-	-	SYM
ejpam-2044	353	14	288	288	NUM
ejpam-2044	353	15	283	283	NUM
ejpam-2044	353	16	let	let	VERB
ejpam-2044	353	17	us	we	PRON
ejpam-2044	353	18	now	now	ADV
ejpam-2044	353	19	calculate	calculate	VERB
ejpam-2044	353	20	partial	partial	ADJ
ejpam-2044	353	21	derivatives	derivative	NOUN
ejpam-2044	353	22	with	with	ADP
ejpam-2044	353	23	respect	respect	NOUN
ejpam-2044	353	24	to	to	ADP
ejpam-2044	353	25	the	the	DET
ejpam-2044	353	26	parameter	parameter	NOUN
ejpam-2044	353	27	p	p	NOUN
ejpam-2044	353	28	from	from	ADP
ejpam-2044	353	29	both	both	DET
ejpam-2044	353	30	sides	side	NOUN
ejpam-2044	353	31	of	of	ADP
ejpam-2044	353	32	the	the	DET
ejpam-2044	353	33	equation	equation	NOUN
ejpam-2044	353	34	(	(	PUNCT
ejpam-2044	353	35	61	61	NUM
ejpam-2044	353	36	)	)	PUNCT
ejpam-2044	353	37	u′′(−πc.z.u.[x	u′′(−πc.z.u.[x	NUM
ejpam-2044	353	38	ε	ε	PROPN
ejpam-2044	353	39	p	p	X
ejpam-2044	353	40	]	]	X
ejpam-2044	353	41	)	)	PUNCT
ejpam-2044	353	42	·	·	PUNCT
ejpam-2044	353	43	�	�	PROPN
ejpam-2044	353	44	∂	∂	NUM
ejpam-2044	353	45	∂	∂	NUM
ejpam-2044	353	46	p	p	NOUN
ejpam-2044	353	47	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	353	48	ε	ε	PROPN
ejpam-2044	353	49	p	p	X
ejpam-2044	353	50	]	]	X
ejpam-2044	353	51	�	�	PROPN
ejpam-2044	353	52	2	2	NUM
ejpam-2044	353	53	−	−	NOUN
ejpam-2044	353	54	u′(−πc.z.u.[x	u′(−πc.z.u.[x	PROPN
ejpam-2044	353	55	ε	ε	PROPN
ejpam-2044	353	56	p	p	X
ejpam-2044	353	57	]	]	X
ejpam-2044	353	58	)	)	PUNCT
ejpam-2044	353	59	·	·	PUNCT
ejpam-2044	353	60	∂	∂	NUM
ejpam-2044	353	61	2	2	NUM
ejpam-2044	353	62	(	(	PUNCT
ejpam-2044	353	63	∂	∂	NOUN
ejpam-2044	353	64	p)2	p)2	NOUN
ejpam-2044	353	65	πc.z.u.[x	πc.z.u.[x	ADP
ejpam-2044	353	66	ε	ε	PROPN
ejpam-2044	353	67	p	p	X
ejpam-2044	353	68	]	]	X
ejpam-2044	353	69	=	=	SYM
ejpam-2044	353	70	0	0	X
ejpam-2044	353	71	.	.	PUNCT
ejpam-2044	354	1	(	(	PUNCT
ejpam-2044	354	2	64	64	NUM
ejpam-2044	354	3	)	)	PUNCT
ejpam-2044	354	4	substituting	substitute	VERB
ejpam-2044	354	5	p	p	NOUN
ejpam-2044	354	6	=	=	NOUN
ejpam-2044	354	7	0	0	NUM
ejpam-2044	354	8	into	into	ADP
ejpam-2044	354	9	the	the	DET
ejpam-2044	354	10	equation	equation	NOUN
ejpam-2044	354	11	(	(	PUNCT
ejpam-2044	354	12	64	64	NUM
ejpam-2044	354	13	)	)	PUNCT
ejpam-2044	354	14	,	,	PUNCT
ejpam-2044	354	15	and	and	CCONJ
ejpam-2044	354	16	using	use	VERB
ejpam-2044	354	17	identity	identity	NOUN
ejpam-2044	354	18	(	(	PUNCT
ejpam-2044	354	19	60	60	NUM
ejpam-2044	354	20	)	)	PUNCT
ejpam-2044	354	21	,	,	PUNCT
ejpam-2044	354	22	obtain	obtain	VERB
ejpam-2044	354	23	u′′(−1	u′′(−1	NOUN
ejpam-2044	354	24	)	)	PUNCT
ejpam-2044	354	25	·	·	PUNCT
ejpam-2044	354	26	�	�	PROPN
ejpam-2044	354	27	∂	∂	NUM
ejpam-2044	354	28	∂	∂	NUM
ejpam-2044	354	29	p	p	NOUN
ejpam-2044	354	30	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	354	31	ε	ε	PROPN
ejpam-2044	354	32	p	p	X
ejpam-2044	354	33	]	]	X
ejpam-2044	354	34	�	�	PROPN
ejpam-2044	354	35	�	�	PROPN
ejpam-2044	354	36	�	�	PROPN
ejpam-2044	354	37	�	�	PROPN
ejpam-2044	354	38	p=0	p=0	PROPN
ejpam-2044	354	39	�	�	PROPN
ejpam-2044	354	40	2	2	NUM
ejpam-2044	354	41	−	−	NOUN
ejpam-2044	354	42	u′(−1	u′(−1	NOUN
ejpam-2044	354	43	)	)	PUNCT
ejpam-2044	354	44	·	·	PUNCT
ejpam-2044	354	45	�	�	PROPN
ejpam-2044	354	46	∂	∂	NUM
ejpam-2044	354	47	2	2	NUM
ejpam-2044	354	48	(	(	PUNCT
ejpam-2044	354	49	∂	∂	NOUN
ejpam-2044	354	50	p)2	p)2	NOUN
ejpam-2044	354	51	πc.z.u.[x	πc.z.u.[x	ADP
ejpam-2044	354	52	ε	ε	PROPN
ejpam-2044	354	53	p	p	X
ejpam-2044	354	54	]	]	X
ejpam-2044	354	55	�	�	PROPN
ejpam-2044	354	56	�	�	PROPN
ejpam-2044	354	57	�	�	PROPN
ejpam-2044	354	58	�	�	PROPN
ejpam-2044	354	59	p=0	p=0	PROPN
ejpam-2044	354	60	�	�	PROPN
ejpam-2044	354	61	=	=	PUNCT
ejpam-2044	354	62	0	0	PROPN
ejpam-2044	354	63	.	.	PUNCT
ejpam-2044	355	1	(	(	PUNCT
ejpam-2044	355	2	65	65	X
ejpam-2044	355	3	)	)	PUNCT
ejpam-2044	355	4	taking	take	VERB
ejpam-2044	355	5	ε	ε	PROPN
ejpam-2044	355	6	small	small	ADJ
ejpam-2044	355	7	enough	enough	ADV
ejpam-2044	355	8	,	,	PUNCT
ejpam-2044	355	9	namely	namely	ADV
ejpam-2044	355	10	ε	ε	X
ejpam-2044	355	11	<	<	X
ejpam-2044	355	12	1	1	NUM
ejpam-2044	355	13	,	,	PUNCT
ejpam-2044	355	14	and	and	CCONJ
ejpam-2044	355	15	taking	take	VERB
ejpam-2044	355	16	into	into	ADP
ejpam-2044	355	17	account	account	NOUN
ejpam-2044	355	18	strict	strict	ADJ
ejpam-2044	355	19	monotonicity	monotonicity	NOUN
ejpam-2044	355	20	of	of	ADP
ejpam-2044	355	21	the	the	DET
ejpam-2044	355	22	function	function	NOUN
ejpam-2044	355	23	u(x	u(x	NOUN
ejpam-2044	355	24	)	)	PUNCT
ejpam-2044	355	25	,	,	PUNCT
ejpam-2044	355	26	without	without	ADP
ejpam-2044	355	27	of	of	ADP
ejpam-2044	355	28	loss	loss	NOUN
ejpam-2044	355	29	of	of	ADP
ejpam-2044	355	30	generality	generality	NOUN
ejpam-2044	355	31	,	,	PUNCT
ejpam-2044	355	32	using	use	VERB
ejpam-2044	355	33	(	(	PUNCT
ejpam-2044	355	34	63	63	NUM
ejpam-2044	355	35	)	)	PUNCT
ejpam-2044	355	36	,	,	PUNCT
ejpam-2044	355	37	we	we	PRON
ejpam-2044	355	38	may	may	AUX
ejpam-2044	355	39	conclude	conclude	VERB
ejpam-2044	355	40	that	that	DET
ejpam-2044	355	41	∂	∂	NOUN
ejpam-2044	355	42	∂	∂	NUM
ejpam-2044	355	43	p	p	NOUN
ejpam-2044	355	44	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	355	45	ε	ε	PROPN
ejpam-2044	355	46	p	p	X
ejpam-2044	355	47	]	]	X
ejpam-2044	355	48	�	�	PROPN
ejpam-2044	355	49	�	�	PROPN
ejpam-2044	355	50	�	�	PROPN
ejpam-2044	355	51	�	�	PROPN
ejpam-2044	355	52	p=0	p=0	PROPN
ejpam-2044	355	53	6=	6=	ADP
ejpam-2044	355	54	0	0	NUM
ejpam-2044	355	55	,	,	PUNCT
ejpam-2044	355	56	(	(	PUNCT
ejpam-2044	355	57	66	66	NUM
ejpam-2044	355	58	)	)	PUNCT
ejpam-2044	355	59	and	and	CCONJ
ejpam-2044	355	60	hence	hence	ADV
ejpam-2044	355	61	,	,	PUNCT
ejpam-2044	355	62	the	the	DET
ejpam-2044	355	63	equation	equation	NOUN
ejpam-2044	355	64	(	(	PUNCT
ejpam-2044	355	65	65	65	NUM
ejpam-2044	355	66	)	)	PUNCT
ejpam-2044	355	67	can	can	AUX
ejpam-2044	355	68	be	be	AUX
ejpam-2044	355	69	rewritten	rewrite	VERB
ejpam-2044	355	70	in	in	ADP
ejpam-2044	355	71	the	the	DET
ejpam-2044	355	72	following	following	ADJ
ejpam-2044	355	73	way	way	NOUN
ejpam-2044	355	74	u′′(−1	u′′(−1	PROPN
ejpam-2044	355	75	)	)	PUNCT
ejpam-2044	355	76	u′(−1	u′(−1	X
ejpam-2044	355	77	)	)	PUNCT
ejpam-2044	356	1	=	=	SYM
ejpam-2044	356	2	�	�	PROPN
ejpam-2044	356	3	∂	∂	NUM
ejpam-2044	356	4	2	2	NUM
ejpam-2044	356	5	(	(	PUNCT
ejpam-2044	356	6	∂	∂	NOUN
ejpam-2044	356	7	p)2	p)2	NOUN
ejpam-2044	356	8	πc.z.u.[x	πc.z.u.[x	ADP
ejpam-2044	356	9	ε	ε	PROPN
ejpam-2044	356	10	p	p	X
ejpam-2044	356	11	]	]	X
ejpam-2044	356	12	�	�	PROPN
ejpam-2044	356	13	�	�	PROPN
ejpam-2044	356	14	�	�	PROPN
ejpam-2044	356	15	�	�	PROPN
ejpam-2044	356	16	p=0	p=0	PROPN
ejpam-2044	356	17	�	�	PROPN
ejpam-2044	356	18	â	â	PART
ejpam-2044	356	19	�	�	PROPN
ejpam-2044	356	20	∂	∂	NUM
ejpam-2044	356	21	∂	∂	NOUN
ejpam-2044	356	22	p	p	NOUN
ejpam-2044	356	23	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	356	24	ε	ε	PROPN
ejpam-2044	356	25	p	p	X
ejpam-2044	356	26	]	]	X
ejpam-2044	356	27	�	�	PROPN
ejpam-2044	356	28	�	�	PROPN
ejpam-2044	356	29	�	�	PROPN
ejpam-2044	356	30	�	�	PROPN
ejpam-2044	356	31	p=0	p=0	PROPN
ejpam-2044	356	32	�	�	PROPN
ejpam-2044	356	33	2	2	NUM
ejpam-2044	356	34	.	.	PUNCT
ejpam-2044	357	1	(	(	PUNCT
ejpam-2044	357	2	67	67	NUM
ejpam-2044	357	3	)	)	PUNCT
ejpam-2044	357	4	for	for	ADP
ejpam-2044	357	5	any	any	DET
ejpam-2044	357	6	θ	θ	PROPN
ejpam-2044	357	7	>	>	X
ejpam-2044	357	8	0	0	NUM
ejpam-2044	357	9	,	,	PUNCT
ejpam-2044	357	10	definition	definition	NOUN
ejpam-2044	357	11	equation	equation	NOUN
ejpam-2044	357	12	(	(	PUNCT
ejpam-2044	357	13	5	5	NUM
ejpam-2044	357	14	)	)	PUNCT
ejpam-2044	357	15	for	for	ADP
ejpam-2044	357	16	the	the	DET
ejpam-2044	357	17	risk	risk	NOUN
ejpam-2044	357	18	θx	θx	PART
ejpam-2044	357	19	εp	εp	NOUN
ejpam-2044	357	20	will	will	AUX
ejpam-2044	357	21	take	take	VERB
ejpam-2044	357	22	the	the	DET
ejpam-2044	357	23	following	follow	VERB
ejpam-2044	357	24	form	form	NOUN
ejpam-2044	357	25	u(−πc.z.u.[θx	u(−πc.z.u.[θx	PROPN
ejpam-2044	357	26	εp	εp	NOUN
ejpam-2044	357	27	]	]	PUNCT
ejpam-2044	357	28	)	)	PUNCT
ejpam-2044	357	29	=	=	SYM
ejpam-2044	357	30	u(−θε	u(−θε	NOUN
ejpam-2044	357	31	)	)	PUNCT
ejpam-2044	357	32	·	·	PUNCT
ejpam-2044	357	33	p+	p+	X
ejpam-2044	357	34	u(−θ	u(−θ	NOUN
ejpam-2044	357	35	)	)	PUNCT
ejpam-2044	357	36	·	·	PUNCT
ejpam-2044	358	1	(	(	PUNCT
ejpam-2044	358	2	1−	1−	NUM
ejpam-2044	358	3	p	p	NOUN
ejpam-2044	358	4	)	)	PUNCT
ejpam-2044	358	5	.	.	PUNCT
ejpam-2044	359	1	(	(	PUNCT
ejpam-2044	359	2	68	68	NUM
ejpam-2044	359	3	)	)	PUNCT
ejpam-2044	359	4	in	in	ADP
ejpam-2044	359	5	the	the	DET
ejpam-2044	359	6	case	case	NOUN
ejpam-2044	359	7	of	of	ADP
ejpam-2044	359	8	scale	scale	NOUN
ejpam-2044	359	9	invariant	invariant	ADJ
ejpam-2044	359	10	customer	customer	NOUN
ejpam-2044	359	11	zero	zero	NUM
ejpam-2044	359	12	utility	utility	NOUN
ejpam-2044	359	13	premium	premium	NOUN
ejpam-2044	359	14	principle	principle	NOUN
ejpam-2044	359	15	equation	equation	NOUN
ejpam-2044	359	16	(	(	PUNCT
ejpam-2044	359	17	68	68	NUM
ejpam-2044	359	18	)	)	PUNCT
ejpam-2044	359	19	can	can	AUX
ejpam-2044	359	20	be	be	AUX
ejpam-2044	359	21	rewritten	rewrite	VERB
ejpam-2044	359	22	in	in	ADP
ejpam-2044	359	23	the	the	DET
ejpam-2044	359	24	following	follow	VERB
ejpam-2044	359	25	way	way	NOUN
ejpam-2044	359	26	u(−θπc.z.u.[x	u(−θπc.z.u.[x	PROPN
ejpam-2044	359	27	ε	ε	PROPN
ejpam-2044	359	28	p	p	X
ejpam-2044	359	29	]	]	X
ejpam-2044	359	30	)	)	PUNCT
ejpam-2044	359	31	=	=	SYM
ejpam-2044	359	32	u(−θε	u(−θε	NOUN
ejpam-2044	359	33	)	)	PUNCT
ejpam-2044	359	34	·	·	PUNCT
ejpam-2044	359	35	p+	p+	X
ejpam-2044	359	36	u(−θ	u(−θ	NOUN
ejpam-2044	359	37	)	)	PUNCT
ejpam-2044	359	38	·	·	PUNCT
ejpam-2044	360	1	(	(	PUNCT
ejpam-2044	360	2	1−	1−	NUM
ejpam-2044	360	3	p	p	NOUN
ejpam-2044	360	4	)	)	PUNCT
ejpam-2044	360	5	.	.	PUNCT
ejpam-2044	361	1	(	(	PUNCT
ejpam-2044	361	2	69	69	NUM
ejpam-2044	361	3	)	)	PUNCT
ejpam-2044	361	4	calculating	calculate	VERB
ejpam-2044	361	5	second	second	ADJ
ejpam-2044	361	6	partial	partial	ADJ
ejpam-2044	361	7	derivatives	derivative	NOUN
ejpam-2044	361	8	with	with	ADP
ejpam-2044	361	9	respect	respect	NOUN
ejpam-2044	361	10	to	to	ADP
ejpam-2044	361	11	p	p	NOUN
ejpam-2044	361	12	from	from	ADP
ejpam-2044	361	13	both	both	DET
ejpam-2044	361	14	sides	side	NOUN
ejpam-2044	361	15	of	of	ADP
ejpam-2044	361	16	the	the	DET
ejpam-2044	361	17	equation	equation	NOUN
ejpam-2044	361	18	(	(	PUNCT
ejpam-2044	361	19	69	69	NUM
ejpam-2044	361	20	)	)	PUNCT
ejpam-2044	361	21	,	,	PUNCT
ejpam-2044	361	22	obtain	obtain	VERB
ejpam-2044	361	23	u′′(−θπc.z.u.[x	u′′(−θπc.z.u.[x	ADJ
ejpam-2044	361	24	ε	ε	PROPN
ejpam-2044	361	25	p	p	X
ejpam-2044	361	26	]	]	X
ejpam-2044	361	27	)	)	PUNCT
ejpam-2044	361	28	·	·	PUNCT
ejpam-2044	361	29	θ	θ	NOUN
ejpam-2044	361	30	2	2	NUM
ejpam-2044	361	31	·	·	SYM
ejpam-2044	361	32	�	�	PROPN
ejpam-2044	361	33	∂	∂	NUM
ejpam-2044	361	34	∂	∂	NOUN
ejpam-2044	361	35	p	p	NOUN
ejpam-2044	361	36	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	361	37	ε	ε	PROPN
ejpam-2044	361	38	p	p	X
ejpam-2044	361	39	]	]	PUNCT
ejpam-2044	361	40	�	�	PROPN
ejpam-2044	361	41	2	2	NUM
ejpam-2044	361	42	−	−	NOUN
ejpam-2044	361	43	u′(−θπc.z.u.[x	u′(−θπc.z.u.[x	NOUN
ejpam-2044	361	44	ε	ε	PROPN
ejpam-2044	361	45	p	p	X
ejpam-2044	361	46	]	]	X
ejpam-2044	361	47	)	)	PUNCT
ejpam-2044	361	48	·	·	PUNCT
ejpam-2044	361	49	θ	θ	X
ejpam-2044	361	50	·	·	PUNCT
ejpam-2044	361	51	∂	∂	NUM
ejpam-2044	361	52	2	2	NUM
ejpam-2044	361	53	(	(	PUNCT
ejpam-2044	361	54	∂	∂	NOUN
ejpam-2044	361	55	p)2	p)2	NOUN
ejpam-2044	361	56	πc.z.u.[x	πc.z.u.[x	ADP
ejpam-2044	361	57	ε	ε	PROPN
ejpam-2044	361	58	p	p	X
ejpam-2044	361	59	]	]	X
ejpam-2044	361	60	=	=	SYM
ejpam-2044	361	61	0	0	X
ejpam-2044	361	62	.	.	PUNCT
ejpam-2044	362	1	(	(	PUNCT
ejpam-2044	362	2	70	70	X
ejpam-2044	362	3	)	)	PUNCT
ejpam-2044	362	4	substituting	substitute	VERB
ejpam-2044	362	5	p	p	NOUN
ejpam-2044	362	6	=	=	NOUN
ejpam-2044	362	7	0	0	NUM
ejpam-2044	362	8	into	into	ADP
ejpam-2044	362	9	the	the	DET
ejpam-2044	362	10	equation	equation	NOUN
ejpam-2044	362	11	(	(	PUNCT
ejpam-2044	362	12	70	70	NUM
ejpam-2044	362	13	)	)	PUNCT
ejpam-2044	362	14	,	,	PUNCT
ejpam-2044	362	15	canceling	cancel	VERB
ejpam-2044	362	16	θ	θ	PROPN
ejpam-2044	362	17	factor	factor	NOUN
ejpam-2044	362	18	,	,	PUNCT
ejpam-2044	362	19	and	and	CCONJ
ejpam-2044	362	20	using	use	VERB
ejpam-2044	362	21	identity	identity	NOUN
ejpam-2044	362	22	(	(	PUNCT
ejpam-2044	362	23	60	60	NUM
ejpam-2044	362	24	)	)	PUNCT
ejpam-2044	362	25	,	,	PUNCT
ejpam-2044	362	26	we	we	PRON
ejpam-2044	362	27	get	get	VERB
ejpam-2044	362	28	u′′(−θ	u′′(−θ	NOUN
ejpam-2044	362	29	)	)	PUNCT
ejpam-2044	362	30	·	·	PUNCT
ejpam-2044	362	31	θ	θ	X
ejpam-2044	362	32	·	·	PUNCT
ejpam-2044	362	33	�	�	PROPN
ejpam-2044	362	34	∂	∂	NUM
ejpam-2044	362	35	∂	∂	NOUN
ejpam-2044	362	36	p	p	NOUN
ejpam-2044	362	37	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	362	38	ε	ε	PROPN
ejpam-2044	362	39	p	p	X
ejpam-2044	362	40	]	]	X
ejpam-2044	362	41	�	�	PROPN
ejpam-2044	362	42	�	�	PROPN
ejpam-2044	362	43	�	�	PROPN
ejpam-2044	362	44	�	�	PROPN
ejpam-2044	362	45	p=0	p=0	PROPN
ejpam-2044	362	46	�	�	PROPN
ejpam-2044	362	47	2	2	NUM
ejpam-2044	362	48	−	−	PROPN
ejpam-2044	362	49	u′(−θ	u′(−θ	PROPN
ejpam-2044	362	50	)	)	PUNCT
ejpam-2044	362	51	·	·	PUNCT
ejpam-2044	362	52	�	�	PROPN
ejpam-2044	362	53	∂	∂	NUM
ejpam-2044	362	54	2	2	NUM
ejpam-2044	362	55	(	(	PUNCT
ejpam-2044	362	56	∂	∂	NOUN
ejpam-2044	362	57	p)2	p)2	NOUN
ejpam-2044	362	58	πc.z.u.[x	πc.z.u.[x	ADP
ejpam-2044	362	59	ε	ε	PROPN
ejpam-2044	362	60	p	p	X
ejpam-2044	362	61	]	]	X
ejpam-2044	362	62	�	�	PROPN
ejpam-2044	362	63	�	�	PROPN
ejpam-2044	362	64	�	�	PROPN
ejpam-2044	362	65	�	�	PROPN
ejpam-2044	362	66	p=0	p=0	PROPN
ejpam-2044	362	67	�	�	PROPN
ejpam-2044	363	1	=	=	PUNCT
ejpam-2044	363	2	0	0	PROPN
ejpam-2044	363	3	.	.	PUNCT
ejpam-2044	364	1	(	(	PUNCT
ejpam-2044	364	2	71	71	NUM
ejpam-2044	364	3	)	)	PUNCT
ejpam-2044	364	4	since	since	SCONJ
ejpam-2044	364	5	u′(−θ	u′(−θ	NOUN
ejpam-2044	364	6	)	)	PUNCT
ejpam-2044	364	7	>	>	X
ejpam-2044	364	8	0	0	NUM
ejpam-2044	364	9	,	,	PUNCT
ejpam-2044	364	10	then	then	ADV
ejpam-2044	364	11	using	use	VERB
ejpam-2044	364	12	relation	relation	NOUN
ejpam-2044	364	13	(	(	PUNCT
ejpam-2044	364	14	66	66	NUM
ejpam-2044	364	15	)	)	PUNCT
ejpam-2044	364	16	,	,	PUNCT
ejpam-2044	364	17	equation	equation	NOUN
ejpam-2044	364	18	(	(	PUNCT
ejpam-2044	364	19	71	71	NUM
ejpam-2044	364	20	)	)	PUNCT
ejpam-2044	364	21	can	can	AUX
ejpam-2044	364	22	be	be	AUX
ejpam-2044	364	23	rewritten	rewrite	VERB
ejpam-2044	364	24	in	in	ADP
ejpam-2044	364	25	the	the	DET
ejpam-2044	364	26	following	following	ADJ
ejpam-2044	364	27	way	way	NOUN
ejpam-2044	364	28	u′′(−θ	u′′(−θ	NOUN
ejpam-2044	364	29	)	)	PUNCT
ejpam-2044	364	30	·	·	PUNCT
ejpam-2044	364	31	θ	θ	SYM
ejpam-2044	364	32	u′(−θ	u′(−θ	NOUN
ejpam-2044	364	33	)	)	PUNCT
ejpam-2044	364	34	=	=	SYM
ejpam-2044	364	35	�	�	PROPN
ejpam-2044	364	36	∂	∂	NUM
ejpam-2044	364	37	2	2	NUM
ejpam-2044	364	38	(	(	PUNCT
ejpam-2044	364	39	∂	∂	NOUN
ejpam-2044	364	40	p)2	p)2	NOUN
ejpam-2044	364	41	πc.z.u.[x	πc.z.u.[x	ADP
ejpam-2044	364	42	ε	ε	PROPN
ejpam-2044	364	43	p	p	X
ejpam-2044	364	44	]	]	X
ejpam-2044	364	45	�	�	PROPN
ejpam-2044	364	46	�	�	PROPN
ejpam-2044	364	47	�	�	PROPN
ejpam-2044	364	48	�	�	PROPN
ejpam-2044	364	49	p=0	p=0	PROPN
ejpam-2044	364	50	�	�	PROPN
ejpam-2044	364	51	â	â	PART
ejpam-2044	364	52	�	�	PROPN
ejpam-2044	364	53	∂	∂	NUM
ejpam-2044	364	54	∂	∂	NOUN
ejpam-2044	364	55	p	p	NOUN
ejpam-2044	364	56	πc.z.u.[x	πc.z.u.[x	VERB
ejpam-2044	364	57	ε	ε	PROPN
ejpam-2044	364	58	p	p	X
ejpam-2044	364	59	]	]	X
ejpam-2044	364	60	�	�	PROPN
ejpam-2044	364	61	�	�	PROPN
ejpam-2044	364	62	�	�	PROPN
ejpam-2044	364	63	�	�	PROPN
ejpam-2044	364	64	p=0	p=0	PROPN
ejpam-2044	364	65	�	�	PROPN
ejpam-2044	364	66	2	2	NUM
ejpam-2044	364	67	.	.	PUNCT
ejpam-2044	365	1	(	(	PUNCT
ejpam-2044	365	2	72	72	NUM
ejpam-2044	365	3	)	)	PUNCT
ejpam-2044	365	4	m.	m.	NOUN
ejpam-2044	365	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	365	6	,	,	PUNCT
ejpam-2044	365	7	v.	v.	ADP
ejpam-2044	365	8	drozdenko	drozdenko	PROPN
ejpam-2044	365	9	/	/	SYM
ejpam-2044	365	10	eur	eur	PROPN
ejpam-2044	365	11	.	.	PUNCT
ejpam-2044	366	1	j.	j.	PROPN
ejpam-2044	366	2	pure	pure	PROPN
ejpam-2044	366	3	appl	appl	PROPN
ejpam-2044	366	4	.	.	PROPN
ejpam-2044	366	5	math	math	PROPN
ejpam-2044	366	6	,	,	PUNCT
ejpam-2044	366	7	7	7	NUM
ejpam-2044	366	8	(	(	PUNCT
ejpam-2044	366	9	2014	2014	NUM
ejpam-2044	366	10	)	)	PUNCT
ejpam-2044	366	11	,	,	PUNCT
ejpam-2044	366	12	267	267	NUM
ejpam-2044	366	13	-	-	SYM
ejpam-2044	366	14	288	288	NUM
ejpam-2044	366	15	284	284	NUM
ejpam-2044	366	16	observe	observe	VERB
ejpam-2044	366	17	that	that	SCONJ
ejpam-2044	366	18	equations	equation	NOUN
ejpam-2044	366	19	(	(	PUNCT
ejpam-2044	366	20	67	67	NUM
ejpam-2044	366	21	)	)	PUNCT
ejpam-2044	366	22	and	and	CCONJ
ejpam-2044	366	23	(	(	PUNCT
ejpam-2044	366	24	72	72	X
ejpam-2044	366	25	)	)	PUNCT
ejpam-2044	366	26	have	have	VERB
ejpam-2044	366	27	equal	equal	ADJ
ejpam-2044	366	28	right	right	ADJ
ejpam-2044	366	29	-	-	PUNCT
ejpam-2044	366	30	hand	hand	NOUN
ejpam-2044	366	31	sides	side	NOUN
ejpam-2044	366	32	,	,	PUNCT
ejpam-2044	366	33	this	this	PRON
ejpam-2044	366	34	means	mean	VERB
ejpam-2044	366	35	that	that	SCONJ
ejpam-2044	366	36	their	their	PRON
ejpam-2044	366	37	left	leave	VERB
ejpam-2044	366	38	-	-	PUNCT
ejpam-2044	366	39	hand	hand	NOUN
ejpam-2044	366	40	sides	side	NOUN
ejpam-2044	366	41	also	also	ADV
ejpam-2044	366	42	have	have	VERB
ejpam-2044	366	43	to	to	PART
ejpam-2044	366	44	be	be	AUX
ejpam-2044	366	45	equal	equal	ADJ
ejpam-2044	366	46	,	,	PUNCT
ejpam-2044	366	47	in	in	ADP
ejpam-2044	366	48	this	this	DET
ejpam-2044	366	49	way	way	NOUN
ejpam-2044	366	50	we	we	PRON
ejpam-2044	366	51	finally	finally	ADV
ejpam-2044	366	52	get	get	VERB
ejpam-2044	366	53	an	an	DET
ejpam-2044	366	54	equation	equation	NOUN
ejpam-2044	366	55	which	which	PRON
ejpam-2044	366	56	the	the	DET
ejpam-2044	366	57	function	function	NOUN
ejpam-2044	366	58	u(x	u(x	VERB
ejpam-2044	366	59	)	)	PUNCT
ejpam-2044	366	60	has	have	VERB
ejpam-2044	366	61	to	to	PART
ejpam-2044	366	62	satisfy	satisfy	VERB
ejpam-2044	366	63	in	in	ADP
ejpam-2044	366	64	the	the	DET
ejpam-2044	366	65	case	case	NOUN
ejpam-2044	366	66	of	of	ADP
ejpam-2044	366	67	scale	scale	NOUN
ejpam-2044	366	68	invariant	invariant	ADJ
ejpam-2044	366	69	customer	customer	NOUN
ejpam-2044	366	70	zero	zero	NUM
ejpam-2044	366	71	utility	utility	NOUN
ejpam-2044	366	72	premium	premium	NOUN
ejpam-2044	366	73	calculation	calculation	NOUN
ejpam-2044	366	74	principle	principle	NOUN
ejpam-2044	366	75	subjected	subject	VERB
ejpam-2044	366	76	to	to	ADP
ejpam-2044	366	77	consideration	consideration	NOUN
ejpam-2044	366	78	of	of	ADP
ejpam-2044	366	79	only	only	ADV
ejpam-2044	366	80	strictly	strictly	ADV
ejpam-2044	366	81	positive	positive	ADJ
ejpam-2044	366	82	risks	risk	NOUN
ejpam-2044	366	83	,	,	PUNCT
ejpam-2044	366	84	namely	namely	ADV
ejpam-2044	366	85	,	,	PUNCT
ejpam-2044	366	86	u′′(−θ	u′′(−θ	NOUN
ejpam-2044	366	87	)	)	PUNCT
ejpam-2044	366	88	·	·	PUNCT
ejpam-2044	366	89	θ	θ	SYM
ejpam-2044	366	90	u′(−θ	u′(−θ	NOUN
ejpam-2044	366	91	)	)	PUNCT
ejpam-2044	366	92	=	=	SYM
ejpam-2044	366	93	u′′(−1	u′′(−1	NOUN
ejpam-2044	366	94	)	)	PUNCT
ejpam-2044	366	95	u′(−1	u′(−1	NUM
ejpam-2044	366	96	)	)	PUNCT
ejpam-2044	366	97	,	,	PUNCT
ejpam-2044	366	98	for	for	ADP
ejpam-2044	366	99	all	all	DET
ejpam-2044	366	100	θ	θ	PROPN
ejpam-2044	366	101	>	>	X
ejpam-2044	366	102	0	0	NUM
ejpam-2044	366	103	.	.	PUNCT
ejpam-2044	367	1	(	(	PUNCT
ejpam-2044	367	2	73	73	NUM
ejpam-2044	367	3	)	)	PUNCT
ejpam-2044	367	4	assigning	assign	VERB
ejpam-2044	367	5	−u′′(−1)/u′(−1	−u′′(−1)/u′(−1	PROPN
ejpam-2044	367	6	)	)	PUNCT
ejpam-2044	368	1	=	=	PRON
ejpam-2044	368	2	:	:	PUNCT
ejpam-2044	368	3	c	c	X
ejpam-2044	368	4	(	(	PUNCT
ejpam-2044	368	5	since	since	SCONJ
ejpam-2044	368	6	u′′(−1	u′′(−1	NOUN
ejpam-2044	368	7	)	)	PUNCT
ejpam-2044	368	8	≤	≤	NUM
ejpam-2044	368	9	0	0	NUM
ejpam-2044	368	10	and	and	CCONJ
ejpam-2044	368	11	u′(−1	u′(−1	NUM
ejpam-2044	368	12	)	)	PUNCT
ejpam-2044	368	13	>	>	X
ejpam-2044	368	14	0	0	PUNCT
ejpam-2044	369	1	then	then	ADV
ejpam-2044	369	2	c	c	X
ejpam-2044	369	3	≥	≥	PROPN
ejpam-2044	369	4	0	0	NUM
ejpam-2044	369	5	)	)	PUNCT
ejpam-2044	369	6	and	and	CCONJ
ejpam-2044	369	7	making	make	VERB
ejpam-2044	369	8	substitution	substitution	NOUN
ejpam-2044	369	9	z(θ	z(θ	NOUN
ejpam-2044	369	10	)	)	PUNCT
ejpam-2044	369	11	:	:	PUNCT
ejpam-2044	369	12	=	=	SYM
ejpam-2044	369	13	u′(−θ	u′(−θ	NOUN
ejpam-2044	369	14	)	)	PUNCT
ejpam-2044	369	15	equation	equation	NOUN
ejpam-2044	369	16	(	(	PUNCT
ejpam-2044	369	17	73	73	NUM
ejpam-2044	369	18	)	)	PUNCT
ejpam-2044	369	19	can	can	AUX
ejpam-2044	369	20	be	be	AUX
ejpam-2044	369	21	rewritten	rewrite	VERB
ejpam-2044	369	22	in	in	ADP
ejpam-2044	369	23	the	the	DET
ejpam-2044	369	24	following	follow	VERB
ejpam-2044	369	25	equivalent	equivalent	ADJ
ejpam-2044	369	26	form	form	NOUN
ejpam-2044	369	27	dz	dz	PROPN
ejpam-2044	369	28	z	z	NOUN
ejpam-2044	369	29	=	=	PUNCT
ejpam-2044	369	30	c	c	PROPN
ejpam-2044	369	31	dθ	dθ	PROPN
ejpam-2044	369	32	θ	θ	PROPN
ejpam-2044	369	33	,	,	PUNCT
ejpam-2044	369	34	therefore	therefore	ADV
ejpam-2044	369	35	log(z(θ	log(z(θ	NOUN
ejpam-2044	369	36	)	)	PUNCT
ejpam-2044	369	37	)	)	PUNCT
ejpam-2044	370	1	=	=	PUNCT
ejpam-2044	370	2	c	c	X
ejpam-2044	370	3	log(θ	log(θ	PROPN
ejpam-2044	370	4	)	)	PUNCT
ejpam-2044	370	5	+	+	X
ejpam-2044	370	6	log(c1	log(c1	NOUN
ejpam-2044	370	7	)	)	PUNCT
ejpam-2044	370	8	,	,	PUNCT
ejpam-2044	370	9	for	for	ADP
ejpam-2044	370	10	some	some	DET
ejpam-2044	370	11	constant	constant	ADJ
ejpam-2044	370	12	c1	c1	NOUN
ejpam-2044	370	13	>	>	X
ejpam-2044	370	14	0	0	PROPN
ejpam-2044	370	15	,	,	PUNCT
ejpam-2044	370	16	and	and	CCONJ
ejpam-2044	370	17	the	the	DET
ejpam-2044	370	18	function	function	NOUN
ejpam-2044	370	19	z(θ	z(θ	NOUN
ejpam-2044	370	20	)	)	PUNCT
ejpam-2044	370	21	itself	itself	PRON
ejpam-2044	370	22	will	will	AUX
ejpam-2044	370	23	have	have	VERB
ejpam-2044	370	24	a	a	DET
ejpam-2044	370	25	form	form	NOUN
ejpam-2044	370	26	z(θ	z(θ	NUM
ejpam-2044	370	27	)	)	PUNCT
ejpam-2044	371	1	=	=	PUNCT
ejpam-2044	371	2	c1θ	c1θ	PROPN
ejpam-2044	371	3	c.	c.	NOUN
ejpam-2044	371	4	switching	switch	VERB
ejpam-2044	371	5	back	back	ADV
ejpam-2044	371	6	to	to	ADP
ejpam-2044	371	7	the	the	DET
ejpam-2044	371	8	function	function	NOUN
ejpam-2044	371	9	u′(−θ	u′(−θ	PROPN
ejpam-2044	371	10	)	)	PUNCT
ejpam-2044	371	11	,	,	PUNCT
ejpam-2044	371	12	obtain	obtain	VERB
ejpam-2044	371	13	u′(−θ	u′(−θ	NOUN
ejpam-2044	371	14	)	)	PUNCT
ejpam-2044	371	15	=	=	PUNCT
ejpam-2044	372	1	c1θ	c1θ	PROPN
ejpam-2044	372	2	c.	c.	NOUN
ejpam-2044	372	3	(	(	PUNCT
ejpam-2044	372	4	74	74	X
ejpam-2044	372	5	)	)	PUNCT
ejpam-2044	372	6	switching	switch	VERB
ejpam-2044	372	7	back	back	ADV
ejpam-2044	372	8	to	to	ADP
ejpam-2044	372	9	the	the	DET
ejpam-2044	372	10	original	original	ADJ
ejpam-2044	372	11	parameter	parameter	NOUN
ejpam-2044	372	12	x	x	X
ejpam-2044	372	13	∈	∈	PROPN
ejpam-2044	372	14	(	(	PUNCT
ejpam-2044	372	15	−∞	−∞	NOUN
ejpam-2044	372	16	,	,	PUNCT
ejpam-2044	372	17	0	0	NUM
ejpam-2044	372	18	)	)	PUNCT
ejpam-2044	372	19	representation	representation	NOUN
ejpam-2044	372	20	(	(	PUNCT
ejpam-2044	372	21	74	74	NUM
ejpam-2044	372	22	)	)	PUNCT
ejpam-2044	372	23	can	can	AUX
ejpam-2044	372	24	be	be	AUX
ejpam-2044	372	25	rewritten	rewrite	VERB
ejpam-2044	372	26	in	in	ADP
ejpam-2044	372	27	the	the	DET
ejpam-2044	372	28	following	following	ADJ
ejpam-2044	372	29	way	way	NOUN
ejpam-2044	372	30	u′(x	u′(x	SYM
ejpam-2044	372	31	)	)	PUNCT
ejpam-2044	372	32	=	=	SYM
ejpam-2044	373	1	c1(−x)c	c1(−x)c	NOUN
ejpam-2044	373	2	.	.	PUNCT
ejpam-2044	374	1	taking	take	VERB
ejpam-2044	374	2	antiderivative	antiderivative	ADJ
ejpam-2044	374	3	,	,	PUNCT
ejpam-2044	374	4	obtain	obtain	VERB
ejpam-2044	374	5	u(x	u(x	NOUN
ejpam-2044	374	6	)	)	PUNCT
ejpam-2044	374	7	=	=	PUNCT
ejpam-2044	375	1	−	−	PROPN
ejpam-2044	375	2	c1	c1	NOUN
ejpam-2044	375	3	c+	c+	VERB
ejpam-2044	375	4	1	1	NUM
ejpam-2044	375	5	(	(	PUNCT
ejpam-2044	375	6	−x)c+1	−x)c+1	PROPN
ejpam-2044	375	7	+	+	CCONJ
ejpam-2044	375	8	c2	c2	PROPN
ejpam-2044	375	9	,	,	PUNCT
ejpam-2044	375	10	therefore	therefore	ADV
ejpam-2044	375	11	the	the	DET
ejpam-2044	375	12	function	function	NOUN
ejpam-2044	375	13	u(x	u(x	VERB
ejpam-2044	375	14	)	)	PUNCT
ejpam-2044	375	15	must	must	AUX
ejpam-2044	375	16	be	be	AUX
ejpam-2044	375	17	a	a	DET
ejpam-2044	375	18	function	function	NOUN
ejpam-2044	375	19	of	of	ADP
ejpam-2044	375	20	the	the	DET
ejpam-2044	375	21	form	form	NOUN
ejpam-2044	375	22	u(x	u(x	VERB
ejpam-2044	375	23	)	)	PUNCT
ejpam-2044	375	24	=	=	PUNCT
ejpam-2044	376	1	−a(−x)κ	−a(−x)κ	PUNCT
ejpam-2044	377	1	+	+	NUM
ejpam-2044	377	2	b	b	NOUN
ejpam-2044	377	3	,	,	PUNCT
ejpam-2044	377	4	for	for	ADP
ejpam-2044	377	5	some	some	DET
ejpam-2044	377	6	real	real	ADJ
ejpam-2044	377	7	constants	constant	NOUN
ejpam-2044	377	8	a	a	DET
ejpam-2044	377	9	,	,	PUNCT
ejpam-2044	377	10	b	b	NOUN
ejpam-2044	377	11	,	,	PUNCT
ejpam-2044	377	12	and	and	CCONJ
ejpam-2044	377	13	κ	κ	X
ejpam-2044	377	14	.	.	PUNCT
ejpam-2044	378	1	moreover	moreover	ADV
ejpam-2044	378	2	,	,	PUNCT
ejpam-2044	378	3	since	since	SCONJ
ejpam-2044	378	4	c1	c1	PROPN
ejpam-2044	378	5	>	>	X
ejpam-2044	378	6	0	0	PUNCT
ejpam-2044	378	7	and	and	CCONJ
ejpam-2044	378	8	c	c	X
ejpam-2044	378	9	>	>	X
ejpam-2044	378	10	0	0	PUNCT
ejpam-2044	379	1	then	then	ADV
ejpam-2044	379	2	a	a	DET
ejpam-2044	379	3	>	>	X
ejpam-2044	379	4	0	0	NUM
ejpam-2044	379	5	,	,	PUNCT
ejpam-2044	379	6	and	and	CCONJ
ejpam-2044	379	7	since	since	SCONJ
ejpam-2044	379	8	c≥	c≥	PROPN
ejpam-2044	379	9	0	0	NUM
ejpam-2044	380	1	then	then	ADV
ejpam-2044	380	2	κ≥	κ≥	PROPN
ejpam-2044	380	3	1	1	PROPN
ejpam-2044	380	4	.	.	PUNCT
ejpam-2044	381	1	this	this	PRON
ejpam-2044	381	2	completes	complete	VERB
ejpam-2044	381	3	the	the	DET
ejpam-2044	381	4	proof	proof	NOUN
ejpam-2044	381	5	of	of	ADP
ejpam-2044	381	6	theorem	theorem	ADJ
ejpam-2044	381	7	5	5	NUM
ejpam-2044	381	8	.	.	SYM
ejpam-2044	381	9	5	5	NUM
ejpam-2044	381	10	.	.	X
ejpam-2044	381	11	swiss	swiss	ADJ
ejpam-2044	381	12	premium	premium	PROPN
ejpam-2044	381	13	principle	principle	NOUN
ejpam-2044	381	14	the	the	DET
ejpam-2044	381	15	following	follow	VERB
ejpam-2044	381	16	theorem	theorem	NOUN
ejpam-2044	381	17	describes	describe	VERB
ejpam-2044	381	18	conditions	condition	NOUN
ejpam-2044	381	19	of	of	ADP
ejpam-2044	381	20	attainment	attainment	NOUN
ejpam-2044	381	21	of	of	ADP
ejpam-2044	381	22	scale	scale	NOUN
ejpam-2044	381	23	invariance	invariance	NOUN
ejpam-2044	381	24	property	property	NOUN
ejpam-2044	381	25	by	by	ADP
ejpam-2044	381	26	swiss	swiss	ADJ
ejpam-2044	381	27	insurance	insurance	NOUN
ejpam-2044	381	28	premium	premium	NOUN
ejpam-2044	381	29	calculation	calculation	NOUN
ejpam-2044	381	30	principle	principle	NOUN
ejpam-2044	381	31	.	.	PUNCT
ejpam-2044	382	1	theorem	theorem	ADJ
ejpam-2044	382	2	6	6	NUM
ejpam-2044	382	3	.	.	PUNCT
ejpam-2044	383	1	for	for	ADP
ejpam-2044	383	2	any	any	DET
ejpam-2044	383	3	∆	∆	PROPN
ejpam-2044	383	4	∈	∈	NOUN
ejpam-2044	384	1	[	[	X
ejpam-2044	384	2	0	0	NUM
ejpam-2044	384	3	,	,	PUNCT
ejpam-2044	384	4	1	1	NUM
ejpam-2044	384	5	]	]	PUNCT
ejpam-2044	384	6	,	,	PUNCT
ejpam-2044	384	7	swiss	swiss	ADJ
ejpam-2044	384	8	premium	premium	NOUN
ejpam-2044	384	9	calculation	calculation	NOUN
ejpam-2044	384	10	principle	principle	NOUN
ejpam-2044	384	11	possesses	possess	VERB
ejpam-2044	384	12	scale	scale	NOUN
ejpam-2044	384	13	invariance	invariance	NOUN
ejpam-2044	384	14	property	property	NOUN
ejpam-2044	384	15	if	if	SCONJ
ejpam-2044	384	16	and	and	CCONJ
ejpam-2044	384	17	only	only	ADV
ejpam-2044	384	18	if	if	SCONJ
ejpam-2044	384	19	v	v	INTJ
ejpam-2044	384	20	(	(	PUNCT
ejpam-2044	384	21	x	x	NOUN
ejpam-2044	384	22	)	)	PUNCT
ejpam-2044	384	23	=	=	NOUN
ejpam-2044	384	24	ax	ax	NOUN
ejpam-2044	384	25	+	+	CCONJ
ejpam-2044	384	26	b	b	NOUN
ejpam-2044	384	27	,	,	PUNCT
ejpam-2044	384	28	for	for	ADP
ejpam-2044	384	29	a	a	DET
ejpam-2044	384	30	>	>	X
ejpam-2044	384	31	0	0	NUM
ejpam-2044	384	32	,	,	PUNCT
ejpam-2044	384	33	i.e.	i.e.	X
ejpam-2044	384	34	,	,	PUNCT
ejpam-2044	384	35	only	only	ADV
ejpam-2044	384	36	in	in	ADP
ejpam-2044	384	37	the	the	DET
ejpam-2044	384	38	case	case	NOUN
ejpam-2044	384	39	when	when	SCONJ
ejpam-2044	384	40	it	it	PRON
ejpam-2044	384	41	coincides	coincide	VERB
ejpam-2044	384	42	with	with	ADP
ejpam-2044	384	43	net	net	ADJ
ejpam-2044	384	44	premium	premium	ADJ
ejpam-2044	384	45	principle	principle	NOUN
ejpam-2044	384	46	.	.	PUNCT
ejpam-2044	385	1	m.	m.	NOUN
ejpam-2044	385	2	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	385	3	,	,	PUNCT
ejpam-2044	385	4	v.	v.	ADP
ejpam-2044	385	5	drozdenko	drozdenko	PROPN
ejpam-2044	385	6	/	/	SYM
ejpam-2044	385	7	eur	eur	PROPN
ejpam-2044	385	8	.	.	PUNCT
ejpam-2044	386	1	j.	j.	PROPN
ejpam-2044	386	2	pure	pure	PROPN
ejpam-2044	386	3	appl	appl	PROPN
ejpam-2044	386	4	.	.	PROPN
ejpam-2044	386	5	math	math	PROPN
ejpam-2044	386	6	,	,	PUNCT
ejpam-2044	386	7	7	7	NUM
ejpam-2044	386	8	(	(	PUNCT
ejpam-2044	386	9	2014	2014	NUM
ejpam-2044	386	10	)	)	PUNCT
ejpam-2044	386	11	,	,	PUNCT
ejpam-2044	386	12	267	267	NUM
ejpam-2044	386	13	-	-	SYM
ejpam-2044	386	14	288	288	NUM
ejpam-2044	386	15	285	285	NUM
ejpam-2044	386	16	proof	proof	NOUN
ejpam-2044	386	17	.	.	PUNCT
ejpam-2044	387	1	let	let	VERB
ejpam-2044	387	2	us	we	PRON
ejpam-2044	387	3	at	at	ADP
ejpam-2044	387	4	the	the	DET
ejpam-2044	387	5	beginning	beginning	NOUN
ejpam-2044	387	6	prove	prove	VERB
ejpam-2044	387	7	the	the	DET
ejpam-2044	387	8	sufficiency	sufficiency	NOUN
ejpam-2044	387	9	of	of	ADP
ejpam-2044	387	10	the	the	DET
ejpam-2044	387	11	statement	statement	NOUN
ejpam-2044	387	12	.	.	PUNCT
ejpam-2044	388	1	from	from	ADP
ejpam-2044	388	2	definition	definition	NOUN
ejpam-2044	388	3	equation	equation	NOUN
ejpam-2044	388	4	(	(	PUNCT
ejpam-2044	388	5	6	6	NUM
ejpam-2044	388	6	)	)	PUNCT
ejpam-2044	388	7	for	for	ADP
ejpam-2044	388	8	any	any	DET
ejpam-2044	388	9	risk	risk	NOUN
ejpam-2044	388	10	x	x	INTJ
ejpam-2044	388	11	,	,	PUNCT
ejpam-2044	388	12	any	any	DET
ejpam-2044	388	13	∆	∆	PROPN
ejpam-2044	388	14	∈	∈	PROPN
ejpam-2044	389	1	[	[	X
ejpam-2044	389	2	0,1	0,1	NUM
ejpam-2044	389	3	]	]	PUNCT
ejpam-2044	389	4	,	,	PUNCT
ejpam-2044	389	5	and	and	CCONJ
ejpam-2044	389	6	function	function	VERB
ejpam-2044	389	7	v	v	NOUN
ejpam-2044	389	8	(	(	PUNCT
ejpam-2044	389	9	x	x	NOUN
ejpam-2044	389	10	)	)	PUNCT
ejpam-2044	389	11	=	=	NOUN
ejpam-2044	389	12	ax	ax	NOUN
ejpam-2044	389	13	+	+	CCONJ
ejpam-2044	389	14	b	b	NOUN
ejpam-2044	389	15	,	,	PUNCT
ejpam-2044	389	16	for	for	ADP
ejpam-2044	389	17	a	a	DET
ejpam-2044	389	18	>	>	X
ejpam-2044	389	19	0	0	NUM
ejpam-2044	389	20	,	,	PUNCT
ejpam-2044	389	21	it	it	PRON
ejpam-2044	389	22	follows	follow	VERB
ejpam-2044	389	23	a(1−∆)πswiss[x	a(1−∆)πswiss[x	NOUN
ejpam-2044	389	24	]	]	PUNCT
ejpam-2044	390	1	+	+	PUNCT
ejpam-2044	390	2	b	b	X
ejpam-2044	390	3	=	=	SYM
ejpam-2044	390	4	e[a(x	e[a(x	ADP
ejpam-2044	390	5	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	390	6	]	]	PUNCT
ejpam-2044	390	7	)	)	PUNCT
ejpam-2044	391	1	+	+	CCONJ
ejpam-2044	391	2	b	b	X
ejpam-2044	391	3	]	]	X
ejpam-2044	391	4	=	=	PUNCT
ejpam-2044	391	5	ae[x	ae[x	PROPN
ejpam-2044	391	6	]	]	PUNCT
ejpam-2044	391	7	−	−	PROPN
ejpam-2044	391	8	a∆πswiss[x	a∆πswiss[x	NOUN
ejpam-2044	391	9	]	]	PUNCT
ejpam-2044	392	1	+	+	CCONJ
ejpam-2044	392	2	b	b	X
ejpam-2044	392	3	,	,	PUNCT
ejpam-2044	392	4	so	so	ADV
ejpam-2044	392	5	,	,	PUNCT
ejpam-2044	392	6	here	here	ADV
ejpam-2044	392	7	we	we	PRON
ejpam-2044	392	8	get	get	VERB
ejpam-2044	392	9	πswiss[x	πswiss[x	NOUN
ejpam-2044	392	10	]	]	X
ejpam-2044	392	11	=	=	SYM
ejpam-2044	392	12	e[x	e[x	NOUN
ejpam-2044	392	13	]	]	X
ejpam-2044	392	14	=	=	PUNCT
ejpam-2044	392	15	πnet[x	πnet[x	X
ejpam-2044	392	16	]	]	X
ejpam-2044	392	17	.	.	PUNCT
ejpam-2044	393	1	on	on	ADP
ejpam-2044	393	2	the	the	DET
ejpam-2044	393	3	other	other	ADJ
ejpam-2044	393	4	hand	hand	NOUN
ejpam-2044	393	5	,	,	PUNCT
ejpam-2044	393	6	for	for	ADP
ejpam-2044	393	7	the	the	DET
ejpam-2044	393	8	same	same	ADJ
ejpam-2044	393	9	risk	risk	NOUN
ejpam-2044	393	10	x	x	X
ejpam-2044	393	11	,	,	PUNCT
ejpam-2044	393	12	any	any	DET
ejpam-2044	393	13	∆	∆	PROPN
ejpam-2044	393	14	∈	∈	NOUN
ejpam-2044	394	1	[	[	X
ejpam-2044	394	2	0	0	NUM
ejpam-2044	394	3	,	,	PUNCT
ejpam-2044	394	4	1	1	NUM
ejpam-2044	394	5	]	]	PUNCT
ejpam-2044	394	6	,	,	PUNCT
ejpam-2044	394	7	the	the	DET
ejpam-2044	394	8	same	same	ADJ
ejpam-2044	394	9	function	function	NOUN
ejpam-2044	394	10	v	v	NOUN
ejpam-2044	394	11	(	(	PUNCT
ejpam-2044	394	12	x	x	NOUN
ejpam-2044	394	13	)	)	PUNCT
ejpam-2044	394	14	,	,	PUNCT
ejpam-2044	394	15	and	and	CCONJ
ejpam-2044	394	16	any	any	DET
ejpam-2044	394	17	θ	θ	PROPN
ejpam-2044	394	18	>	>	X
ejpam-2044	394	19	0	0	NUM
ejpam-2044	394	20	from	from	ADP
ejpam-2044	394	21	definition	definition	NOUN
ejpam-2044	394	22	equation	equation	NOUN
ejpam-2044	394	23	(	(	PUNCT
ejpam-2044	394	24	6	6	X
ejpam-2044	394	25	)	)	PUNCT
ejpam-2044	394	26	it	it	PRON
ejpam-2044	394	27	follows	follow	VERB
ejpam-2044	394	28	a(1−∆)πswiss[θx	a(1−∆)πswiss[θx	PROPN
ejpam-2044	394	29	]	]	PUNCT
ejpam-2044	395	1	+	+	NUM
ejpam-2044	395	2	b	b	X
ejpam-2044	395	3	=	=	SYM
ejpam-2044	395	4	e[a(θx	e[a(θx	NOUN
ejpam-2044	395	5	−∆πswiss[θx	−∆πswiss[θx	NOUN
ejpam-2044	395	6	]	]	PUNCT
ejpam-2044	395	7	)	)	PUNCT
ejpam-2044	396	1	+	+	CCONJ
ejpam-2044	396	2	b	b	X
ejpam-2044	396	3	]	]	X
ejpam-2044	396	4	=	=	SYM
ejpam-2044	396	5	aθe[x	aθe[x	NOUN
ejpam-2044	396	6	]	]	X
ejpam-2044	396	7	−	−	X
ejpam-2044	396	8	a∆πswiss[θx	a∆πswiss[θx	NOUN
ejpam-2044	396	9	]	]	PUNCT
ejpam-2044	397	1	+	+	CCONJ
ejpam-2044	397	2	b	b	X
ejpam-2044	397	3	,	,	PUNCT
ejpam-2044	397	4	therefore	therefore	ADV
ejpam-2044	397	5	,	,	PUNCT
ejpam-2044	397	6	in	in	ADP
ejpam-2044	397	7	the	the	DET
ejpam-2044	397	8	considered	consider	VERB
ejpam-2044	397	9	case	case	NOUN
ejpam-2044	397	10	,	,	PUNCT
ejpam-2044	397	11	πswiss[θx	πswiss[θx	NOUN
ejpam-2044	397	12	]	]	PUNCT
ejpam-2044	397	13	=	=	PUNCT
ejpam-2044	397	14	θe[x	θe[x	NOUN
ejpam-2044	397	15	]	]	PUNCT
ejpam-2044	397	16	=	=	PUNCT
ejpam-2044	397	17	θπswiss[x	θπswiss[x	ADJ
ejpam-2044	397	18	]	]	X
ejpam-2044	397	19	,	,	PUNCT
ejpam-2044	397	20	and	and	CCONJ
ejpam-2044	397	21	as	as	SCONJ
ejpam-2044	397	22	we	we	PRON
ejpam-2044	397	23	see	see	VERB
ejpam-2044	397	24	,	,	PUNCT
ejpam-2044	397	25	swiss	swiss	ADJ
ejpam-2044	397	26	premium	premium	NOUN
ejpam-2044	397	27	calculation	calculation	NOUN
ejpam-2044	397	28	principle	principle	NOUN
ejpam-2044	397	29	possesses	possess	VERB
ejpam-2044	397	30	scale	scale	NOUN
ejpam-2044	397	31	invariance	invariance	NOUN
ejpam-2044	397	32	property	property	NOUN
ejpam-2044	397	33	in	in	ADP
ejpam-2044	397	34	the	the	DET
ejpam-2044	397	35	case	case	NOUN
ejpam-2044	397	36	of	of	ADP
ejpam-2044	397	37	increasing	increase	VERB
ejpam-2044	397	38	linear	linear	ADJ
ejpam-2044	397	39	function	function	NOUN
ejpam-2044	397	40	v	v	NOUN
ejpam-2044	397	41	(	(	PUNCT
ejpam-2044	397	42	x	x	NOUN
ejpam-2044	397	43	)	)	PUNCT
ejpam-2044	397	44	.	.	PUNCT
ejpam-2044	398	1	the	the	DET
ejpam-2044	398	2	proof	proof	NOUN
ejpam-2044	398	3	of	of	ADP
ejpam-2044	398	4	the	the	DET
ejpam-2044	398	5	sufficiency	sufficiency	NOUN
ejpam-2044	398	6	was	be	AUX
ejpam-2044	398	7	finished	finish	VERB
ejpam-2044	398	8	,	,	PUNCT
ejpam-2044	398	9	so	so	SCONJ
ejpam-2044	398	10	we	we	PRON
ejpam-2044	398	11	can	can	AUX
ejpam-2044	398	12	start	start	VERB
ejpam-2044	398	13	to	to	PART
ejpam-2044	398	14	prove	prove	VERB
ejpam-2044	398	15	the	the	DET
ejpam-2044	398	16	necessity	necessity	NOUN
ejpam-2044	398	17	.	.	PUNCT
ejpam-2044	399	1	in	in	ADP
ejpam-2044	399	2	order	order	NOUN
ejpam-2044	399	3	to	to	PART
ejpam-2044	399	4	show	show	VERB
ejpam-2044	399	5	that	that	SCONJ
ejpam-2044	399	6	swiss	swiss	ADJ
ejpam-2044	399	7	premium	premium	NOUN
ejpam-2044	399	8	calculation	calculation	NOUN
ejpam-2044	399	9	principle	principle	NOUN
ejpam-2044	399	10	with	with	ADP
ejpam-2044	399	11	non	non	ADJ
ejpam-2044	399	12	-	-	ADJ
ejpam-2044	399	13	linear	linear	ADJ
ejpam-2044	399	14	functions	function	NOUN
ejpam-2044	399	15	v	v	NOUN
ejpam-2044	399	16	(	(	PUNCT
ejpam-2044	399	17	x	x	NOUN
ejpam-2044	399	18	)	)	PUNCT
ejpam-2044	399	19	will	will	AUX
ejpam-2044	399	20	not	not	PART
ejpam-2044	399	21	possess	possess	VERB
ejpam-2044	399	22	scale	scale	NOUN
ejpam-2044	399	23	invariance	invariance	NOUN
ejpam-2044	399	24	property	property	NOUN
ejpam-2044	399	25	let	let	VERB
ejpam-2044	399	26	us	we	PRON
ejpam-2044	399	27	consider	consider	VERB
ejpam-2044	399	28	a	a	DET
ejpam-2044	399	29	risk	risk	NOUN
ejpam-2044	399	30	x	x	PUNCT
ejpam-2044	399	31	taking	take	VERB
ejpam-2044	399	32	value	value	NOUN
ejpam-2044	399	33	t	t	NOUN
ejpam-2044	399	34	(	(	PUNCT
ejpam-2044	399	35	here	here	ADV
ejpam-2044	399	36	parameter	parameter	PROPN
ejpam-2044	399	37	t	t	PROPN
ejpam-2044	399	38	takes	take	VERB
ejpam-2044	399	39	non	non	ADJ
ejpam-2044	399	40	-	-	ADJ
ejpam-2044	399	41	zero	zero	ADJ
ejpam-2044	399	42	real	real	ADJ
ejpam-2044	399	43	values	value	NOUN
ejpam-2044	399	44	)	)	PUNCT
ejpam-2044	399	45	and	and	CCONJ
ejpam-2044	399	46	0	0	NUM
ejpam-2044	399	47	with	with	ADP
ejpam-2044	399	48	probabilities	probability	NOUN
ejpam-2044	399	49	p	p	NOUN
ejpam-2044	399	50	and	and	CCONJ
ejpam-2044	399	51	1−p	1−p	NUM
ejpam-2044	399	52	respectively	respectively	ADV
ejpam-2044	399	53	.	.	PUNCT
ejpam-2044	400	1	being	be	AUX
ejpam-2044	400	2	a	a	DET
ejpam-2044	400	3	random	random	ADJ
ejpam-2044	400	4	function	function	NOUN
ejpam-2044	400	5	of	of	ADP
ejpam-2044	400	6	the	the	DET
ejpam-2044	400	7	parameters	parameter	NOUN
ejpam-2044	400	8	p	p	NOUN
ejpam-2044	400	9	and	and	CCONJ
ejpam-2044	400	10	t	t	X
ejpam-2044	400	11	the	the	DET
ejpam-2044	400	12	risk	risk	NOUN
ejpam-2044	400	13	x	x	PUNCT
ejpam-2044	400	14	within	within	ADP
ejpam-2044	400	15	the	the	DET
ejpam-2044	400	16	proof	proof	NOUN
ejpam-2044	400	17	of	of	ADP
ejpam-2044	400	18	theorem	theorem	NOUN
ejpam-2044	400	19	6	6	NUM
ejpam-2044	400	20	will	will	AUX
ejpam-2044	400	21	be	be	AUX
ejpam-2044	400	22	denoted	denote	VERB
ejpam-2044	400	23	as	as	SCONJ
ejpam-2044	400	24	x	x	PROPN
ejpam-2044	400	25	t	t	PROPN
ejpam-2044	400	26	p.	p.	NOUN
ejpam-2044	400	27	observe	observe	VERB
ejpam-2044	400	28	that	that	SCONJ
ejpam-2044	400	29	swiss	swiss	ADJ
ejpam-2044	400	30	premium	premium	NOUN
ejpam-2044	400	31	calculation	calculation	NOUN
ejpam-2044	400	32	principle	principle	NOUN
ejpam-2044	400	33	is	be	AUX
ejpam-2044	400	34	invariant	invariant	ADJ
ejpam-2044	400	35	with	with	ADP
ejpam-2044	400	36	respect	respect	NOUN
ejpam-2044	400	37	to	to	ADP
ejpam-2044	400	38	linear	linear	ADJ
ejpam-2044	400	39	transformations	transformation	NOUN
ejpam-2044	400	40	of	of	ADP
ejpam-2044	400	41	the	the	DET
ejpam-2044	400	42	function	function	NOUN
ejpam-2044	400	43	v	v	NOUN
ejpam-2044	400	44	(	(	PUNCT
ejpam-2044	400	45	x	x	NOUN
ejpam-2044	400	46	)	)	PUNCT
ejpam-2044	400	47	,	,	PUNCT
ejpam-2044	400	48	i.e.	i.e.	X
ejpam-2044	400	49	,	,	PUNCT
ejpam-2044	400	50	principle	principle	NOUN
ejpam-2044	400	51	based	base	VERB
ejpam-2044	400	52	on	on	ADP
ejpam-2044	400	53	a	a	DET
ejpam-2044	400	54	function	function	NOUN
ejpam-2044	400	55	v	v	NOUN
ejpam-2044	400	56	(	(	PUNCT
ejpam-2044	400	57	x	x	NOUN
ejpam-2044	400	58	)	)	PUNCT
ejpam-2044	400	59	and	and	CCONJ
ejpam-2044	400	60	principle	principle	NOUN
ejpam-2044	400	61	based	base	VERB
ejpam-2044	400	62	on	on	ADP
ejpam-2044	400	63	the	the	DET
ejpam-2044	400	64	function	function	NOUN
ejpam-2044	400	65	v	v	NOUN
ejpam-2044	400	66	(	(	PUNCT
ejpam-2044	400	67	x	x	NOUN
ejpam-2044	400	68	)	)	PUNCT
ejpam-2044	400	69	:	:	PUNCT
ejpam-2044	401	1	=	=	SYM
ejpam-2044	401	2	l1v	l1v	VERB
ejpam-2044	401	3	(	(	PUNCT
ejpam-2044	401	4	x)+	x)+	NUM
ejpam-2044	401	5	l2	l2	NOUN
ejpam-2044	401	6	,	,	PUNCT
ejpam-2044	401	7	for	for	ADP
ejpam-2044	401	8	l1	l1	PROPN
ejpam-2044	401	9	>	>	X
ejpam-2044	401	10	0	0	PROPN
ejpam-2044	401	11	,	,	PUNCT
ejpam-2044	401	12	will	will	AUX
ejpam-2044	401	13	produce	produce	VERB
ejpam-2044	401	14	the	the	DET
ejpam-2044	401	15	same	same	ADJ
ejpam-2044	401	16	premiums	premium	NOUN
ejpam-2044	401	17	for	for	ADP
ejpam-2044	401	18	the	the	DET
ejpam-2044	401	19	same	same	ADJ
ejpam-2044	401	20	risks	risk	NOUN
ejpam-2044	401	21	.	.	PUNCT
ejpam-2044	402	1	here	here	ADV
ejpam-2044	402	2	condition	condition	NOUN
ejpam-2044	402	3	l1	l1	PROPN
ejpam-2044	402	4	>	>	X
ejpam-2044	402	5	0	0	NUM
ejpam-2044	402	6	is	be	AUX
ejpam-2044	402	7	imposed	impose	VERB
ejpam-2044	402	8	because	because	SCONJ
ejpam-2044	402	9	otherwise	otherwise	ADV
ejpam-2044	402	10	the	the	DET
ejpam-2044	402	11	assumption	assumption	NOUN
ejpam-2044	402	12	of	of	ADP
ejpam-2044	402	13	positivity	positivity	NOUN
ejpam-2044	402	14	of	of	ADP
ejpam-2044	402	15	first	first	ADJ
ejpam-2044	402	16	derivative	derivative	NOUN
ejpam-2044	402	17	of	of	ADP
ejpam-2044	402	18	the	the	PRON
ejpam-2044	402	19	function	function	NOUN
ejpam-2044	402	20	v	v	NOUN
ejpam-2044	402	21	(	(	PUNCT
ejpam-2044	402	22	x	x	X
ejpam-2044	402	23	)	)	PUNCT
ejpam-2044	402	24	will	will	AUX
ejpam-2044	402	25	vanish	vanish	VERB
ejpam-2044	402	26	.	.	PUNCT
ejpam-2044	403	1	in	in	ADP
ejpam-2044	403	2	order	order	NOUN
ejpam-2044	403	3	to	to	PART
ejpam-2044	403	4	simplify	simplify	VERB
ejpam-2044	403	5	the	the	DET
ejpam-2044	403	6	computations	computation	NOUN
ejpam-2044	403	7	,	,	PUNCT
ejpam-2044	403	8	we	we	PRON
ejpam-2044	403	9	will	will	AUX
ejpam-2044	403	10	first	first	ADV
ejpam-2044	403	11	obtain	obtain	VERB
ejpam-2044	403	12	all	all	DET
ejpam-2044	403	13	possible	possible	ADJ
ejpam-2044	403	14	representations	representation	NOUN
ejpam-2044	403	15	(	(	PUNCT
ejpam-2044	403	16	in	in	ADP
ejpam-2044	403	17	the	the	DET
ejpam-2044	403	18	case	case	NOUN
ejpam-2044	403	19	when	when	SCONJ
ejpam-2044	403	20	swiss	swiss	ADJ
ejpam-2044	403	21	premium	premium	NOUN
ejpam-2044	403	22	calculation	calculation	NOUN
ejpam-2044	403	23	principle	principle	NOUN
ejpam-2044	403	24	is	be	AUX
ejpam-2044	403	25	scale	scale	NOUN
ejpam-2044	403	26	invariant	invariant	ADJ
ejpam-2044	403	27	)	)	PUNCT
ejpam-2044	403	28	for	for	ADP
ejpam-2044	403	29	the	the	DET
ejpam-2044	403	30	scaled	scale	VERB
ejpam-2044	403	31	function	function	NOUN
ejpam-2044	403	32	v	v	NOUN
ejpam-2044	403	33	(	(	PUNCT
ejpam-2044	403	34	x	x	X
ejpam-2044	403	35	)	)	PUNCT
ejpam-2044	403	36	with	with	ADP
ejpam-2044	403	37	l1	l1	PROPN
ejpam-2044	403	38	=	=	SYM
ejpam-2044	403	39	1	1	NUM
ejpam-2044	403	40	/	/	SYM
ejpam-2044	403	41	v	v	NUM
ejpam-2044	403	42	′(0	′(0	PROPN
ejpam-2044	403	43	)	)	PUNCT
ejpam-2044	403	44	and	and	CCONJ
ejpam-2044	403	45	l2	l2	NOUN
ejpam-2044	403	46	=	=	SYM
ejpam-2044	403	47	−v	−v	NOUN
ejpam-2044	403	48	(	(	PUNCT
ejpam-2044	403	49	0)/v	0)/v	PROPN
ejpam-2044	403	50	′(0	′(0	NOUN
ejpam-2044	403	51	)	)	PUNCT
ejpam-2044	403	52	,	,	PUNCT
ejpam-2044	403	53	and	and	CCONJ
ejpam-2044	403	54	then	then	ADV
ejpam-2044	403	55	we	we	PRON
ejpam-2044	403	56	will	will	AUX
ejpam-2044	403	57	switch	switch	VERB
ejpam-2044	403	58	back	back	ADV
ejpam-2044	403	59	to	to	ADP
ejpam-2044	403	60	the	the	DET
ejpam-2044	403	61	original	original	ADJ
ejpam-2044	403	62	function	function	NOUN
ejpam-2044	403	63	v	v	NOUN
ejpam-2044	403	64	(	(	PUNCT
ejpam-2044	403	65	x	x	NOUN
ejpam-2044	403	66	)	)	PUNCT
ejpam-2044	403	67	.	.	PUNCT
ejpam-2044	404	1	observe	observe	VERB
ejpam-2044	404	2	that	that	SCONJ
ejpam-2044	404	3	the	the	DET
ejpam-2044	404	4	just	just	ADV
ejpam-2044	404	5	defined	define	VERB
ejpam-2044	404	6	function	function	NOUN
ejpam-2044	404	7	v	v	NOUN
ejpam-2044	404	8	(	(	PUNCT
ejpam-2044	404	9	x	x	NOUN
ejpam-2044	404	10	)	)	PUNCT
ejpam-2044	404	11	satisfies	satisfy	VERB
ejpam-2044	404	12	the	the	DET
ejpam-2044	404	13	following	follow	VERB
ejpam-2044	404	14	boundary	boundary	ADJ
ejpam-2044	404	15	conditions	condition	NOUN
ejpam-2044	404	16	v	v	NOUN
ejpam-2044	404	17	(	(	PUNCT
ejpam-2044	404	18	0	0	NUM
ejpam-2044	404	19	)	)	PUNCT
ejpam-2044	404	20	=	=	SYM
ejpam-2044	404	21	0	0	NUM
ejpam-2044	404	22	,	,	PUNCT
ejpam-2044	404	23	and	and	CCONJ
ejpam-2044	404	24	v	v	ADP
ejpam-2044	404	25	′	′	NUM
ejpam-2044	404	26	(	(	PUNCT
ejpam-2044	404	27	0	0	NUM
ejpam-2044	404	28	)	)	PUNCT
ejpam-2044	404	29	=	=	SYM
ejpam-2044	405	1	1	1	X
ejpam-2044	405	2	.	.	PUNCT
ejpam-2044	405	3	(	(	PUNCT
ejpam-2044	405	4	75	75	NUM
ejpam-2044	405	5	)	)	PUNCT
ejpam-2044	405	6	definition	definition	NOUN
ejpam-2044	405	7	equation	equation	NOUN
ejpam-2044	405	8	(	(	PUNCT
ejpam-2044	405	9	6	6	NUM
ejpam-2044	405	10	)	)	PUNCT
ejpam-2044	405	11	based	base	VERB
ejpam-2044	405	12	on	on	ADP
ejpam-2044	405	13	the	the	DET
ejpam-2044	405	14	function	function	NOUN
ejpam-2044	405	15	v	v	NOUN
ejpam-2044	405	16	(	(	PUNCT
ejpam-2044	405	17	x	x	NOUN
ejpam-2044	405	18	)	)	PUNCT
ejpam-2044	405	19	for	for	ADP
ejpam-2044	405	20	the	the	DET
ejpam-2044	405	21	risk	risk	NOUN
ejpam-2044	405	22	x	x	X
ejpam-2044	405	23	t	t	NOUN
ejpam-2044	405	24	p	p	NOUN
ejpam-2044	405	25	and	and	CCONJ
ejpam-2044	405	26	∆	∆	PROPN
ejpam-2044	405	27	∈	∈	PROPN
ejpam-2044	405	28	[	[	X
ejpam-2044	405	29	0,1	0,1	NUM
ejpam-2044	405	30	]	]	PUNCT
ejpam-2044	405	31	will	will	AUX
ejpam-2044	405	32	take	take	VERB
ejpam-2044	405	33	the	the	DET
ejpam-2044	405	34	following	follow	VERB
ejpam-2044	405	35	form	form	NOUN
ejpam-2044	405	36	v	v	NOUN
ejpam-2044	405	37	(	(	PUNCT
ejpam-2044	405	38	(	(	PUNCT
ejpam-2044	405	39	1−∆)πswiss[x	1−∆)πswiss[x	NUM
ejpam-2044	405	40	t	t	NOUN
ejpam-2044	405	41	p	p	X
ejpam-2044	405	42	]	]	X
ejpam-2044	405	43	)	)	PUNCT
ejpam-2044	405	44	=	=	SYM
ejpam-2044	405	45	v	v	X
ejpam-2044	405	46	(	(	PUNCT
ejpam-2044	405	47	t	t	PROPN
ejpam-2044	405	48	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	405	49	t	t	PROPN
ejpam-2044	405	50	p])p+	p])p+	PROPN
ejpam-2044	405	51	v	v	PROPN
ejpam-2044	405	52	(	(	PUNCT
ejpam-2044	405	53	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	405	54	t	t	NOUN
ejpam-2044	405	55	p])(1−	p])(1−	NOUN
ejpam-2044	405	56	p	p	NOUN
ejpam-2044	405	57	)	)	PUNCT
ejpam-2044	405	58	.	.	PUNCT
ejpam-2044	406	1	(	(	PUNCT
ejpam-2044	406	2	76	76	X
ejpam-2044	406	3	)	)	PUNCT
ejpam-2044	406	4	putting	put	VERB
ejpam-2044	406	5	p	p	NOUN
ejpam-2044	406	6	=	=	NOUN
ejpam-2044	406	7	0	0	NUM
ejpam-2044	406	8	into	into	ADP
ejpam-2044	406	9	the	the	DET
ejpam-2044	406	10	equation	equation	NOUN
ejpam-2044	406	11	(	(	PUNCT
ejpam-2044	406	12	76	76	NUM
ejpam-2044	406	13	)	)	PUNCT
ejpam-2044	406	14	,	,	PUNCT
ejpam-2044	406	15	obtain	obtain	VERB
ejpam-2044	406	16	v	v	NOUN
ejpam-2044	406	17	(	(	PUNCT
ejpam-2044	406	18	(	(	PUNCT
ejpam-2044	406	19	1−∆)πswiss[x	1−∆)πswiss[x	NUM
ejpam-2044	406	20	t	t	NOUN
ejpam-2044	406	21	0	0	NUM
ejpam-2044	406	22	]	]	PUNCT
ejpam-2044	406	23	)	)	PUNCT
ejpam-2044	407	1	=	=	SYM
ejpam-2044	407	2	v	v	X
ejpam-2044	407	3	(	(	PUNCT
ejpam-2044	407	4	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	407	5	t	t	NOUN
ejpam-2044	407	6	0	0	NUM
ejpam-2044	407	7	]	]	PUNCT
ejpam-2044	407	8	)	)	PUNCT
ejpam-2044	407	9	.	.	PUNCT
ejpam-2044	408	1	(	(	PUNCT
ejpam-2044	408	2	77	77	NUM
ejpam-2044	408	3	)	)	PUNCT
ejpam-2044	408	4	m.	m.	NOUN
ejpam-2044	408	5	pratsiovytyi	pratsiovytyi	NOUN
ejpam-2044	408	6	,	,	PUNCT
ejpam-2044	408	7	v.	v.	ADP
ejpam-2044	408	8	drozdenko	drozdenko	PROPN
ejpam-2044	408	9	/	/	SYM
ejpam-2044	408	10	eur	eur	PROPN
ejpam-2044	408	11	.	.	PUNCT
ejpam-2044	409	1	j.	j.	PROPN
ejpam-2044	409	2	pure	pure	PROPN
ejpam-2044	409	3	appl	appl	PROPN
ejpam-2044	409	4	.	.	PROPN
ejpam-2044	409	5	math	math	PROPN
ejpam-2044	409	6	,	,	PUNCT
ejpam-2044	409	7	7	7	NUM
ejpam-2044	409	8	(	(	PUNCT
ejpam-2044	409	9	2014	2014	NUM
ejpam-2044	409	10	)	)	PUNCT
ejpam-2044	409	11	,	,	PUNCT
ejpam-2044	409	12	267	267	X
ejpam-2044	409	13	-	-	SYM
ejpam-2044	409	14	288	288	NUM
ejpam-2044	409	15	286	286	NUM
ejpam-2044	409	16	since	since	SCONJ
ejpam-2044	409	17	v	v	NOUN
ejpam-2044	409	18	′	′	NUM
ejpam-2044	409	19	(	(	PUNCT
ejpam-2044	409	20	x	x	NOUN
ejpam-2044	409	21	)	)	PUNCT
ejpam-2044	409	22	>	>	X
ejpam-2044	409	23	0	0	PUNCT
ejpam-2044	410	1	for	for	ADP
ejpam-2044	410	2	all	all	DET
ejpam-2044	410	3	x	x	NOUN
ejpam-2044	410	4	,	,	PUNCT
ejpam-2044	410	5	then	then	ADV
ejpam-2044	410	6	from	from	ADP
ejpam-2044	410	7	the	the	DET
ejpam-2044	410	8	equation	equation	NOUN
ejpam-2044	410	9	(	(	PUNCT
ejpam-2044	410	10	77	77	NUM
ejpam-2044	410	11	)	)	PUNCT
ejpam-2044	410	12	it	it	PRON
ejpam-2044	410	13	follows	follow	VERB
ejpam-2044	410	14	(	(	PUNCT
ejpam-2044	410	15	1−∆)πswiss[x	1−∆)πswiss[x	NUM
ejpam-2044	410	16	t	t	NOUN
ejpam-2044	410	17	0	0	NUM
ejpam-2044	410	18	]	]	X
ejpam-2044	411	1	=	=	X
ejpam-2044	411	2	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	411	3	t	t	NOUN
ejpam-2044	411	4	0	0	NUM
ejpam-2044	411	5	]	]	PUNCT
ejpam-2044	411	6	,	,	PUNCT
ejpam-2044	411	7	which	which	PRON
ejpam-2044	411	8	yields	yield	VERB
ejpam-2044	411	9	πswiss[x	πswiss[x	PROPN
ejpam-2044	411	10	t	t	PROPN
ejpam-2044	411	11	0	0	NUM
ejpam-2044	411	12	]	]	X
ejpam-2044	411	13	=	=	SYM
ejpam-2044	411	14	0	0	X
ejpam-2044	411	15	.	.	PUNCT
ejpam-2044	412	1	(	(	PUNCT
ejpam-2044	412	2	78	78	X
ejpam-2044	412	3	)	)	PUNCT
ejpam-2044	412	4	let	let	VERB
ejpam-2044	412	5	us	we	PRON
ejpam-2044	412	6	calculate	calculate	VERB
ejpam-2044	412	7	partial	partial	ADJ
ejpam-2044	412	8	derivatives	derivative	NOUN
ejpam-2044	412	9	with	with	ADP
ejpam-2044	412	10	respect	respect	NOUN
ejpam-2044	412	11	to	to	ADP
ejpam-2044	412	12	p	p	NOUN
ejpam-2044	412	13	from	from	ADP
ejpam-2044	412	14	both	both	DET
ejpam-2044	412	15	sides	side	NOUN
ejpam-2044	412	16	of	of	ADP
ejpam-2044	412	17	the	the	DET
ejpam-2044	412	18	equation	equation	NOUN
ejpam-2044	412	19	(	(	PUNCT
ejpam-2044	412	20	76	76	NUM
ejpam-2044	412	21	)	)	PUNCT
ejpam-2044	412	22	v	v	NOUN
ejpam-2044	412	23	′	′	NUM
ejpam-2044	413	1	(	(	PUNCT
ejpam-2044	413	2	(	(	PUNCT
ejpam-2044	413	3	1−∆)πswiss[x	1−∆)πswiss[x	NUM
ejpam-2044	413	4	t	t	NOUN
ejpam-2044	413	5	p	p	X
ejpam-2044	413	6	]	]	X
ejpam-2044	413	7	)	)	PUNCT
ejpam-2044	413	8	·	·	PUNCT
ejpam-2044	413	9	(	(	PUNCT
ejpam-2044	413	10	1−∆	1−∆	NUM
ejpam-2044	413	11	)	)	PUNCT
ejpam-2044	413	12	·	·	PUNCT
ejpam-2044	413	13	∂	∂	NUM
ejpam-2044	414	1	∂	∂	NUM
ejpam-2044	414	2	p	p	NOUN
ejpam-2044	414	3	πswiss[x	πswiss[x	PROPN
ejpam-2044	414	4	t	t	PROPN
ejpam-2044	414	5	p	p	X
ejpam-2044	414	6	]	]	X
ejpam-2044	414	7	=	=	NUM
ejpam-2044	414	8	v	v	NOUN
ejpam-2044	414	9	(	(	PUNCT
ejpam-2044	414	10	t	t	PROPN
ejpam-2044	414	11	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	414	12	t	t	NOUN
ejpam-2044	414	13	p])−	p])−	NOUN
ejpam-2044	414	14	v	v	ADP
ejpam-2044	414	15	(	(	PUNCT
ejpam-2044	414	16	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	414	17	t	t	NOUN
ejpam-2044	415	1	p	p	X
ejpam-2044	415	2	]	]	X
ejpam-2044	415	3	)	)	PUNCT
ejpam-2044	415	4	−∆	−∆	NOUN
ejpam-2044	415	5	·	·	PUNCT
ejpam-2044	416	1	v	v	NUM
ejpam-2044	416	2	′(t	′(t	NOUN
ejpam-2044	416	3	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	416	4	t	t	NOUN
ejpam-2044	417	1	p	p	X
ejpam-2044	417	2	]	]	X
ejpam-2044	417	3	)	)	PUNCT
ejpam-2044	417	4	·	·	PUNCT
ejpam-2044	417	5	∂	∂	NUM
ejpam-2044	417	6	∂	∂	NUM
ejpam-2044	417	7	p	p	NOUN
ejpam-2044	417	8	πswiss[x	πswiss[x	PROPN
ejpam-2044	417	9	t	t	PROPN
ejpam-2044	417	10	p	p	X
ejpam-2044	417	11	]	]	X
ejpam-2044	417	12	·	·	PUNCT
ejpam-2044	418	1	p	p	X
ejpam-2044	418	2	−∆	−∆	NOUN
ejpam-2044	418	3	·	·	PUNCT
ejpam-2044	418	4	v	v	ADP
ejpam-2044	418	5	′(−∆πswiss[x	′(−∆πswiss[x	PROPN
ejpam-2044	418	6	t	t	NOUN
ejpam-2044	418	7	p	p	X
ejpam-2044	418	8	]	]	X
ejpam-2044	418	9	)	)	PUNCT
ejpam-2044	418	10	·	·	PUNCT
ejpam-2044	418	11	∂	∂	NUM
ejpam-2044	418	12	∂	∂	NUM
ejpam-2044	418	13	p	p	NOUN
ejpam-2044	418	14	πswiss[x	πswiss[x	PROPN
ejpam-2044	418	15	t	t	PROPN
ejpam-2044	418	16	p	p	X
ejpam-2044	418	17	]	]	X
ejpam-2044	418	18	·	·	PUNCT
ejpam-2044	418	19	(	(	PUNCT
ejpam-2044	418	20	1−	1−	NUM
ejpam-2044	418	21	p	p	NOUN
ejpam-2044	418	22	)	)	PUNCT
ejpam-2044	418	23	.	.	PUNCT
ejpam-2044	419	1	(	(	PUNCT
ejpam-2044	419	2	79	79	X
ejpam-2044	419	3	)	)	PUNCT
ejpam-2044	419	4	putting	put	VERB
ejpam-2044	419	5	p	p	NOUN
ejpam-2044	419	6	=	=	NOUN
ejpam-2044	419	7	0	0	NUM
ejpam-2044	419	8	into	into	ADP
ejpam-2044	419	9	the	the	DET
ejpam-2044	419	10	equation	equation	NOUN
ejpam-2044	419	11	(	(	PUNCT
ejpam-2044	419	12	79	79	NUM
ejpam-2044	419	13	)	)	PUNCT
ejpam-2044	419	14	,	,	PUNCT
ejpam-2044	419	15	we	we	PRON
ejpam-2044	419	16	get	get	VERB
ejpam-2044	419	17	v	v	NOUN
ejpam-2044	419	18	′	′	NUM
ejpam-2044	419	19	(	(	PUNCT
ejpam-2044	419	20	(	(	PUNCT
ejpam-2044	419	21	1−∆)πswiss[x	1−∆)πswiss[x	NUM
ejpam-2044	419	22	t	t	NOUN
ejpam-2044	419	23	0	0	NUM
ejpam-2044	419	24	]	]	PUNCT
ejpam-2044	419	25	)	)	PUNCT
ejpam-2044	419	26	·	·	PUNCT
ejpam-2044	419	27	(	(	PUNCT
ejpam-2044	419	28	1−∆	1−∆	NUM
ejpam-2044	419	29	)	)	PUNCT
ejpam-2044	419	30	·	·	PUNCT
ejpam-2044	419	31	∂	∂	NUM
ejpam-2044	420	1	∂	∂	NUM
ejpam-2044	420	2	p	p	NOUN
ejpam-2044	420	3	πswiss[x	πswiss[x	PROPN
ejpam-2044	420	4	t	t	PROPN
ejpam-2044	420	5	p	p	X
ejpam-2044	420	6	]	]	X
ejpam-2044	420	7	�	�	PROPN
ejpam-2044	420	8	�	�	PROPN
ejpam-2044	420	9	�	�	PROPN
ejpam-2044	420	10	�	�	PROPN
ejpam-2044	420	11	p=0	p=0	PROPN
ejpam-2044	421	1	=	=	NOUN
ejpam-2044	421	2	v	v	PROPN
ejpam-2044	421	3	(	(	PUNCT
ejpam-2044	421	4	t	t	NOUN
ejpam-2044	421	5	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	421	6	t	t	NOUN
ejpam-2044	421	7	0])−	0])−	NUM
ejpam-2044	421	8	v	v	X
ejpam-2044	421	9	(	(	PUNCT
ejpam-2044	421	10	−∆πswiss[x	−∆πswiss[x	X
ejpam-2044	421	11	t	t	NOUN
ejpam-2044	421	12	0	0	NUM
ejpam-2044	421	13	]	]	SYM
ejpam-2044	421	14	)	)	PUNCT
ejpam-2044	421	15	−∆	−∆	NOUN
ejpam-2044	421	16	·	·	PUNCT
ejpam-2044	421	17	v	v	ADP
ejpam-2044	421	18	′(−∆πswiss[x	′(−∆πswiss[x	PROPN
ejpam-2044	421	19	t	t	NOUN
ejpam-2044	421	20	0	0	NUM
ejpam-2044	421	21	]	]	PUNCT
ejpam-2044	421	22	)	)	PUNCT
ejpam-2044	421	23	·	·	PUNCT
ejpam-2044	421	24	∂	∂	NUM
ejpam-2044	422	1	∂	∂	NUM
ejpam-2044	422	2	p	p	NOUN
ejpam-2044	422	3	πswiss[x	πswiss[x	PROPN
ejpam-2044	422	4	t	t	PROPN
ejpam-2044	422	5	p	p	X
ejpam-2044	422	6	]	]	X
ejpam-2044	422	7	�	�	PROPN
ejpam-2044	422	8	�	�	PROPN
ejpam-2044	422	9	�	�	PROPN
ejpam-2044	422	10	�	�	PROPN
ejpam-2044	422	11	p=0	p=0	PROPN
ejpam-2044	422	12	.	.	PUNCT
ejpam-2044	423	1	(	(	PUNCT
ejpam-2044	423	2	80	80	NUM
ejpam-2044	423	3	)	)	PUNCT
ejpam-2044	423	4	combination	combination	NOUN
ejpam-2044	423	5	of	of	ADP
ejpam-2044	423	6	(	(	PUNCT
ejpam-2044	423	7	80	80	NUM
ejpam-2044	423	8	)	)	PUNCT
ejpam-2044	423	9	and	and	CCONJ
ejpam-2044	423	10	(	(	PUNCT
ejpam-2044	423	11	78	78	NUM
ejpam-2044	423	12	)	)	PUNCT
ejpam-2044	423	13	yields	yield	NOUN
ejpam-2044	423	14	v	v	NOUN
ejpam-2044	423	15	′	′	NUM
ejpam-2044	423	16	(	(	PUNCT
ejpam-2044	423	17	0	0	NUM
ejpam-2044	423	18	)	)	PUNCT
ejpam-2044	423	19	·	·	PUNCT
ejpam-2044	423	20	(	(	PUNCT
ejpam-2044	423	21	1−∆	1−∆	NUM
ejpam-2044	423	22	)	)	PUNCT
ejpam-2044	423	23	·	·	PUNCT
ejpam-2044	423	24	∂	∂	NUM
ejpam-2044	424	1	∂	∂	NUM
ejpam-2044	424	2	p	p	NOUN
ejpam-2044	424	3	πswiss[x	πswiss[x	PROPN
ejpam-2044	424	4	t	t	PROPN
ejpam-2044	424	5	p	p	X
ejpam-2044	424	6	]	]	X
ejpam-2044	424	7	�	�	PROPN
ejpam-2044	424	8	�	�	PROPN
ejpam-2044	424	9	�	�	PROPN
ejpam-2044	424	10	�	�	PROPN
ejpam-2044	424	11	p=0	p=0	PROPN
ejpam-2044	424	12	=	=	SYM
ejpam-2044	424	13	v	v	PROPN
ejpam-2044	424	14	(	(	PUNCT
ejpam-2044	424	15	t)−	t)−	PROPN
ejpam-2044	424	16	v	v	NOUN
ejpam-2044	424	17	(	(	PUNCT
ejpam-2044	424	18	0)−∆	0)−∆	X
ejpam-2044	424	19	·	·	PUNCT
ejpam-2044	424	20	v	v	NUM
ejpam-2044	424	21	′(0	′(0	PROPN
ejpam-2044	424	22	)	)	PUNCT
ejpam-2044	424	23	·	·	PUNCT
ejpam-2044	424	24	∂	∂	NUM
ejpam-2044	424	25	∂	∂	NUM
ejpam-2044	424	26	p	p	NOUN
ejpam-2044	424	27	πswiss[x	πswiss[x	PROPN
ejpam-2044	424	28	t	t	PROPN
ejpam-2044	424	29	p	p	X
ejpam-2044	424	30	]	]	X
ejpam-2044	424	31	�	�	PROPN
ejpam-2044	424	32	�	�	PROPN
ejpam-2044	424	33	�	�	PROPN
ejpam-2044	424	34	�	�	PROPN
ejpam-2044	424	35	p=0	p=0	PROPN
ejpam-2044	424	36	.	.	PUNCT
ejpam-2044	425	1	(	(	PUNCT
ejpam-2044	425	2	81	81	NUM
ejpam-2044	425	3	)	)	PUNCT
ejpam-2044	425	4	substituting	substitute	VERB
ejpam-2044	425	5	boundary	boundary	ADJ
ejpam-2044	425	6	conditions	condition	NOUN
ejpam-2044	425	7	v	v	NOUN
ejpam-2044	425	8	(	(	PUNCT
ejpam-2044	425	9	0	0	NUM
ejpam-2044	425	10	)	)	PUNCT
ejpam-2044	425	11	=	=	SYM
ejpam-2044	425	12	0	0	NUM
ejpam-2044	425	13	and	and	CCONJ
ejpam-2044	425	14	v	v	NOUN
ejpam-2044	426	1	′	′	NUM
ejpam-2044	427	1	(	(	PUNCT
ejpam-2044	427	2	0	0	NUM
ejpam-2044	427	3	)	)	PUNCT
ejpam-2044	427	4	=	=	SYM
ejpam-2044	427	5	1	1	NUM
ejpam-2044	427	6	into	into	ADP
ejpam-2044	427	7	the	the	DET
ejpam-2044	427	8	equation	equation	NOUN
ejpam-2044	427	9	(	(	PUNCT
ejpam-2044	427	10	81	81	NUM
ejpam-2044	427	11	)	)	PUNCT
ejpam-2044	427	12	we	we	PRON
ejpam-2044	427	13	obtain	obtain	VERB
ejpam-2044	427	14	a	a	DET
ejpam-2044	427	15	representation	representation	NOUN
ejpam-2044	427	16	for	for	ADP
ejpam-2044	427	17	the	the	DET
ejpam-2044	427	18	partial	partial	ADJ
ejpam-2044	427	19	derivative	derivative	NOUN
ejpam-2044	427	20	with	with	ADP
ejpam-2044	427	21	respect	respect	NOUN
ejpam-2044	427	22	to	to	ADP
ejpam-2044	427	23	the	the	DET
ejpam-2044	427	24	parameter	parameter	NOUN
ejpam-2044	427	25	p	p	NOUN
ejpam-2044	427	26	of	of	ADP
ejpam-2044	427	27	the	the	DET
ejpam-2044	427	28	premium	premium	NOUN
ejpam-2044	427	29	at	at	ADP
ejpam-2044	427	30	the	the	DET
ejpam-2044	427	31	point	point	NOUN
ejpam-2044	427	32	p	p	X
ejpam-2044	427	33	=	=	NOUN
ejpam-2044	427	34	0	0	NUM
ejpam-2044	427	35	,	,	PUNCT
ejpam-2044	427	36	namely	namely	ADV
ejpam-2044	427	37	,	,	PUNCT
ejpam-2044	427	38	∂	∂	NUM
ejpam-2044	427	39	∂	∂	NOUN
ejpam-2044	427	40	p	p	NOUN
ejpam-2044	427	41	πswiss[x	πswiss[x	PROPN
ejpam-2044	427	42	t	t	PROPN
ejpam-2044	427	43	p	p	X
ejpam-2044	427	44	]	]	X
ejpam-2044	427	45	�	�	PROPN
ejpam-2044	427	46	�	�	PROPN
ejpam-2044	427	47	�	�	PROPN
ejpam-2044	427	48	�	�	PROPN
ejpam-2044	427	49	p=0	p=0	PROPN
ejpam-2044	427	50	=	=	SYM
ejpam-2044	427	51	v	v	PROPN
ejpam-2044	427	52	(	(	PUNCT
ejpam-2044	427	53	t	t	PROPN
ejpam-2044	427	54	)	)	PUNCT
ejpam-2044	427	55	.	.	PUNCT
ejpam-2044	428	1	(	(	PUNCT
ejpam-2044	428	2	82	82	NUM
ejpam-2044	428	3	)	)	PUNCT
ejpam-2044	428	4	on	on	ADP
ejpam-2044	428	5	the	the	DET
ejpam-2044	428	6	other	other	ADJ
ejpam-2044	428	7	hand	hand	NOUN
ejpam-2044	428	8	,	,	PUNCT
ejpam-2044	428	9	equation	equation	NOUN
ejpam-2044	428	10	(	(	PUNCT
ejpam-2044	428	11	6	6	NUM
ejpam-2044	428	12	)	)	PUNCT
ejpam-2044	428	13	for	for	ADP
ejpam-2044	428	14	the	the	DET
ejpam-2044	428	15	risk	risk	NOUN
ejpam-2044	428	16	θx	θx	ADP
ejpam-2044	428	17	t	t	PROPN
ejpam-2044	428	18	p	p	NOUN
ejpam-2044	428	19	based	base	VERB
ejpam-2044	428	20	on	on	ADP
ejpam-2044	428	21	v	v	NUM
ejpam-2044	428	22	(	(	PUNCT
ejpam-2044	428	23	x	x	NOUN
ejpam-2044	428	24	)	)	PUNCT
ejpam-2044	428	25	for	for	ADP
ejpam-2044	428	26	any	any	DET
ejpam-2044	428	27	θ	θ	PROPN
ejpam-2044	428	28	>	>	PUNCT
ejpam-2044	428	29	0	0	PUNCT
ejpam-2044	428	30	and	and	CCONJ
ejpam-2044	428	31	any	any	DET
ejpam-2044	428	32	∆	∆	ADJ
ejpam-2044	428	33	∈	∈	NOUN
ejpam-2044	429	1	[	[	X
ejpam-2044	429	2	0,1	0,1	NUM
ejpam-2044	429	3	]	]	PUNCT
ejpam-2044	429	4	,	,	PUNCT
ejpam-2044	429	5	will	will	AUX
ejpam-2044	429	6	have	have	VERB
ejpam-2044	429	7	the	the	DET
ejpam-2044	429	8	following	follow	VERB
ejpam-2044	429	9	form	form	NOUN
ejpam-2044	429	10	v	v	NOUN
ejpam-2044	429	11	(	(	PUNCT
ejpam-2044	429	12	(	(	PUNCT
ejpam-2044	429	13	1−∆)πswiss[θx	1−∆)πswiss[θx	NOUN
ejpam-2044	429	14	t	t	NOUN
ejpam-2044	429	15	p	p	X
ejpam-2044	429	16	]	]	X
ejpam-2044	429	17	)	)	PUNCT
ejpam-2044	429	18	=	=	SYM
ejpam-2044	429	19	v	v	X
ejpam-2044	429	20	(	(	PUNCT
ejpam-2044	429	21	tθ−∆πswiss[θx	tθ−∆πswiss[θx	NOUN
ejpam-2044	429	22	t	t	NOUN
ejpam-2044	429	23	p	p	X
ejpam-2044	429	24	]	]	X
ejpam-2044	429	25	)	)	PUNCT
ejpam-2044	429	26	·	·	PUNCT
ejpam-2044	429	27	p+	p+	PROPN
ejpam-2044	429	28	v	v	X
ejpam-2044	429	29	(	(	PUNCT
ejpam-2044	429	30	−∆πswiss[θx	−∆πswiss[θx	NOUN
ejpam-2044	429	31	t	t	NOUN
ejpam-2044	429	32	p	p	X
ejpam-2044	429	33	]	]	X
ejpam-2044	429	34	)	)	PUNCT
ejpam-2044	429	35	·	·	PUNCT
ejpam-2044	429	36	(	(	PUNCT
ejpam-2044	429	37	1−	1−	NUM
ejpam-2044	429	38	p	p	NOUN
ejpam-2044	429	39	)	)	PUNCT
ejpam-2044	429	40	.	.	PUNCT
ejpam-2044	430	1	(	(	PUNCT
ejpam-2044	430	2	83	83	NUM
ejpam-2044	430	3	)	)	PUNCT
ejpam-2044	430	4	since	since	SCONJ
ejpam-2044	430	5	in	in	ADP
ejpam-2044	430	6	the	the	DET
ejpam-2044	430	7	case	case	NOUN
ejpam-2044	430	8	of	of	ADP
ejpam-2044	430	9	scale	scale	NOUN
ejpam-2044	430	10	invariant	invariant	ADJ
ejpam-2044	430	11	swiss	swiss	ADJ
ejpam-2044	430	12	premium	premium	NOUN
ejpam-2044	430	13	calculation	calculation	NOUN
ejpam-2044	430	14	principle	principle	NOUN
ejpam-2044	430	15	for	for	ADP
ejpam-2044	430	16	any	any	DET
ejpam-2044	430	17	θ	θ	PROPN
ejpam-2044	430	18	>	>	X
ejpam-2044	430	19	0	0	NUM
ejpam-2044	431	1	the	the	DET
ejpam-2044	431	2	following	follow	VERB
ejpam-2044	431	3	identity	identity	NOUN
ejpam-2044	431	4	must	must	AUX
ejpam-2044	431	5	hold	hold	VERB
ejpam-2044	431	6	πswiss[θx	πswiss[θx	PROPN
ejpam-2044	431	7	t	t	NOUN
ejpam-2044	431	8	p	p	X
ejpam-2044	431	9	]	]	X
ejpam-2044	431	10	=	=	PUNCT
ejpam-2044	431	11	θπswiss[x	θπswiss[x	PROPN
ejpam-2044	431	12	t	t	PROPN
ejpam-2044	431	13	p	p	X
ejpam-2044	431	14	]	]	X
ejpam-2044	431	15	,	,	PUNCT
ejpam-2044	431	16	m.	m.	NOUN
ejpam-2044	431	17	pratsiovytyi	pratsiovytyi	PROPN
ejpam-2044	431	18	,	,	PUNCT
ejpam-2044	431	19	v.	v.	ADP
ejpam-2044	431	20	drozdenko	drozdenko	PROPN
ejpam-2044	431	21	/	/	SYM
ejpam-2044	431	22	eur	eur	PROPN
ejpam-2044	431	23	.	.	PUNCT
ejpam-2044	432	1	j.	j.	PROPN
ejpam-2044	432	2	pure	pure	PROPN
ejpam-2044	432	3	appl	appl	PROPN
ejpam-2044	432	4	.	.	PROPN
ejpam-2044	432	5	math	math	PROPN
ejpam-2044	432	6	,	,	PUNCT
ejpam-2044	432	7	7	7	NUM
ejpam-2044	432	8	(	(	PUNCT
ejpam-2044	432	9	2014	2014	NUM
ejpam-2044	432	10	)	)	PUNCT
ejpam-2044	432	11	,	,	PUNCT
ejpam-2044	432	12	267	267	NUM
ejpam-2044	432	13	-	-	SYM
ejpam-2044	432	14	288	288	NUM
ejpam-2044	432	15	287	287	NUM
ejpam-2044	432	16	then	then	ADV
ejpam-2044	432	17	,	,	PUNCT
ejpam-2044	432	18	in	in	ADP
ejpam-2044	432	19	the	the	DET
ejpam-2044	432	20	case	case	NOUN
ejpam-2044	432	21	of	of	ADP
ejpam-2044	432	22	scale	scale	NOUN
ejpam-2044	432	23	invariant	invariant	ADJ
ejpam-2044	432	24	swiss	swiss	ADJ
ejpam-2044	432	25	principle	principle	NOUN
ejpam-2044	432	26	,	,	PUNCT
ejpam-2044	432	27	equation	equation	NOUN
ejpam-2044	432	28	(	(	PUNCT
ejpam-2044	432	29	83	83	NUM
ejpam-2044	432	30	)	)	PUNCT
ejpam-2044	432	31	can	can	AUX
ejpam-2044	432	32	be	be	AUX
ejpam-2044	432	33	rewritten	rewrite	VERB
ejpam-2044	432	34	in	in	ADP
ejpam-2044	432	35	the	the	DET
ejpam-2044	432	36	following	follow	VERB
ejpam-2044	432	37	equivalent	equivalent	ADJ
ejpam-2044	432	38	form	form	NOUN
ejpam-2044	432	39	v	v	NOUN
ejpam-2044	432	40	(	(	PUNCT
ejpam-2044	432	41	(	(	PUNCT
ejpam-2044	432	42	1−∆)θπswiss[x	1−∆)θπswiss[x	NUM
ejpam-2044	432	43	t	t	NOUN
ejpam-2044	432	44	p	p	X
ejpam-2044	432	45	]	]	X
ejpam-2044	432	46	)	)	PUNCT
ejpam-2044	432	47	=	=	SYM
ejpam-2044	432	48	v	v	X
ejpam-2044	432	49	(	(	PUNCT
ejpam-2044	432	50	tθ−∆θπswiss[x	tθ−∆θπswiss[x	NOUN
ejpam-2044	432	51	t	t	X
ejpam-2044	433	1	p	p	X
ejpam-2044	433	2	]	]	X
ejpam-2044	433	3	)	)	PUNCT
ejpam-2044	433	4	·	·	PUNCT
ejpam-2044	433	5	p+	p+	PROPN
ejpam-2044	433	6	v	v	X
ejpam-2044	433	7	(	(	PUNCT
ejpam-2044	433	8	−∆θπswiss[x	−∆θπswiss[x	PROPN
ejpam-2044	433	9	t	t	NOUN
ejpam-2044	433	10	p	p	X
ejpam-2044	433	11	]	]	X
ejpam-2044	433	12	)	)	PUNCT
ejpam-2044	433	13	·	·	PUNCT
ejpam-2044	434	1	(	(	PUNCT
ejpam-2044	434	2	1−	1−	NUM
ejpam-2044	434	3	p	p	NOUN
ejpam-2044	434	4	)	)	PUNCT
ejpam-2044	434	5	.	.	PUNCT
ejpam-2044	435	1	(	(	PUNCT
ejpam-2044	435	2	84	84	NUM
ejpam-2044	435	3	)	)	PUNCT
ejpam-2044	435	4	let	let	VERB
ejpam-2044	435	5	us	we	PRON
ejpam-2044	435	6	now	now	ADV
ejpam-2044	435	7	calculate	calculate	VERB
ejpam-2044	435	8	partial	partial	ADJ
ejpam-2044	435	9	derivatives	derivative	NOUN
ejpam-2044	435	10	with	with	ADP
ejpam-2044	435	11	respect	respect	NOUN
ejpam-2044	435	12	to	to	ADP
ejpam-2044	435	13	the	the	DET
ejpam-2044	435	14	parameter	parameter	NOUN
ejpam-2044	435	15	p	p	NOUN
ejpam-2044	435	16	from	from	ADP
ejpam-2044	435	17	both	both	DET
ejpam-2044	435	18	sides	side	NOUN
ejpam-2044	435	19	of	of	ADP
ejpam-2044	435	20	the	the	DET
ejpam-2044	435	21	equation	equation	NOUN
ejpam-2044	435	22	(	(	PUNCT
ejpam-2044	435	23	84	84	NUM
ejpam-2044	435	24	)	)	PUNCT
ejpam-2044	435	25	v	v	NOUN
ejpam-2044	435	26	′	′	NUM
ejpam-2044	436	1	(	(	PUNCT
ejpam-2044	436	2	(	(	PUNCT
ejpam-2044	436	3	1−∆)θπswiss[x	1−∆)θπswiss[x	NUM
ejpam-2044	436	4	t	t	NOUN
ejpam-2044	436	5	p	p	X
ejpam-2044	436	6	]	]	X
ejpam-2044	436	7	)	)	PUNCT
ejpam-2044	436	8	·	·	PUNCT
ejpam-2044	436	9	(	(	PUNCT
ejpam-2044	436	10	1−∆	1−∆	NUM
ejpam-2044	436	11	)	)	PUNCT
ejpam-2044	436	12	·	·	PUNCT
ejpam-2044	436	13	θ	θ	X
ejpam-2044	436	14	·	·	PUNCT
ejpam-2044	436	15	∂	∂	NUM
ejpam-2044	436	16	∂	∂	NOUN
ejpam-2044	436	17	p	p	NOUN
ejpam-2044	436	18	πswiss[x	πswiss[x	PROPN
ejpam-2044	436	19	t	t	PROPN
ejpam-2044	436	20	p	p	X
ejpam-2044	436	21	]	]	X
ejpam-2044	436	22	=	=	SYM
ejpam-2044	436	23	v	v	NOUN
ejpam-2044	436	24	(	(	PUNCT
ejpam-2044	436	25	θt	θt	PROPN
ejpam-2044	436	26	−∆θπswiss[x	−∆θπswiss[x	PROPN
ejpam-2044	436	27	t	t	PROPN
ejpam-2044	436	28	p])−	p])−	NOUN
ejpam-2044	436	29	v	v	ADP
ejpam-2044	436	30	(	(	PUNCT
ejpam-2044	436	31	−∆θπswiss[x	−∆θπswiss[x	PROPN
ejpam-2044	436	32	t	t	NOUN
ejpam-2044	436	33	p	p	X
ejpam-2044	436	34	]	]	X
ejpam-2044	436	35	)	)	PUNCT
ejpam-2044	436	36	−∆	−∆	NOUN
ejpam-2044	436	37	·	·	PUNCT
ejpam-2044	436	38	θ	θ	X
ejpam-2044	436	39	·	·	PUNCT
ejpam-2044	436	40	v	v	ADP
ejpam-2044	436	41	′(θt	′(θt	PROPN
ejpam-2044	436	42	−∆θπswiss[x	−∆θπswiss[x	PROPN
ejpam-2044	436	43	t	t	NOUN
ejpam-2044	436	44	p	p	X
ejpam-2044	436	45	]	]	X
ejpam-2044	436	46	)	)	PUNCT
ejpam-2044	436	47	·	·	PUNCT
ejpam-2044	436	48	∂	∂	NUM
ejpam-2044	436	49	∂	∂	NUM
ejpam-2044	436	50	p	p	NOUN
ejpam-2044	436	51	πswiss[x	πswiss[x	PROPN
ejpam-2044	436	52	t	t	PROPN
ejpam-2044	436	53	p	p	X
ejpam-2044	436	54	]	]	X
ejpam-2044	436	55	·	·	PUNCT
ejpam-2044	436	56	p	p	X
ejpam-2044	436	57	−∆	−∆	X
ejpam-2044	436	58	·	·	SYM
ejpam-2044	436	59	θ	θ	X
ejpam-2044	436	60	·	·	PUNCT
ejpam-2044	436	61	v	v	X
ejpam-2044	436	62	′(−∆θπswiss[x	′(−∆θπswiss[x	PROPN
ejpam-2044	436	63	t	t	PROPN
ejpam-2044	437	1	p	p	X
ejpam-2044	437	2	]	]	X
ejpam-2044	437	3	)	)	PUNCT
ejpam-2044	437	4	·	·	PUNCT
ejpam-2044	438	1	∂	∂	NUM
ejpam-2044	439	1	∂	∂	NUM
ejpam-2044	439	2	p	p	NOUN
ejpam-2044	439	3	πswiss[x	πswiss[x	PROPN
ejpam-2044	439	4	t	t	PROPN
ejpam-2044	439	5	p	p	X
ejpam-2044	439	6	]	]	X
ejpam-2044	439	7	·	·	PUNCT
ejpam-2044	439	8	(	(	PUNCT
ejpam-2044	439	9	1−	1−	NUM
ejpam-2044	439	10	p	p	NOUN
ejpam-2044	439	11	)	)	PUNCT
ejpam-2044	439	12	.	.	PUNCT
ejpam-2044	440	1	(	(	PUNCT
ejpam-2044	440	2	85	85	NUM
ejpam-2044	440	3	)	)	PUNCT
ejpam-2044	440	4	substituting	substitute	VERB
ejpam-2044	440	5	p	p	NOUN
ejpam-2044	440	6	=	=	NOUN
ejpam-2044	440	7	0	0	NUM
ejpam-2044	440	8	into	into	ADP
ejpam-2044	440	9	the	the	DET
ejpam-2044	440	10	equation	equation	NOUN
ejpam-2044	440	11	(	(	PUNCT
ejpam-2044	440	12	85	85	NUM
ejpam-2044	440	13	)	)	PUNCT
ejpam-2044	440	14	and	and	CCONJ
ejpam-2044	440	15	applying	apply	VERB
ejpam-2044	440	16	identities	identity	NOUN
ejpam-2044	440	17	(	(	PUNCT
ejpam-2044	440	18	78	78	NUM
ejpam-2044	440	19	)	)	PUNCT
ejpam-2044	440	20	and	and	CCONJ
ejpam-2044	440	21	(	(	PUNCT
ejpam-2044	440	22	82	82	NUM
ejpam-2044	440	23	)	)	PUNCT
ejpam-2044	440	24	,	,	PUNCT
ejpam-2044	440	25	obtain	obtain	VERB
ejpam-2044	440	26	v	v	NOUN
ejpam-2044	440	27	′	′	NUM
ejpam-2044	440	28	(	(	PUNCT
ejpam-2044	440	29	0	0	NUM
ejpam-2044	440	30	)	)	PUNCT
ejpam-2044	440	31	·	·	PUNCT
ejpam-2044	440	32	(	(	PUNCT
ejpam-2044	440	33	1−∆	1−∆	NUM
ejpam-2044	440	34	)	)	PUNCT
ejpam-2044	440	35	·	·	PUNCT
ejpam-2044	440	36	θ	θ	X
ejpam-2044	440	37	·	·	PUNCT
ejpam-2044	440	38	v	v	X
ejpam-2044	440	39	(	(	PUNCT
ejpam-2044	440	40	t	t	NOUN
ejpam-2044	440	41	)	)	PUNCT
ejpam-2044	440	42	=	=	NOUN
ejpam-2044	440	43	v	v	NOUN
ejpam-2044	440	44	(	(	PUNCT
ejpam-2044	440	45	tθ)−	tθ)−	NOUN
ejpam-2044	440	46	v	v	NOUN
ejpam-2044	440	47	(	(	PUNCT
ejpam-2044	440	48	0)−∆	0)−∆	X
ejpam-2044	440	49	·	·	PUNCT
ejpam-2044	440	50	θ	θ	X
ejpam-2044	440	51	·	·	PUNCT
ejpam-2044	440	52	v	v	NUM
ejpam-2044	440	53	′(0	′(0	PROPN
ejpam-2044	440	54	)	)	PUNCT
ejpam-2044	440	55	·	·	PUNCT
ejpam-2044	441	1	v	v	X
ejpam-2044	441	2	(	(	PUNCT
ejpam-2044	441	3	t	t	PROPN
ejpam-2044	441	4	)	)	PUNCT
ejpam-2044	441	5	.	.	PUNCT
ejpam-2044	442	1	(	(	PUNCT
ejpam-2044	442	2	86	86	NUM
ejpam-2044	442	3	)	)	PUNCT
ejpam-2044	442	4	using	use	VERB
ejpam-2044	442	5	boundary	boundary	ADJ
ejpam-2044	442	6	conditions	condition	NOUN
ejpam-2044	442	7	v	v	NOUN
ejpam-2044	442	8	(	(	PUNCT
ejpam-2044	442	9	0	0	NUM
ejpam-2044	442	10	)	)	PUNCT
ejpam-2044	442	11	=	=	SYM
ejpam-2044	442	12	0	0	NUM
ejpam-2044	442	13	and	and	CCONJ
ejpam-2044	442	14	v	v	NOUN
ejpam-2044	442	15	′	′	NUM
ejpam-2044	442	16	(	(	PUNCT
ejpam-2044	442	17	0	0	NUM
ejpam-2044	442	18	)	)	PUNCT
ejpam-2044	442	19	=	=	SYM
ejpam-2044	442	20	1	1	NUM
ejpam-2044	442	21	equation	equation	NOUN
ejpam-2044	442	22	(	(	PUNCT
ejpam-2044	442	23	86	86	NUM
ejpam-2044	442	24	)	)	PUNCT
ejpam-2044	442	25	will	will	AUX
ejpam-2044	442	26	be	be	AUX
ejpam-2044	442	27	simplified	simplify	VERB
ejpam-2044	442	28	to	to	ADP
ejpam-2044	442	29	the	the	DET
ejpam-2044	442	30	following	follow	VERB
ejpam-2044	442	31	one	one	NUM
ejpam-2044	442	32	v	v	NOUN
ejpam-2044	442	33	(	(	PUNCT
ejpam-2044	442	34	tθ	tθ	NOUN
ejpam-2044	442	35	)	)	PUNCT
ejpam-2044	442	36	=	=	SYM
ejpam-2044	442	37	θv	θv	PROPN
ejpam-2044	442	38	(	(	PUNCT
ejpam-2044	442	39	t	t	PROPN
ejpam-2044	442	40	)	)	PUNCT
ejpam-2044	442	41	.	.	PUNCT
ejpam-2044	443	1	(	(	PUNCT
ejpam-2044	443	2	87	87	NUM
ejpam-2044	443	3	)	)	PUNCT
ejpam-2044	443	4	taking	take	VERB
ejpam-2044	443	5	partial	partial	ADJ
ejpam-2044	443	6	derivatives	derivative	NOUN
ejpam-2044	443	7	with	with	ADP
ejpam-2044	443	8	respect	respect	NOUN
ejpam-2044	443	9	to	to	ADP
ejpam-2044	443	10	the	the	DET
ejpam-2044	443	11	parameter	parameter	NOUN
ejpam-2044	443	12	t	t	PROPN
ejpam-2044	443	13	from	from	ADP
ejpam-2044	443	14	both	both	DET
ejpam-2044	443	15	sides	side	NOUN
ejpam-2044	443	16	of	of	ADP
ejpam-2044	443	17	the	the	DET
ejpam-2044	443	18	equation	equation	NOUN
ejpam-2044	443	19	(	(	PUNCT
ejpam-2044	443	20	87	87	NUM
ejpam-2044	443	21	)	)	PUNCT
ejpam-2044	443	22	,	,	PUNCT
ejpam-2044	443	23	obtain	obtain	VERB
ejpam-2044	443	24	θv	θv	PROPN
ejpam-2044	444	1	′	′	NUM
ejpam-2044	444	2	(	(	PUNCT
ejpam-2044	444	3	θt	θt	PROPN
ejpam-2044	444	4	)	)	PUNCT
ejpam-2044	444	5	=	=	SYM
ejpam-2044	444	6	θv	θv	PROPN
ejpam-2044	444	7	′	′	NUM
ejpam-2044	444	8	(	(	PUNCT
ejpam-2044	444	9	t	t	PROPN
ejpam-2044	444	10	)	)	PUNCT
ejpam-2044	444	11	,	,	PUNCT
ejpam-2044	444	12	or	or	CCONJ
ejpam-2044	444	13	equivalently	equivalently	ADV
ejpam-2044	444	14	,	,	PUNCT
ejpam-2044	444	15	v	v	ADP
ejpam-2044	444	16	′	′	NUM
ejpam-2044	444	17	(	(	PUNCT
ejpam-2044	444	18	θt	θt	PROPN
ejpam-2044	444	19	)	)	PUNCT
ejpam-2044	444	20	=	=	SYM
ejpam-2044	445	1	v	v	NUM
ejpam-2044	445	2	′	′	NUM
ejpam-2044	445	3	(	(	PUNCT
ejpam-2044	445	4	t	t	PROPN
ejpam-2044	445	5	)	)	PUNCT
ejpam-2044	445	6	.	.	PUNCT
ejpam-2044	446	1	(	(	PUNCT
ejpam-2044	446	2	88	88	NUM
ejpam-2044	446	3	)	)	PUNCT
ejpam-2044	446	4	by	by	ADP
ejpam-2044	446	5	fixing	fix	VERB
ejpam-2044	446	6	value	value	NOUN
ejpam-2044	446	7	of	of	ADP
ejpam-2044	446	8	the	the	DET
ejpam-2044	446	9	parameter	parameter	NOUN
ejpam-2044	446	10	t	t	PROPN
ejpam-2044	446	11	in	in	ADP
ejpam-2044	446	12	(	(	PUNCT
ejpam-2044	446	13	88	88	NUM
ejpam-2044	446	14	)	)	PUNCT
ejpam-2044	446	15	to	to	ADP
ejpam-2044	446	16	a	a	DET
ejpam-2044	446	17	constant	constant	ADJ
ejpam-2044	446	18	from	from	ADP
ejpam-2044	446	19	r\	r\	PROPN
ejpam-2044	446	20	{	{	PUNCT
ejpam-2044	446	21	0	0	NOUN
ejpam-2044	446	22	}	}	PUNCT
ejpam-2044	446	23	and	and	CCONJ
ejpam-2044	446	24	varying	vary	VERB
ejpam-2044	446	25	values	value	NOUN
ejpam-2044	446	26	of	of	ADP
ejpam-2044	446	27	the	the	DET
ejpam-2044	446	28	parameter	parameter	NOUN
ejpam-2044	446	29	θ	θ	PROPN
ejpam-2044	446	30	we	we	PRON
ejpam-2044	446	31	will	will	AUX
ejpam-2044	446	32	make	make	VERB
ejpam-2044	446	33	v	v	NOUN
ejpam-2044	446	34	′	′	NUM
ejpam-2044	446	35	(	(	PUNCT
ejpam-2044	446	36	θt	θt	PROPN
ejpam-2044	446	37	)	)	PUNCT
ejpam-2044	446	38	a	a	DET
ejpam-2044	446	39	function	function	NOUN
ejpam-2044	446	40	of	of	ADP
ejpam-2044	446	41	changing	change	VERB
ejpam-2044	446	42	parameter	parameter	NOUN
ejpam-2044	446	43	while	while	SCONJ
ejpam-2044	446	44	the	the	DET
ejpam-2044	446	45	value	value	NOUN
ejpam-2044	446	46	v	v	X
ejpam-2044	446	47	′	′	NUM
ejpam-2044	446	48	(	(	PUNCT
ejpam-2044	446	49	t	t	NOUN
ejpam-2044	446	50	)	)	PUNCT
ejpam-2044	446	51	will	will	AUX
ejpam-2044	446	52	be	be	AUX
ejpam-2044	446	53	fixed	fix	VERB
ejpam-2044	446	54	to	to	ADP
ejpam-2044	446	55	a	a	DET
ejpam-2044	446	56	constant	constant	ADJ
ejpam-2044	446	57	.	.	PUNCT
ejpam-2044	447	1	taking	take	VERB
ejpam-2044	447	2	into	into	ADP
ejpam-2044	447	3	account	account	NOUN
ejpam-2044	447	4	this	this	DET
ejpam-2044	447	5	fact	fact	NOUN
ejpam-2044	447	6	as	as	ADV
ejpam-2044	447	7	well	well	ADV
ejpam-2044	447	8	as	as	ADP
ejpam-2044	447	9	continuity	continuity	NOUN
ejpam-2044	447	10	of	of	ADP
ejpam-2044	447	11	function	function	NOUN
ejpam-2044	447	12	v	v	ADP
ejpam-2044	447	13	′	′	NUM
ejpam-2044	447	14	(	(	PUNCT
ejpam-2044	447	15	·	·	PUNCT
ejpam-2044	447	16	)	)	PUNCT
ejpam-2044	447	17	(	(	PUNCT
ejpam-2044	447	18	which	which	PRON
ejpam-2044	447	19	follows	follow	VERB
ejpam-2044	447	20	from	from	ADP
ejpam-2044	447	21	differentiability	differentiability	NOUN
ejpam-2044	447	22	)	)	PUNCT
ejpam-2044	447	23	and	and	CCONJ
ejpam-2044	447	24	using	use	VERB
ejpam-2044	447	25	boundary	boundary	ADJ
ejpam-2044	447	26	condition	condition	NOUN
ejpam-2044	447	27	v	v	ADP
ejpam-2044	447	28	′	′	NUM
ejpam-2044	447	29	(	(	PUNCT
ejpam-2044	447	30	0	0	NUM
ejpam-2044	447	31	)	)	PUNCT
ejpam-2044	447	32	=	=	SYM
ejpam-2044	447	33	1	1	NUM
ejpam-2044	447	34	we	we	PRON
ejpam-2044	447	35	conclude	conclude	VERB
ejpam-2044	447	36	that	that	PRON
ejpam-2044	447	37	v	v	ADP
ejpam-2044	447	38	′	′	NUM
ejpam-2044	447	39	(	(	PUNCT
ejpam-2044	447	40	x	x	X
ejpam-2044	447	41	)	)	PUNCT
ejpam-2044	447	42	=	=	SYM
ejpam-2044	447	43	1	1	NUM
ejpam-2044	447	44	,	,	PUNCT
ejpam-2044	447	45	for	for	SCONJ
ejpam-2044	447	46	x	x	PROPN
ejpam-2044	447	47	∈	∈	PROPN
ejpam-2044	447	48	r.	r.	NOUN
ejpam-2044	447	49	taking	take	VERB
ejpam-2044	447	50	antiderivative	antiderivative	NOUN
ejpam-2044	447	51	of	of	ADP
ejpam-2044	447	52	the	the	DET
ejpam-2044	447	53	function	function	NOUN
ejpam-2044	447	54	v	v	ADP
ejpam-2044	447	55	′	′	NUM
ejpam-2044	447	56	(	(	PUNCT
ejpam-2044	447	57	x	x	NOUN
ejpam-2044	447	58	)	)	PUNCT
ejpam-2044	447	59	and	and	CCONJ
ejpam-2044	447	60	using	use	VERB
ejpam-2044	447	61	boundary	boundary	ADJ
ejpam-2044	447	62	condition	condition	NOUN
ejpam-2044	447	63	v	v	ADP
ejpam-2044	447	64	(	(	PUNCT
ejpam-2044	447	65	0	0	NUM
ejpam-2044	447	66	)	)	PUNCT
ejpam-2044	447	67	=	=	SYM
ejpam-2044	447	68	0	0	NUM
ejpam-2044	447	69	we	we	PRON
ejpam-2044	447	70	find	find	VERB
ejpam-2044	447	71	the	the	DET
ejpam-2044	447	72	admissible	admissible	ADJ
ejpam-2044	447	73	representation	representation	NOUN
ejpam-2044	447	74	for	for	ADP
ejpam-2044	447	75	the	the	DET
ejpam-2044	447	76	function	function	NOUN
ejpam-2044	447	77	v	v	NOUN
ejpam-2044	447	78	(	(	PUNCT
ejpam-2044	447	79	x	x	NOUN
ejpam-2044	447	80	)	)	PUNCT
ejpam-2044	447	81	,	,	PUNCT
ejpam-2044	447	82	namely	namely	ADV
ejpam-2044	447	83	,	,	PUNCT
ejpam-2044	447	84	v	v	NOUN
ejpam-2044	447	85	(	(	PUNCT
ejpam-2044	447	86	x	x	NOUN
ejpam-2044	447	87	)	)	PUNCT
ejpam-2044	447	88	=	=	SYM
ejpam-2044	448	1	x	x	X
ejpam-2044	448	2	,	,	PUNCT
ejpam-2044	448	3	for	for	ADP
ejpam-2044	448	4	x	x	PROPN
ejpam-2044	448	5	∈	∈	PROPN
ejpam-2044	448	6	r.	r.	NOUN
ejpam-2044	448	7	switching	switch	VERB
ejpam-2044	448	8	back	back	ADV
ejpam-2044	448	9	to	to	ADP
ejpam-2044	448	10	the	the	DET
ejpam-2044	448	11	original	original	ADJ
ejpam-2044	448	12	function	function	NOUN
ejpam-2044	448	13	v	v	NOUN
ejpam-2044	448	14	(	(	PUNCT
ejpam-2044	448	15	x	x	X
ejpam-2044	448	16	)	)	PUNCT
ejpam-2044	448	17	obtain	obtain	VERB
ejpam-2044	448	18	v	v	NOUN
ejpam-2044	448	19	(	(	PUNCT
ejpam-2044	448	20	x	x	NOUN
ejpam-2044	448	21	)	)	PUNCT
ejpam-2044	448	22	=	=	NOUN
ejpam-2044	448	23	ax	ax	NOUN
ejpam-2044	448	24	+	+	CCONJ
ejpam-2044	448	25	b	b	NOUN
ejpam-2044	448	26	,	,	PUNCT
ejpam-2044	448	27	for	for	ADP
ejpam-2044	448	28	x	x	PROPN
ejpam-2044	448	29	∈	∈	PROPN
ejpam-2044	448	30	r	r	NOUN
ejpam-2044	448	31	,	,	PUNCT
ejpam-2044	448	32	and	and	CCONJ
ejpam-2044	448	33	some	some	DET
ejpam-2044	448	34	real	real	ADJ
ejpam-2044	448	35	constants	constant	NOUN
ejpam-2044	448	36	a	a	PRON
ejpam-2044	448	37	and	and	CCONJ
ejpam-2044	448	38	b.	b.	PROPN
ejpam-2044	448	39	initial	initial	ADJ
ejpam-2044	448	40	assumption	assumption	NOUN
ejpam-2044	448	41	concerning	concern	VERB
ejpam-2044	448	42	positivity	positivity	NOUN
ejpam-2044	448	43	of	of	ADP
ejpam-2044	448	44	first	first	ADJ
ejpam-2044	448	45	derivative	derivative	NOUN
ejpam-2044	448	46	of	of	ADP
ejpam-2044	448	47	the	the	DET
ejpam-2044	448	48	function	function	NOUN
ejpam-2044	448	49	v	v	NOUN
ejpam-2044	448	50	(	(	PUNCT
ejpam-2044	448	51	x	x	X
ejpam-2044	448	52	)	)	PUNCT
ejpam-2044	448	53	gives	give	VERB
ejpam-2044	448	54	us	we	PRON
ejpam-2044	448	55	additional	additional	ADJ
ejpam-2044	448	56	restriction	restriction	NOUN
ejpam-2044	448	57	on	on	ADP
ejpam-2044	448	58	the	the	DET
ejpam-2044	448	59	parameter	parameter	NOUN
ejpam-2044	448	60	a	a	PRON
ejpam-2044	448	61	,	,	PUNCT
ejpam-2044	448	62	namely	namely	ADV
ejpam-2044	448	63	,	,	PUNCT
ejpam-2044	448	64	parameter	parameter	NOUN
ejpam-2044	448	65	a	a	PRON
ejpam-2044	448	66	must	must	AUX
ejpam-2044	448	67	be	be	AUX
ejpam-2044	448	68	a	a	DET
ejpam-2044	448	69	strictly	strictly	ADV
ejpam-2044	448	70	positive	positive	ADJ
ejpam-2044	448	71	constant	constant	ADJ
ejpam-2044	448	72	.	.	PUNCT
ejpam-2044	449	1	since	since	SCONJ
ejpam-2044	449	2	,	,	PUNCT
ejpam-2044	449	3	in	in	ADP
ejpam-2044	449	4	the	the	DET
ejpam-2044	449	5	case	case	NOUN
ejpam-2044	449	6	of	of	ADP
ejpam-2044	449	7	∆	∆	PROPN
ejpam-2044	449	8	=	=	SYM
ejpam-2044	449	9	0	0	NUM
ejpam-2044	449	10	,	,	PUNCT
ejpam-2044	449	11	swiss	swiss	ADJ
ejpam-2044	449	12	premium	premium	NOUN
ejpam-2044	449	13	principle	principle	NOUN
ejpam-2044	449	14	entirely	entirely	ADV
ejpam-2044	449	15	coincides	coincide	VERB
ejpam-2044	449	16	with	with	ADP
ejpam-2044	449	17	mean	mean	ADJ
ejpam-2044	449	18	value	value	NOUN
ejpam-2044	449	19	premium	premium	NOUN
ejpam-2044	449	20	principle	principle	NOUN
ejpam-2044	449	21	then	then	ADV
ejpam-2044	449	22	we	we	PRON
ejpam-2044	449	23	can	can	AUX
ejpam-2044	449	24	formulate	formulate	VERB
ejpam-2044	449	25	the	the	DET
ejpam-2044	449	26	following	follow	VERB
ejpam-2044	449	27	corollary	corollary	NOUN
ejpam-2044	449	28	to	to	ADP
ejpam-2044	449	29	theorem	theorem	ADJ
ejpam-2044	449	30	2	2	NUM
ejpam-2044	449	31	.	.	PUNCT
ejpam-2044	450	1	references	reference	NOUN
ejpam-2044	450	2	288	288	NUM
ejpam-2044	450	3	corollary	corollary	ADJ
ejpam-2044	450	4	3	3	NUM
ejpam-2044	450	5	.	.	PUNCT
ejpam-2044	451	1	in	in	ADP
ejpam-2044	451	2	the	the	DET
ejpam-2044	451	3	case	case	NOUN
ejpam-2044	451	4	of∆=	of∆=	PROPN
ejpam-2044	451	5	0	0	NUM
ejpam-2044	451	6	,	,	PUNCT
ejpam-2044	451	7	swiss	swiss	ADJ
ejpam-2044	451	8	premium	premium	NOUN
ejpam-2044	451	9	calculation	calculation	NOUN
ejpam-2044	451	10	principle	principle	NOUN
ejpam-2044	451	11	subjected	subject	VERB
ejpam-2044	451	12	to	to	ADP
ejpam-2044	451	13	consideration	consideration	NOUN
ejpam-2044	451	14	of	of	ADP
ejpam-2044	451	15	only	only	ADV
ejpam-2044	451	16	strictly	strictly	ADV
ejpam-2044	451	17	positive	positive	ADJ
ejpam-2044	451	18	risks	risk	NOUN
ejpam-2044	451	19	possesses	possess	VERB
ejpam-2044	451	20	scale	scale	NOUN
ejpam-2044	451	21	invariance	invariance	NOUN
ejpam-2044	451	22	property	property	NOUN
ejpam-2044	451	23	if	if	SCONJ
ejpam-2044	452	1	and	and	CCONJ
ejpam-2044	452	2	only	only	ADV
ejpam-2044	452	3	if	if	SCONJ
ejpam-2044	452	4	v	v	INTJ
ejpam-2044	452	5	(	(	PUNCT
ejpam-2044	452	6	x	x	NOUN
ejpam-2044	452	7	)	)	PUNCT
ejpam-2044	452	8	=	=	PUNCT
ejpam-2044	453	1	axκ+	axκ+	ADP
ejpam-2044	453	2	b	b	PROPN
ejpam-2044	453	3	,	,	PUNCT
ejpam-2044	453	4	for	for	ADP
ejpam-2044	453	5	a	a	DET
ejpam-2044	453	6	>	>	X
ejpam-2044	453	7	0	0	PUNCT
ejpam-2044	453	8	and	and	CCONJ
ejpam-2044	453	9	κ≥	κ≥	PROPN
ejpam-2044	453	10	1	1	NUM
ejpam-2044	453	11	,	,	PUNCT
ejpam-2044	453	12	defined	define	VERB
ejpam-2044	453	13	for	for	ADP
ejpam-2044	453	14	x	x	PROPN
ejpam-2044	453	15	∈	∈	PROPN
ejpam-2044	453	16	(	(	PUNCT
ejpam-2044	453	17	0,+∞	0,+∞	NUM
ejpam-2044	453	18	)	)	PUNCT
ejpam-2044	453	19	.	.	PUNCT
ejpam-2044	454	1	references	reference	NOUN
ejpam-2044	454	2	[	[	X
ejpam-2044	454	3	1	1	X
ejpam-2044	454	4	]	]	PUNCT
ejpam-2044	454	5	s.	s.	PROPN
ejpam-2044	454	6	asmussen	asmussen	PROPN
ejpam-2044	454	7	and	and	CCONJ
ejpam-2044	454	8	h.	h.	PROPN
ejpam-2044	454	9	albrecher	albrecher	PROPN
ejpam-2044	454	10	.	.	PUNCT
ejpam-2044	455	1	ruin	ruin	NOUN
ejpam-2044	455	2	probabilities	probability	NOUN
ejpam-2044	455	3	(	(	PUNCT
ejpam-2044	455	4	second	second	ADJ
ejpam-2044	455	5	edition	edition	NOUN
ejpam-2044	455	6	)	)	PUNCT
ejpam-2044	455	7	,	,	PUNCT
ejpam-2044	455	8	world	world	NOUN
ejpam-2044	455	9	sientific	sientific	PROPN
ejpam-2044	455	10	,	,	PUNCT
ejpam-2044	455	11	singapore	singapore	PROPN
ejpam-2044	455	12	,	,	PUNCT
ejpam-2044	455	13	2010	2010	NUM
ejpam-2044	455	14	.	.	PUNCT
ejpam-2044	456	1	[	[	X
ejpam-2044	456	2	2	2	NUM
ejpam-2044	456	3	]	]	X
ejpam-2044	456	4	p.j	p.j	PROPN
ejpam-2044	456	5	.	.	PROPN
ejpam-2044	456	6	boland	boland	PROPN
ejpam-2044	456	7	.	.	PUNCT
ejpam-2044	457	1	statistical	statistical	ADJ
ejpam-2044	457	2	and	and	CCONJ
ejpam-2044	457	3	probabilistic	probabilistic	ADJ
ejpam-2044	457	4	methods	method	NOUN
ejpam-2044	457	5	in	in	ADP
ejpam-2044	457	6	actuarial	actuarial	ADJ
ejpam-2044	457	7	science	science	NOUN
ejpam-2044	457	8	,	,	PUNCT
ejpam-2044	457	9	chapman	chapman	PROPN
ejpam-2044	457	10	&	&	CCONJ
ejpam-2044	457	11	hall	hall	PROPN
ejpam-2044	457	12	,	,	PUNCT
ejpam-2044	457	13	boca	boca	PROPN
ejpam-2044	457	14	raton	raton	PROPN
ejpam-2044	457	15	,	,	PUNCT
ejpam-2044	457	16	2007	2007	NUM
ejpam-2044	457	17	.	.	PUNCT
ejpam-2044	458	1	[	[	X
ejpam-2044	458	2	3	3	X
ejpam-2044	458	3	]	]	X
ejpam-2044	458	4	n.l	n.l	PROPN
ejpam-2044	458	5	.	.	PROPN
ejpam-2044	458	6	bowers	bower	NOUN
ejpam-2044	458	7	,	,	PUNCT
ejpam-2044	458	8	h.-u	h.-u	NOUN
ejpam-2044	458	9	.	.	PUNCT
ejpam-2044	459	1	gerber	gerber	PROPN
ejpam-2044	459	2	,	,	PUNCT
ejpam-2044	459	3	j.c	j.c	PROPN
ejpam-2044	459	4	.	.	PROPN
ejpam-2044	459	5	hickman	hickman	PROPN
ejpam-2044	459	6	,	,	PUNCT
ejpam-2044	459	7	d.a	d.a	PROPN
ejpam-2044	459	8	.	.	PROPN
ejpam-2044	459	9	jones	jones	PROPN
ejpam-2044	459	10	,	,	PUNCT
ejpam-2044	459	11	and	and	CCONJ
ejpam-2044	459	12	c.j	c.j	PROPN
ejpam-2044	459	13	.	.	PROPN
ejpam-2044	459	14	nesbit	nesbit	PROPN
ejpam-2044	459	15	.	.	PUNCT
ejpam-2044	460	1	actuarial	actuarial	ADJ
ejpam-2044	460	2	mathematics	mathematic	NOUN
ejpam-2044	460	3	(	(	PUNCT
ejpam-2044	460	4	second	second	ADJ
ejpam-2044	460	5	edition	edition	NOUN
ejpam-2044	460	6	)	)	PUNCT
ejpam-2044	460	7	,	,	PUNCT
ejpam-2044	460	8	the	the	DET
ejpam-2044	460	9	society	society	NOUN
ejpam-2044	460	10	of	of	ADP
ejpam-2044	460	11	actuaries	actuary	NOUN
ejpam-2044	460	12	,	,	PUNCT
ejpam-2044	460	13	illinois	illinois	PROPN
ejpam-2044	460	14	,	,	PUNCT
ejpam-2044	460	15	1997	1997	NUM
ejpam-2044	460	16	.	.	PUNCT
ejpam-2044	461	1	[	[	X
ejpam-2044	461	2	4	4	X
ejpam-2044	461	3	]	]	X
ejpam-2044	461	4	h.	h.	PROPN
ejpam-2044	461	5	bühlmann	bühlmann	PROPN
ejpam-2044	461	6	.	.	PUNCT
ejpam-2044	462	1	mathematical	mathematical	ADJ
ejpam-2044	462	2	methods	method	NOUN
ejpam-2044	462	3	in	in	ADP
ejpam-2044	462	4	risk	risk	NOUN
ejpam-2044	462	5	theory	theory	NOUN
ejpam-2044	462	6	,	,	PUNCT
ejpam-2044	462	7	springer	springer	NOUN
ejpam-2044	462	8	,	,	PUNCT
ejpam-2044	462	9	berlin	berlin	PROPN
ejpam-2044	462	10	,	,	PUNCT
ejpam-2044	462	11	1970	1970	NUM
ejpam-2044	462	12	.	.	PUNCT
ejpam-2044	463	1	[	[	X
ejpam-2044	463	2	5	5	NUM
ejpam-2044	463	3	]	]	PUNCT
ejpam-2044	463	4	d.c.m	d.c.m	NOUN
ejpam-2044	463	5	.	.	PUNCT
ejpam-2044	463	6	dickson	dickson	PROPN
ejpam-2044	463	7	.	.	PUNCT
ejpam-2044	464	1	insurance	insurance	NOUN
ejpam-2044	464	2	risk	risk	NOUN
ejpam-2044	464	3	and	and	CCONJ
ejpam-2044	464	4	ruin	ruin	NOUN
ejpam-2044	464	5	,	,	PUNCT
ejpam-2044	464	6	cambridge	cambridge	PROPN
ejpam-2044	464	7	university	university	PROPN
ejpam-2044	464	8	press	press	PROPN
ejpam-2044	464	9	,	,	PUNCT
ejpam-2044	464	10	cambridge	cambridge	PROPN
ejpam-2044	464	11	,	,	PUNCT
ejpam-2044	464	12	2005	2005	NUM
ejpam-2044	464	13	.	.	PUNCT
ejpam-2044	465	1	[	[	X
ejpam-2044	465	2	6	6	NUM
ejpam-2044	465	3	]	]	PUNCT
ejpam-2044	465	4	h.-u	h.-u	NOUN
ejpam-2044	465	5	.	.	PUNCT
ejpam-2044	466	1	gerber	gerber	NOUN
ejpam-2044	466	2	.	.	PUNCT
ejpam-2044	467	1	an	an	DET
ejpam-2044	467	2	introduction	introduction	NOUN
ejpam-2044	467	3	to	to	ADP
ejpam-2044	467	4	mathematical	mathematical	ADJ
ejpam-2044	467	5	risk	risk	NOUN
ejpam-2044	467	6	theory	theory	NOUN
ejpam-2044	467	7	,	,	PUNCT
ejpam-2044	467	8	s.s	s.s	PROPN
ejpam-2044	467	9	.	.	PROPN
ejpam-2044	467	10	huebner	huebner	PROPN
ejpam-2044	467	11	foundation	foundation	PROPN
ejpam-2044	467	12	for	for	ADP
ejpam-2044	467	13	insurance	insurance	NOUN
ejpam-2044	467	14	education	education	NOUN
ejpam-2044	467	15	,	,	PUNCT
ejpam-2044	467	16	philadelpia	philadelpia	PROPN
ejpam-2044	467	17	,	,	PUNCT
ejpam-2044	467	18	1979	1979	NUM
ejpam-2044	467	19	.	.	PUNCT
ejpam-2044	468	1	[	[	X
ejpam-2044	468	2	7	7	X
ejpam-2044	468	3	]	]	X
ejpam-2044	468	4	f.e	f.e	PROPN
ejpam-2044	468	5	.	.	PROPN
ejpam-2044	468	6	de	de	PROPN
ejpam-2044	468	7	vylder	vylder	PROPN
ejpam-2044	468	8	,	,	PUNCT
ejpam-2044	468	9	m.	m.	NOUN
ejpam-2044	468	10	goovaerts	goovaerts	PROPN
ejpam-2044	468	11	,	,	PUNCT
ejpam-2044	468	12	and	and	CCONJ
ejpam-2044	468	13	j.	j.	PROPN
ejpam-2044	468	14	haezendonck	haezendonck	ADV
ejpam-2044	468	15	(	(	PUNCT
ejpam-2044	468	16	editors	editor	NOUN
ejpam-2044	468	17	)	)	PUNCT
ejpam-2044	468	18	.	.	PUNCT
ejpam-2044	469	1	premium	premium	NOUN
ejpam-2044	469	2	calculation	calculation	NOUN
ejpam-2044	469	3	in	in	ADP
ejpam-2044	469	4	insurance	insurance	NOUN
ejpam-2044	469	5	(	(	PUNCT
ejpam-2044	469	6	collection	collection	NOUN
ejpam-2044	469	7	of	of	ADP
ejpam-2044	469	8	articles	article	NOUN
ejpam-2044	469	9	)	)	PUNCT
ejpam-2044	469	10	,	,	PUNCT
ejpam-2044	469	11	kluwer	kluwer	NOUN
ejpam-2044	469	12	academic	academic	ADJ
ejpam-2044	469	13	publishers	publisher	NOUN
ejpam-2044	469	14	,	,	PUNCT
ejpam-2044	469	15	boston	boston	PROPN
ejpam-2044	469	16	,	,	PUNCT
ejpam-2044	469	17	1984	1984	NUM
ejpam-2044	469	18	.	.	PUNCT
ejpam-2044	470	1	[	[	X
ejpam-2044	470	2	8	8	NUM
ejpam-2044	470	3	]	]	X
ejpam-2044	470	4	f.e	f.e	PROPN
ejpam-2044	470	5	.	.	PROPN
ejpam-2044	470	6	de	de	PROPN
ejpam-2044	470	7	vylder	vylder	PROPN
ejpam-2044	470	8	,	,	PUNCT
ejpam-2044	470	9	m.	m.	NOUN
ejpam-2044	470	10	goovaerts	goovaerts	PROPN
ejpam-2044	470	11	,	,	PUNCT
ejpam-2044	470	12	and	and	CCONJ
ejpam-2044	470	13	j.	j.	PROPN
ejpam-2044	470	14	haezendonck	haezendonck	ADV
ejpam-2044	470	15	(	(	PUNCT
ejpam-2044	470	16	editors	editor	NOUN
ejpam-2044	470	17	)	)	PUNCT
ejpam-2044	470	18	.	.	PUNCT
ejpam-2044	471	1	insurance	insurance	NOUN
ejpam-2044	471	2	and	and	CCONJ
ejpam-2044	471	3	risk	risk	NOUN
ejpam-2044	471	4	theory	theory	NOUN
ejpam-2044	471	5	(	(	PUNCT
ejpam-2044	471	6	collection	collection	NOUN
ejpam-2044	471	7	of	of	ADP
ejpam-2044	471	8	articles	article	NOUN
ejpam-2044	471	9	)	)	PUNCT
ejpam-2044	471	10	,	,	PUNCT
ejpam-2044	471	11	kluwer	kluwer	NOUN
ejpam-2044	471	12	academic	academic	ADJ
ejpam-2044	471	13	publishers	publisher	NOUN
ejpam-2044	471	14	,	,	PUNCT
ejpam-2044	471	15	boston	boston	PROPN
ejpam-2044	471	16	,	,	PUNCT
ejpam-2044	471	17	1986	1986	NUM
ejpam-2044	471	18	.	.	PUNCT
ejpam-2044	472	1	[	[	X
ejpam-2044	472	2	9	9	NUM
ejpam-2044	472	3	]	]	X
ejpam-2044	472	4	r.	r.	PROPN
ejpam-2044	472	5	kaas	kaas	PROPN
ejpam-2044	472	6	,	,	PUNCT
ejpam-2044	472	7	m.	m.	NOUN
ejpam-2044	472	8	goovaerts	goovaerts	PROPN
ejpam-2044	472	9	,	,	PUNCT
ejpam-2044	472	10	j.	j.	PROPN
ejpam-2044	472	11	dhaene	dhaene	PROPN
ejpam-2044	472	12	,	,	PUNCT
ejpam-2044	472	13	and	and	CCONJ
ejpam-2044	472	14	m.	m.	NOUN
ejpam-2044	472	15	denuit	denuit	PROPN
ejpam-2044	472	16	.	.	PUNCT
ejpam-2044	473	1	modern	modern	ADJ
ejpam-2044	473	2	actuarial	actuarial	ADJ
ejpam-2044	473	3	risk	risk	NOUN
ejpam-2044	473	4	theory	theory	NOUN
ejpam-2044	473	5	using	use	VERB
ejpam-2044	473	6	r	r	NOUN
ejpam-2044	473	7	,	,	PUNCT
ejpam-2044	473	8	springer	springer	NOUN
ejpam-2044	473	9	,	,	PUNCT
ejpam-2044	473	10	berlin	berlin	PROPN
ejpam-2044	473	11	,	,	PUNCT
ejpam-2044	473	12	2008	2008	NUM
ejpam-2044	473	13	.	.	PUNCT
ejpam-2044	474	1	[	[	X
ejpam-2044	474	2	10	10	NUM
ejpam-2044	474	3	]	]	X
ejpam-2044	474	4	e.	e.	PROPN
ejpam-2044	474	5	kremer	kremer	PROPN
ejpam-2044	474	6	.	.	PROPN
ejpam-2044	474	7	applied	apply	VERB
ejpam-2044	474	8	risk	risk	NOUN
ejpam-2044	474	9	theory	theory	NOUN
ejpam-2044	474	10	,	,	PUNCT
ejpam-2044	474	11	shaker	shaker	NOUN
ejpam-2044	474	12	,	,	PUNCT
ejpam-2044	474	13	aachen	aachen	PROPN
ejpam-2044	474	14	,	,	PUNCT
ejpam-2044	474	15	1999	1999	NUM
ejpam-2044	474	16	.	.	PUNCT
ejpam-2044	475	1	[	[	X
ejpam-2044	475	2	11	11	NUM
ejpam-2044	475	3	]	]	PUNCT
ejpam-2044	475	4	t.	t.	PROPN
ejpam-2044	475	5	rolski	rolski	PROPN
ejpam-2044	475	6	,	,	PUNCT
ejpam-2044	475	7	h.	h.	PROPN
ejpam-2044	475	8	schmidli	schmidli	PROPN
ejpam-2044	475	9	,	,	PUNCT
ejpam-2044	475	10	v.	v.	CCONJ
ejpam-2044	475	11	schmidt	schmidt	PROPN
ejpam-2044	475	12	,	,	PUNCT
ejpam-2044	475	13	and	and	CCONJ
ejpam-2044	475	14	j.	j.	PROPN
ejpam-2044	475	15	teugels	teugels	PROPN
ejpam-2044	475	16	.	.	PUNCT
ejpam-2044	476	1	stochastic	stochastic	ADJ
ejpam-2044	476	2	processes	process	NOUN
ejpam-2044	476	3	for	for	ADP
ejpam-2044	476	4	insurance	insurance	NOUN
ejpam-2044	476	5	and	and	CCONJ
ejpam-2044	476	6	finance	finance	NOUN
ejpam-2044	476	7	,	,	PUNCT
ejpam-2044	476	8	john	john	PROPN
ejpam-2044	476	9	wiley	wiley	PROPN
ejpam-2044	476	10	&	&	CCONJ
ejpam-2044	476	11	sons	sons	PROPN
ejpam-2044	476	12	,	,	PUNCT
ejpam-2044	476	13	chichester	chichester	PROPN
ejpam-2044	476	14	,	,	PUNCT
ejpam-2044	476	15	1999	1999	NUM
ejpam-2044	476	16	.	.	PUNCT
ejpam-2044	477	1	[	[	X
ejpam-2044	477	2	12	12	NUM
ejpam-2044	477	3	]	]	X
ejpam-2044	477	4	e.	e.	PROPN
ejpam-2044	477	5	straub	straub	PROPN
ejpam-2044	477	6	.	.	PUNCT
ejpam-2044	478	1	non	non	ADJ
ejpam-2044	478	2	-	-	ADJ
ejpam-2044	478	3	life	life	ADJ
ejpam-2044	478	4	insurance	insurance	NOUN
ejpam-2044	478	5	mathematics	mathematic	NOUN
ejpam-2044	478	6	,	,	PUNCT
ejpam-2044	478	7	springer	springer	NOUN
ejpam-2044	478	8	,	,	PUNCT
ejpam-2044	478	9	berlin	berlin	PROPN
ejpam-2044	478	10	,	,	PUNCT
ejpam-2044	478	11	1988	1988	NUM
ejpam-2044	478	12	.	.	PUNCT