id	sid	tid	token	lemma	pos
ejpam-3478	1	1	european	european	PROPN
ejpam-3478	1	2	journal	journal	PROPN
ejpam-3478	1	3	of	of	ADP
ejpam-3478	1	4	pure	pure	ADJ
ejpam-3478	1	5	and	and	CCONJ
ejpam-3478	1	6	applied	apply	VERB
ejpam-3478	1	7	mathematics	mathematic	NOUN
ejpam-3478	1	8	vol	vol	NOUN
ejpam-3478	1	9	.	.	PROPN
ejpam-3478	2	1	12	12	NUM
ejpam-3478	2	2	,	,	PUNCT
ejpam-3478	2	3	no	no	INTJ
ejpam-3478	2	4	.	.	NOUN
ejpam-3478	2	5	3	3	NUM
ejpam-3478	2	6	,	,	PUNCT
ejpam-3478	2	7	2019	2019	NUM
ejpam-3478	2	8	,	,	PUNCT
ejpam-3478	2	9	1315	1315	NUM
ejpam-3478	2	10	-	-	SYM
ejpam-3478	2	11	1336	1336	NUM
ejpam-3478	2	12	issn	issn	PROPN
ejpam-3478	2	13	1307	1307	NUM
ejpam-3478	2	14	-	-	SYM
ejpam-3478	2	15	5543	5543	NUM
ejpam-3478	2	16	–	–	PUNCT
ejpam-3478	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3478	2	18	published	publish	VERB
ejpam-3478	2	19	by	by	ADP
ejpam-3478	2	20	new	new	PROPN
ejpam-3478	2	21	york	york	PROPN
ejpam-3478	2	22	business	business	PROPN
ejpam-3478	2	23	global	global	ADJ
ejpam-3478	2	24	strategic	strategic	ADJ
ejpam-3478	2	25	asset	asset	NOUN
ejpam-3478	2	26	allocation	allocation	NOUN
ejpam-3478	2	27	for	for	ADP
ejpam-3478	2	28	life	life	NOUN
ejpam-3478	2	29	insurers	insurer	NOUN
ejpam-3478	2	30	with	with	ADP
ejpam-3478	2	31	stochastic	stochastic	ADJ
ejpam-3478	2	32	liability†	liability†	ADJ
ejpam-3478	2	33	c.	c.	PROPN
ejpam-3478	2	34	atkinson1	atkinson1	PROPN
ejpam-3478	2	35	,	,	PUNCT
ejpam-3478	3	1	s.	s.	PROPN
ejpam-3478	3	2	mokkhavesa2,∗	mokkhavesa2,∗	PROPN
ejpam-3478	3	3	,	,	PUNCT
ejpam-3478	3	4	p.	p.	NOUN
ejpam-3478	3	5	ingpochai3	ingpochai3	NOUN
ejpam-3478	3	6	1	1	NUM
ejpam-3478	3	7	mathematics	mathematics	PROPN
ejpam-3478	3	8	department	department	NOUN
ejpam-3478	3	9	,	,	PUNCT
ejpam-3478	3	10	imperial	imperial	ADJ
ejpam-3478	3	11	college	college	PROPN
ejpam-3478	3	12	,	,	PUNCT
ejpam-3478	3	13	london	london	PROPN
ejpam-3478	3	14	,	,	PUNCT
ejpam-3478	3	15	180	180	NUM
ejpam-3478	3	16	queen	queen	PROPN
ejpam-3478	3	17	’s	’s	PART
ejpam-3478	3	18	gate	gate	NOUN
ejpam-3478	3	19	,	,	PUNCT
ejpam-3478	3	20	london	london	PROPN
ejpam-3478	3	21	sw7	sw7	PROPN
ejpam-3478	3	22	2az	2az	PROPN
ejpam-3478	3	23	,	,	PUNCT
ejpam-3478	3	24	u.k	u.k	PROPN
ejpam-3478	3	25	.	.	PROPN
ejpam-3478	3	26	2	2	NUM
ejpam-3478	3	27	muang	muang	PROPN
ejpam-3478	3	28	thai	thai	PROPN
ejpam-3478	3	29	life	life	PROPN
ejpam-3478	3	30	assurance	assurance	PROPN
ejpam-3478	3	31	pcl	pcl	PROPN
ejpam-3478	3	32	,	,	PUNCT
ejpam-3478	3	33	250	250	NUM
ejpam-3478	3	34	rachadaphisek	rachadaphisek	PROPN
ejpam-3478	3	35	rd	rd	PROPN
ejpam-3478	3	36	.	.	PROPN
ejpam-3478	3	37	,	,	PUNCT
ejpam-3478	3	38	huaykwang	huaykwang	PROPN
ejpam-3478	3	39	,	,	PUNCT
ejpam-3478	3	40	bangkok	bangkok	PROPN
ejpam-3478	3	41	10320	10320	NUM
ejpam-3478	3	42	,	,	PUNCT
ejpam-3478	3	43	thailand	thailand	PROPN
ejpam-3478	3	44	3	3	NUM
ejpam-3478	3	45	aigen	aigen	NOUN
ejpam-3478	3	46	,	,	PUNCT
ejpam-3478	3	47	250	250	NUM
ejpam-3478	3	48	rachadaphisek	rachadaphisek	PROPN
ejpam-3478	3	49	rd	rd	PROPN
ejpam-3478	3	50	.	.	PROPN
ejpam-3478	3	51	,	,	PUNCT
ejpam-3478	3	52	huaykwang	huaykwang	PROPN
ejpam-3478	3	53	,	,	PUNCT
ejpam-3478	3	54	bangkok	bangkok	PROPN
ejpam-3478	3	55	10320	10320	NUM
ejpam-3478	3	56	,	,	PUNCT
ejpam-3478	3	57	thailand	thailand	PROPN
ejpam-3478	3	58	abstract	abstract	PROPN
ejpam-3478	3	59	.	.	PUNCT
ejpam-3478	4	1	the	the	DET
ejpam-3478	4	2	problem	problem	NOUN
ejpam-3478	4	3	of	of	ADP
ejpam-3478	4	4	strategic	strategic	ADJ
ejpam-3478	4	5	asset	asset	NOUN
ejpam-3478	4	6	allocation	allocation	NOUN
ejpam-3478	4	7	and	and	CCONJ
ejpam-3478	4	8	product	product	NOUN
ejpam-3478	4	9	mix	mix	NOUN
ejpam-3478	4	10	choice	choice	NOUN
ejpam-3478	4	11	of	of	ADP
ejpam-3478	4	12	a	a	DET
ejpam-3478	4	13	life	life	NOUN
ejpam-3478	4	14	insurance	insurance	NOUN
ejpam-3478	4	15	company	company	NOUN
ejpam-3478	4	16	is	be	AUX
ejpam-3478	4	17	considered	consider	VERB
ejpam-3478	4	18	where	where	SCONJ
ejpam-3478	4	19	account	account	NOUN
ejpam-3478	4	20	is	be	AUX
ejpam-3478	4	21	taken	take	VERB
ejpam-3478	4	22	of	of	ADP
ejpam-3478	4	23	the	the	DET
ejpam-3478	4	24	stochastic	stochastic	ADJ
ejpam-3478	4	25	risk	risk	NOUN
ejpam-3478	4	26	associated	associate	VERB
ejpam-3478	4	27	with	with	ADP
ejpam-3478	4	28	both	both	DET
ejpam-3478	4	29	assets	asset	NOUN
ejpam-3478	4	30	and	and	CCONJ
ejpam-3478	4	31	liabilities	liability	NOUN
ejpam-3478	4	32	.	.	PUNCT
ejpam-3478	5	1	using	use	VERB
ejpam-3478	5	2	the	the	DET
ejpam-3478	5	3	methods	method	NOUN
ejpam-3478	5	4	of	of	ADP
ejpam-3478	5	5	stochastic	stochastic	ADJ
ejpam-3478	5	6	dynamic	dynamic	ADJ
ejpam-3478	5	7	programming	programming	NOUN
ejpam-3478	5	8	we	we	PRON
ejpam-3478	5	9	derive	derive	VERB
ejpam-3478	5	10	equations	equation	NOUN
ejpam-3478	5	11	for	for	ADP
ejpam-3478	5	12	optimal	optimal	ADJ
ejpam-3478	5	13	weights	weight	NOUN
ejpam-3478	5	14	of	of	ADP
ejpam-3478	5	15	both	both	CCONJ
ejpam-3478	5	16	risky	risky	ADJ
ejpam-3478	5	17	and	and	CCONJ
ejpam-3478	5	18	riskless	riskless	NOUN
ejpam-3478	5	19	assets	asset	NOUN
ejpam-3478	5	20	under	under	ADP
ejpam-3478	5	21	continuous	continuous	ADJ
ejpam-3478	5	22	time	time	NOUN
ejpam-3478	5	23	.	.	PUNCT
ejpam-3478	6	1	the	the	DET
ejpam-3478	6	2	resulting	result	VERB
ejpam-3478	6	3	equations	equation	NOUN
ejpam-3478	6	4	can	can	AUX
ejpam-3478	6	5	be	be	AUX
ejpam-3478	6	6	solved	solve	VERB
ejpam-3478	6	7	exactly	exactly	ADV
ejpam-3478	6	8	for	for	ADP
ejpam-3478	6	9	some	some	DET
ejpam-3478	6	10	parameter	parameter	NOUN
ejpam-3478	6	11	values	value	NOUN
ejpam-3478	6	12	and	and	CCONJ
ejpam-3478	6	13	utility	utility	NOUN
ejpam-3478	6	14	functions	function	NOUN
ejpam-3478	6	15	.	.	PUNCT
ejpam-3478	7	1	when	when	SCONJ
ejpam-3478	7	2	this	this	PRON
ejpam-3478	7	3	is	be	AUX
ejpam-3478	7	4	not	not	PART
ejpam-3478	7	5	possible	possible	ADJ
ejpam-3478	7	6	a	a	DET
ejpam-3478	7	7	general	general	ADJ
ejpam-3478	7	8	perturbation	perturbation	NOUN
ejpam-3478	7	9	expansion	expansion	NOUN
ejpam-3478	7	10	method	method	NOUN
ejpam-3478	7	11	is	be	AUX
ejpam-3478	7	12	set	set	VERB
ejpam-3478	7	13	up	up	ADP
ejpam-3478	7	14	for	for	ADP
ejpam-3478	7	15	which	which	PRON
ejpam-3478	7	16	explicit	explicit	ADJ
ejpam-3478	7	17	solutions	solution	NOUN
ejpam-3478	7	18	are	be	AUX
ejpam-3478	7	19	derived	derive	VERB
ejpam-3478	7	20	for	for	ADP
ejpam-3478	7	21	the	the	DET
ejpam-3478	7	22	first	first	ADJ
ejpam-3478	7	23	terms	term	NOUN
ejpam-3478	7	24	but	but	CCONJ
ejpam-3478	7	25	the	the	DET
ejpam-3478	7	26	method	method	NOUN
ejpam-3478	7	27	can	can	AUX
ejpam-3478	7	28	be	be	AUX
ejpam-3478	7	29	generalized	generalize	VERB
ejpam-3478	7	30	to	to	ADP
ejpam-3478	7	31	any	any	DET
ejpam-3478	7	32	order	order	NOUN
ejpam-3478	7	33	in	in	ADP
ejpam-3478	7	34	the	the	DET
ejpam-3478	7	35	expansion	expansion	NOUN
ejpam-3478	7	36	parameter	parameter	NOUN
ejpam-3478	7	37	.	.	PUNCT
ejpam-3478	8	1	2010	2010	NUM
ejpam-3478	8	2	mathematics	mathematic	NOUN
ejpam-3478	8	3	subject	subject	NOUN
ejpam-3478	8	4	classifications	classification	NOUN
ejpam-3478	8	5	:	:	PUNCT
ejpam-3478	8	6	35q93	35q93	NUM
ejpam-3478	8	7	,	,	PUNCT
ejpam-3478	8	8	49j20	49j20	NUM
ejpam-3478	8	9	,	,	PUNCT
ejpam-3478	8	10	49l20	49l20	NUM
ejpam-3478	8	11	,	,	PUNCT
ejpam-3478	8	12	91b16	91b16	NUM
ejpam-3478	8	13	,	,	PUNCT
ejpam-3478	8	14	91b30	91b30	NUM
ejpam-3478	8	15	,	,	PUNCT
ejpam-3478	8	16	91g80	91g80	NUM
ejpam-3478	8	17	key	key	ADJ
ejpam-3478	8	18	words	word	NOUN
ejpam-3478	8	19	and	and	CCONJ
ejpam-3478	8	20	phrases	phrase	NOUN
ejpam-3478	8	21	:	:	PUNCT
ejpam-3478	8	22	optimal	optimal	ADJ
ejpam-3478	8	23	control	control	NOUN
ejpam-3478	8	24	problems	problem	NOUN
ejpam-3478	8	25	involving	involve	VERB
ejpam-3478	8	26	partial	partial	ADJ
ejpam-3478	8	27	differential	differential	ADJ
ejpam-3478	8	28	equations	equation	NOUN
ejpam-3478	8	29	,	,	PUNCT
ejpam-3478	8	30	stochastic	stochastic	ADJ
ejpam-3478	8	31	dynamic	dynamic	ADJ
ejpam-3478	8	32	programming	programming	NOUN
ejpam-3478	8	33	,	,	PUNCT
ejpam-3478	8	34	utility	utility	NOUN
ejpam-3478	8	35	theory	theory	NOUN
ejpam-3478	8	36	,	,	PUNCT
ejpam-3478	8	37	insurance	insurance	NOUN
ejpam-3478	8	38	,	,	PUNCT
ejpam-3478	8	39	stochastic	stochastic	ADJ
ejpam-3478	8	40	control	control	NOUN
ejpam-3478	8	41	,	,	PUNCT
ejpam-3478	8	42	pde	pde	PROPN
ejpam-3478	8	43	1	1	NUM
ejpam-3478	8	44	.	.	PUNCT
ejpam-3478	9	1	introduction	introduction	NOUN
ejpam-3478	9	2	the	the	DET
ejpam-3478	9	3	financial	financial	ADJ
ejpam-3478	9	4	management	management	NOUN
ejpam-3478	9	5	of	of	ADP
ejpam-3478	9	6	an	an	DET
ejpam-3478	9	7	insurance	insurance	NOUN
ejpam-3478	9	8	company	company	NOUN
ejpam-3478	9	9	involves	involve	VERB
ejpam-3478	9	10	the	the	DET
ejpam-3478	9	11	analysis	analysis	NOUN
ejpam-3478	9	12	of	of	ADP
ejpam-3478	9	13	the	the	DET
ejpam-3478	9	14	assets	asset	NOUN
ejpam-3478	9	15	and	and	CCONJ
ejpam-3478	9	16	liabilities	liability	NOUN
ejpam-3478	9	17	on	on	ADP
ejpam-3478	9	18	a	a	DET
ejpam-3478	9	19	unified	unified	ADJ
ejpam-3478	9	20	basis	basis	NOUN
ejpam-3478	9	21	.	.	PUNCT
ejpam-3478	10	1	the	the	DET
ejpam-3478	10	2	premiums	premium	NOUN
ejpam-3478	10	3	paid	pay	VERB
ejpam-3478	10	4	by	by	ADP
ejpam-3478	10	5	the	the	DET
ejpam-3478	10	6	policyholder	policyholder	NOUN
ejpam-3478	10	7	should	should	AUX
ejpam-3478	10	8	be	be	AUX
ejpam-3478	10	9	prudently	prudently	ADV
ejpam-3478	10	10	invested	invest	VERB
ejpam-3478	10	11	so	so	SCONJ
ejpam-3478	10	12	that	that	SCONJ
ejpam-3478	10	13	the	the	DET
ejpam-3478	10	14	company	company	NOUN
ejpam-3478	10	15	can	can	AUX
ejpam-3478	10	16	honor	honor	VERB
ejpam-3478	10	17	the	the	DET
ejpam-3478	10	18	contractual	contractual	ADJ
ejpam-3478	10	19	obligation	obligation	NOUN
ejpam-3478	10	20	that	that	PRON
ejpam-3478	10	21	comes	come	VERB
ejpam-3478	10	22	with	with	ADP
ejpam-3478	10	23	the	the	DET
ejpam-3478	10	24	policy	policy	NOUN
ejpam-3478	10	25	with	with	ADP
ejpam-3478	10	26	a	a	DET
ejpam-3478	10	27	high	high	ADJ
ejpam-3478	10	28	level	level	NOUN
ejpam-3478	10	29	of	of	ADP
ejpam-3478	10	30	confidence	confidence	NOUN
ejpam-3478	10	31	.	.	PUNCT
ejpam-3478	11	1	in	in	ADP
ejpam-3478	11	2	its	its	PRON
ejpam-3478	11	3	most	most	ADV
ejpam-3478	11	4	basic	basic	ADJ
ejpam-3478	11	5	form	form	NOUN
ejpam-3478	11	6	,	,	PUNCT
ejpam-3478	11	7	asset	asset	NOUN
ejpam-3478	11	8	-	-	PUNCT
ejpam-3478	11	9	liability	liability	NOUN
ejpam-3478	11	10	management	management	NOUN
ejpam-3478	11	11	(	(	PUNCT
ejpam-3478	11	12	alm	alm	NOUN
ejpam-3478	11	13	)	)	PUNCT
ejpam-3478	11	14	dictates	dictate	VERB
ejpam-3478	11	15	the	the	DET
ejpam-3478	11	16	investment	investment	NOUN
ejpam-3478	11	17	choice	choice	NOUN
ejpam-3478	11	18	on	on	ADP
ejpam-3478	11	19	the	the	DET
ejpam-3478	11	20	asset	asset	NOUN
ejpam-3478	11	21	side	side	NOUN
ejpam-3478	11	22	and	and	CCONJ
ejpam-3478	11	23	the	the	DET
ejpam-3478	11	24	choice	choice	NOUN
ejpam-3478	11	25	of	of	ADP
ejpam-3478	11	26	products	product	NOUN
ejpam-3478	11	27	marketed	market	VERB
ejpam-3478	11	28	on	on	ADP
ejpam-3478	11	29	the	the	DET
ejpam-3478	11	30	liability	liability	NOUN
ejpam-3478	11	31	side	side	NOUN
ejpam-3478	11	32	.	.	PUNCT
ejpam-3478	12	1	moreover	moreover	ADV
ejpam-3478	12	2	,	,	PUNCT
ejpam-3478	12	3	alm	alm	NOUN
ejpam-3478	12	4	deals	deal	NOUN
ejpam-3478	12	5	with	with	ADP
ejpam-3478	12	6	the	the	DET
ejpam-3478	12	7	planning	planning	NOUN
ejpam-3478	12	8	of	of	ADP
ejpam-3478	12	9	financial	financial	ADJ
ejpam-3478	12	10	resources	resource	NOUN
ejpam-3478	12	11	with	with	ADP
ejpam-3478	12	12	uncertainty	uncertainty	NOUN
ejpam-3478	12	13	about	about	ADP
ejpam-3478	12	14	the	the	DET
ejpam-3478	12	15	economic	economic	ADJ
ejpam-3478	12	16	,	,	PUNCT
ejpam-3478	12	17	capital	capital	NOUN
ejpam-3478	12	18	markets	market	NOUN
ejpam-3478	12	19	and	and	CCONJ
ejpam-3478	12	20	actuarial	actuarial	ADJ
ejpam-3478	12	21	conditions	condition	NOUN
ejpam-3478	12	22	.	.	PUNCT
ejpam-3478	13	1	the	the	DET
ejpam-3478	13	2	two	two	NUM
ejpam-3478	13	3	controls	control	NOUN
ejpam-3478	13	4	available	available	ADJ
ejpam-3478	13	5	to	to	ADP
ejpam-3478	13	6	the	the	DET
ejpam-3478	13	7	management	management	NOUN
ejpam-3478	13	8	of	of	ADP
ejpam-3478	13	9	the	the	DET
ejpam-3478	13	10	insurance	insurance	NOUN
ejpam-3478	13	11	company	company	NOUN
ejpam-3478	13	12	are	be	AUX
ejpam-3478	13	13	thus	thus	ADV
ejpam-3478	13	14	the	the	DET
ejpam-3478	13	15	†the	†the	DET
ejpam-3478	13	16	authors	author	NOUN
ejpam-3478	13	17	would	would	AUX
ejpam-3478	13	18	like	like	VERB
ejpam-3478	13	19	to	to	PART
ejpam-3478	13	20	thank	thank	VERB
ejpam-3478	13	21	mrs	mrs	PROPN
ejpam-3478	13	22	vanee	vanee	PROPN
ejpam-3478	13	23	lamsam	lamsam	PROPN
ejpam-3478	13	24	for	for	ADP
ejpam-3478	13	25	her	her	PRON
ejpam-3478	13	26	kind	kind	ADJ
ejpam-3478	13	27	support	support	NOUN
ejpam-3478	13	28	.	.	PUNCT
ejpam-3478	14	1	∗corresponding	∗corresponde	VERB
ejpam-3478	14	2	author	author	NOUN
ejpam-3478	14	3	.	.	PUNCT
ejpam-3478	15	1	doi	doi	NOUN
ejpam-3478	15	2	:	:	PUNCT
ejpam-3478	15	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3478	https://doi.org/10.29020/nybg.ejpam.v12i3.3478	ADJ
ejpam-3478	15	4	email	email	NOUN
ejpam-3478	15	5	addresses	address	NOUN
ejpam-3478	15	6	:	:	PUNCT
ejpam-3478	15	7	c.atkinson@imperial.ac.uk	c.atkinson@imperial.ac.uk	PROPN
ejpam-3478	15	8	(	(	PUNCT
ejpam-3478	15	9	c.	c.	PROPN
ejpam-3478	15	10	atkinson	atkinson	PROPN
ejpam-3478	15	11	)	)	PUNCT
ejpam-3478	15	12	,	,	PUNCT
ejpam-3478	15	13	drsutee@gmail.com	drsutee@gmail.com	X
ejpam-3478	15	14	(	(	PUNCT
ejpam-3478	15	15	s.	s.	PROPN
ejpam-3478	15	16	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	15	17	)	)	PUNCT
ejpam-3478	15	18	,	,	PUNCT
ejpam-3478	15	19	hall	hall	NOUN
ejpam-3478	15	20	ingpochai@hotmail.com	ingpochai@hotmail.com	PROPN
ejpam-3478	16	1	(	(	PUNCT
ejpam-3478	16	2	p.	p.	NOUN
ejpam-3478	16	3	ingpochai	ingpochai	PROPN
ejpam-3478	16	4	)	)	PUNCT
ejpam-3478	17	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3478	18	1	1315	1315	NUM
ejpam-3478	18	2	c	c	X
ejpam-3478	18	3	©	©	PROPN
ejpam-3478	18	4	2019	2019	NUM
ejpam-3478	18	5	ejpam	ejpam	NOUN
ejpam-3478	18	6	all	all	DET
ejpam-3478	18	7	rights	right	NOUN
ejpam-3478	18	8	reserved	reserve	VERB
ejpam-3478	18	9	.	.	PUNCT
ejpam-3478	19	1	c.	c.	PROPN
ejpam-3478	19	2	atkinson	atkinson	PROPN
ejpam-3478	19	3	,	,	PUNCT
ejpam-3478	19	4	s.	s.	PROPN
ejpam-3478	19	5	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	19	6	,	,	PUNCT
ejpam-3478	19	7	p.	p.	PROPN
ejpam-3478	19	8	ingpochai	ingpochai	PROPN
ejpam-3478	19	9	/	/	SYM
ejpam-3478	19	10	eur	eur	PROPN
ejpam-3478	19	11	.	.	PUNCT
ejpam-3478	20	1	j.	j.	PROPN
ejpam-3478	20	2	pure	pure	PROPN
ejpam-3478	20	3	appl	appl	PROPN
ejpam-3478	20	4	.	.	PROPN
ejpam-3478	20	5	math	math	PROPN
ejpam-3478	20	6	,	,	PUNCT
ejpam-3478	20	7	12	12	NUM
ejpam-3478	20	8	(	(	PUNCT
ejpam-3478	20	9	3	3	NUM
ejpam-3478	20	10	)	)	PUNCT
ejpam-3478	20	11	(	(	PUNCT
ejpam-3478	20	12	2019	2019	NUM
ejpam-3478	20	13	)	)	PUNCT
ejpam-3478	20	14	,	,	PUNCT
ejpam-3478	20	15	1315	1315	NUM
ejpam-3478	20	16	-	-	SYM
ejpam-3478	20	17	1336	1336	NUM
ejpam-3478	20	18	1316	1316	NUM
ejpam-3478	20	19	allocation	allocation	NOUN
ejpam-3478	20	20	of	of	ADP
ejpam-3478	20	21	the	the	DET
ejpam-3478	20	22	premiums	premium	NOUN
ejpam-3478	20	23	received	receive	VERB
ejpam-3478	20	24	from	from	ADP
ejpam-3478	20	25	the	the	DET
ejpam-3478	20	26	policyholders	policyholder	NOUN
ejpam-3478	20	27	to	to	ADP
ejpam-3478	20	28	the	the	DET
ejpam-3478	20	29	various	various	ADJ
ejpam-3478	20	30	invested	invest	VERB
ejpam-3478	20	31	assets	asset	NOUN
ejpam-3478	20	32	as	as	ADV
ejpam-3478	20	33	well	well	ADV
ejpam-3478	20	34	as	as	ADP
ejpam-3478	20	35	the	the	DET
ejpam-3478	20	36	decision	decision	NOUN
ejpam-3478	20	37	to	to	PART
ejpam-3478	20	38	market	market	VERB
ejpam-3478	20	39	different	different	ADJ
ejpam-3478	20	40	insurance	insurance	NOUN
ejpam-3478	20	41	products†.	products†.	NOUN
ejpam-3478	20	42	insurers	insurer	NOUN
ejpam-3478	20	43	currently	currently	ADV
ejpam-3478	20	44	use	use	VERB
ejpam-3478	20	45	cashflow	cashflow	ADJ
ejpam-3478	20	46	projection	projection	NOUN
ejpam-3478	20	47	of	of	ADP
ejpam-3478	20	48	liabilities	liability	NOUN
ejpam-3478	20	49	based	base	VERB
ejpam-3478	20	50	on	on	ADP
ejpam-3478	20	51	monte	monte	PROPN
ejpam-3478	20	52	carlo	carlo	PROPN
ejpam-3478	20	53	simulation	simulation	PROPN
ejpam-3478	20	54	as	as	ADP
ejpam-3478	20	55	a	a	DET
ejpam-3478	20	56	starting	starting	NOUN
ejpam-3478	20	57	point	point	NOUN
ejpam-3478	20	58	for	for	ADP
ejpam-3478	20	59	the	the	DET
ejpam-3478	20	60	strategic	strategic	ADJ
ejpam-3478	20	61	asset	asset	NOUN
ejpam-3478	20	62	allocation	allocation	NOUN
ejpam-3478	20	63	exercise	exercise	NOUN
ejpam-3478	20	64	.	.	PUNCT
ejpam-3478	21	1	several	several	ADJ
ejpam-3478	21	2	papers	paper	NOUN
ejpam-3478	21	3	e.g.	e.g.	ADV
ejpam-3478	21	4	gerstner	gerstner	NOUN
ejpam-3478	21	5	,	,	PUNCT
ejpam-3478	21	6	griebel	griebel	NOUN
ejpam-3478	21	7	and	and	CCONJ
ejpam-3478	21	8	holtz	holtz	NOUN
ejpam-3478	21	9	(	(	PUNCT
ejpam-3478	21	10	2009	2009	NUM
ejpam-3478	21	11	)	)	PUNCT
ejpam-3478	21	12	used	use	VERB
ejpam-3478	21	13	deterministic	deterministic	ADJ
ejpam-3478	21	14	numerical	numerical	PROPN
ejpam-3478	21	15	simulation	simulation	NOUN
ejpam-3478	21	16	to	to	PART
ejpam-3478	21	17	model	model	VERB
ejpam-3478	21	18	asset	asset	NOUN
ejpam-3478	21	19	-	-	PUNCT
ejpam-3478	21	20	liability	liability	NOUN
ejpam-3478	21	21	management	management	NOUN
ejpam-3478	21	22	(	(	PUNCT
ejpam-3478	21	23	alm	alm	NOUN
ejpam-3478	21	24	)	)	PUNCT
ejpam-3478	21	25	.	.	PUNCT
ejpam-3478	22	1	these	these	DET
ejpam-3478	22	2	numerical	numerical	ADJ
ejpam-3478	22	3	techniques	technique	NOUN
ejpam-3478	22	4	are	be	AUX
ejpam-3478	22	5	often	often	ADV
ejpam-3478	22	6	cumbersome	cumbersome	ADJ
ejpam-3478	22	7	and	and	CCONJ
ejpam-3478	22	8	lack	lack	VERB
ejpam-3478	22	9	the	the	DET
ejpam-3478	22	10	transparency	transparency	NOUN
ejpam-3478	22	11	offered	offer	VERB
ejpam-3478	22	12	by	by	ADP
ejpam-3478	22	13	analytical	analytical	ADJ
ejpam-3478	22	14	method	method	NOUN
ejpam-3478	22	15	which	which	PRON
ejpam-3478	22	16	we	we	PRON
ejpam-3478	22	17	apply	apply	VERB
ejpam-3478	22	18	in	in	ADP
ejpam-3478	22	19	this	this	DET
ejpam-3478	22	20	paper	paper	NOUN
ejpam-3478	22	21	.	.	PUNCT
ejpam-3478	23	1	here	here	ADV
ejpam-3478	23	2	,	,	PUNCT
ejpam-3478	23	3	we	we	PRON
ejpam-3478	23	4	show	show	VERB
ejpam-3478	23	5	that	that	SCONJ
ejpam-3478	23	6	if	if	SCONJ
ejpam-3478	23	7	the	the	DET
ejpam-3478	23	8	utility	utility	NOUN
ejpam-3478	23	9	of	of	ADP
ejpam-3478	23	10	the	the	DET
ejpam-3478	23	11	company	company	NOUN
ejpam-3478	23	12	is	be	AUX
ejpam-3478	23	13	of	of	ADP
ejpam-3478	23	14	the	the	DET
ejpam-3478	23	15	constant	constant	ADJ
ejpam-3478	23	16	relative	relative	ADJ
ejpam-3478	23	17	risk	risk	NOUN
ejpam-3478	23	18	aversion	aversion	NOUN
ejpam-3478	23	19	(	(	PUNCT
ejpam-3478	23	20	crra	crra	NOUN
ejpam-3478	23	21	)	)	PUNCT
ejpam-3478	23	22	form	form	NOUN
ejpam-3478	23	23	then	then	ADV
ejpam-3478	23	24	the	the	DET
ejpam-3478	23	25	solution	solution	NOUN
ejpam-3478	23	26	can	can	AUX
ejpam-3478	23	27	be	be	AUX
ejpam-3478	23	28	found	find	VERB
ejpam-3478	23	29	exactly	exactly	ADV
ejpam-3478	23	30	for	for	ADP
ejpam-3478	23	31	the	the	DET
ejpam-3478	23	32	case	case	NOUN
ejpam-3478	23	33	where	where	SCONJ
ejpam-3478	23	34	the	the	DET
ejpam-3478	23	35	correlation	correlation	NOUN
ejpam-3478	23	36	ρ	ρ	NOUN
ejpam-3478	23	37	between	between	ADP
ejpam-3478	23	38	the	the	DET
ejpam-3478	23	39	risky	risky	ADJ
ejpam-3478	23	40	asset	asset	NOUN
ejpam-3478	23	41	and	and	CCONJ
ejpam-3478	23	42	the	the	DET
ejpam-3478	23	43	risky	risky	ADJ
ejpam-3478	23	44	insurance	insurance	NOUN
ejpam-3478	23	45	liability	liability	NOUN
ejpam-3478	23	46	is	be	AUX
ejpam-3478	23	47	zero	zero	NUM
ejpam-3478	23	48	.	.	PUNCT
ejpam-3478	24	1	for	for	ADP
ejpam-3478	24	2	the	the	DET
ejpam-3478	24	3	non	non	ADJ
ejpam-3478	24	4	-	-	ADJ
ejpam-3478	24	5	zero	zero	NUM
ejpam-3478	24	6	correlation	correlation	NOUN
ejpam-3478	24	7	case	case	NOUN
ejpam-3478	24	8	,	,	PUNCT
ejpam-3478	24	9	we	we	PRON
ejpam-3478	24	10	find	find	VERB
ejpam-3478	24	11	that	that	SCONJ
ejpam-3478	24	12	we	we	PRON
ejpam-3478	24	13	can	can	AUX
ejpam-3478	24	14	solve	solve	VERB
ejpam-3478	24	15	for	for	ADP
ejpam-3478	24	16	the	the	DET
ejpam-3478	24	17	solution	solution	NOUN
ejpam-3478	24	18	provided	provide	VERB
ejpam-3478	24	19	that	that	SCONJ
ejpam-3478	24	20	the	the	DET
ejpam-3478	24	21	interest	interest	NOUN
ejpam-3478	24	22	rates	rate	NOUN
ejpam-3478	24	23	for	for	ADP
ejpam-3478	24	24	savings	saving	NOUN
ejpam-3478	24	25	(	(	PUNCT
ejpam-3478	24	26	ra	ra	NOUN
ejpam-3478	24	27	)	)	PUNCT
ejpam-3478	24	28	and	and	CCONJ
ejpam-3478	24	29	loans	loan	NOUN
ejpam-3478	24	30	(	(	PUNCT
ejpam-3478	24	31	rl	rl	NOUN
ejpam-3478	24	32	)	)	PUNCT
ejpam-3478	24	33	are	be	AUX
ejpam-3478	24	34	the	the	DET
ejpam-3478	24	35	same	same	ADJ
ejpam-3478	24	36	.	.	PUNCT
ejpam-3478	25	1	to	to	PART
ejpam-3478	25	2	solve	solve	VERB
ejpam-3478	25	3	for	for	ADP
ejpam-3478	25	4	the	the	DET
ejpam-3478	25	5	scenario	scenario	NOUN
ejpam-3478	25	6	where	where	SCONJ
ejpam-3478	25	7	the	the	DET
ejpam-3478	25	8	interest	interest	NOUN
ejpam-3478	25	9	rates	rate	NOUN
ejpam-3478	25	10	on	on	ADP
ejpam-3478	25	11	savings	saving	NOUN
ejpam-3478	25	12	and	and	CCONJ
ejpam-3478	25	13	loans	loan	NOUN
ejpam-3478	25	14	differ	differ	VERB
ejpam-3478	25	15	only	only	ADV
ejpam-3478	25	16	slightly	slightly	ADV
ejpam-3478	25	17	,	,	PUNCT
ejpam-3478	25	18	we	we	PRON
ejpam-3478	25	19	devise	devise	VERB
ejpam-3478	25	20	a	a	DET
ejpam-3478	25	21	perturbation	perturbation	NOUN
ejpam-3478	25	22	method	method	NOUN
ejpam-3478	25	23	and	and	CCONJ
ejpam-3478	25	24	find	find	VERB
ejpam-3478	25	25	a	a	DET
ejpam-3478	25	26	first	first	ADJ
ejpam-3478	25	27	and	and	CCONJ
ejpam-3478	25	28	second	second	ADJ
ejpam-3478	25	29	order	order	NOUN
ejpam-3478	25	30	solution	solution	NOUN
ejpam-3478	25	31	though	though	SCONJ
ejpam-3478	25	32	the	the	DET
ejpam-3478	25	33	method	method	NOUN
ejpam-3478	25	34	can	can	AUX
ejpam-3478	25	35	be	be	AUX
ejpam-3478	25	36	generalized	generalize	VERB
ejpam-3478	25	37	to	to	ADP
ejpam-3478	25	38	any	any	DET
ejpam-3478	25	39	order	order	NOUN
ejpam-3478	25	40	.	.	PUNCT
ejpam-3478	26	1	this	this	DET
ejpam-3478	26	2	work	work	NOUN
ejpam-3478	26	3	is	be	AUX
ejpam-3478	26	4	based	base	VERB
ejpam-3478	26	5	on	on	ADP
ejpam-3478	26	6	merton	merton	PROPN
ejpam-3478	26	7	’s	’s	PART
ejpam-3478	26	8	continuous	continuous	ADJ
ejpam-3478	26	9	time	time	NOUN
ejpam-3478	26	10	optimal	optimal	ADJ
ejpam-3478	26	11	portfolio	portfolio	NOUN
ejpam-3478	26	12	selection	selection	NOUN
ejpam-3478	26	13	and	and	CCONJ
ejpam-3478	26	14	consumption	consumption	NOUN
ejpam-3478	26	15	rule	rule	NOUN
ejpam-3478	26	16	,	,	PUNCT
ejpam-3478	26	17	merton	merton	X
ejpam-3478	26	18	(	(	PUNCT
ejpam-3478	26	19	1990	1990	NUM
ejpam-3478	26	20	)	)	PUNCT
ejpam-3478	26	21	.	.	PUNCT
ejpam-3478	27	1	here	here	ADV
ejpam-3478	27	2	an	an	DET
ejpam-3478	27	3	investor	investor	NOUN
ejpam-3478	27	4	wishes	wish	VERB
ejpam-3478	27	5	to	to	PART
ejpam-3478	27	6	maximise	maximise	VERB
ejpam-3478	27	7	the	the	DET
ejpam-3478	27	8	expected	expect	VERB
ejpam-3478	27	9	utility	utility	NOUN
ejpam-3478	27	10	of	of	ADP
ejpam-3478	27	11	consumption	consumption	NOUN
ejpam-3478	27	12	over	over	ADP
ejpam-3478	27	13	his	his	PRON
ejpam-3478	27	14	life	life	NOUN
ejpam-3478	27	15	time	time	NOUN
ejpam-3478	27	16	.	.	PUNCT
ejpam-3478	28	1	for	for	ADP
ejpam-3478	28	2	the	the	DET
ejpam-3478	28	3	case	case	NOUN
ejpam-3478	28	4	of	of	ADP
ejpam-3478	28	5	the	the	DET
ejpam-3478	28	6	utility	utility	NOUN
ejpam-3478	28	7	functions	function	NOUN
ejpam-3478	28	8	of	of	ADP
ejpam-3478	28	9	the	the	DET
ejpam-3478	28	10	type	type	NOUN
ejpam-3478	28	11	constant	constant	ADJ
ejpam-3478	28	12	relative	relative	ADJ
ejpam-3478	28	13	risk	risk	NOUN
ejpam-3478	28	14	aversion	aversion	NOUN
ejpam-3478	28	15	(	(	PUNCT
ejpam-3478	28	16	crra	crra	NOUN
ejpam-3478	28	17	)	)	PUNCT
ejpam-3478	28	18	,	,	PUNCT
ejpam-3478	28	19	one	one	PRON
ejpam-3478	28	20	can	can	AUX
ejpam-3478	28	21	find	find	VERB
ejpam-3478	28	22	the	the	DET
ejpam-3478	28	23	optimal	optimal	ADJ
ejpam-3478	28	24	allocation	allocation	NOUN
ejpam-3478	28	25	and	and	CCONJ
ejpam-3478	28	26	consumption	consumption	NOUN
ejpam-3478	28	27	rule	rule	NOUN
ejpam-3478	28	28	which	which	PRON
ejpam-3478	28	29	will	will	AUX
ejpam-3478	28	30	maximise	maximise	VERB
ejpam-3478	28	31	the	the	DET
ejpam-3478	28	32	lifetime	lifetime	NOUN
ejpam-3478	28	33	expected	expect	VERB
ejpam-3478	28	34	utility	utility	NOUN
ejpam-3478	28	35	of	of	ADP
ejpam-3478	28	36	the	the	DET
ejpam-3478	28	37	investor	investor	NOUN
ejpam-3478	28	38	.	.	PUNCT
ejpam-3478	29	1	2	2	X
ejpam-3478	29	2	.	.	X
ejpam-3478	29	3	governing	govern	VERB
ejpam-3478	29	4	equations	equation	NOUN
ejpam-3478	29	5	2.1	2.1	NUM
ejpam-3478	29	6	.	.	PUNCT
ejpam-3478	30	1	evolution	evolution	NOUN
ejpam-3478	30	2	of	of	ADP
ejpam-3478	30	3	the	the	DET
ejpam-3478	30	4	liability	liability	NOUN
ejpam-3478	30	5	l	l	NOUN
ejpam-3478	30	6	let	let	VERB
ejpam-3478	30	7	l	l	NOUN
ejpam-3478	30	8	be	be	AUX
ejpam-3478	30	9	the	the	DET
ejpam-3478	30	10	liabilities	liability	NOUN
ejpam-3478	30	11	of	of	ADP
ejpam-3478	30	12	the	the	DET
ejpam-3478	30	13	company	company	NOUN
ejpam-3478	30	14	.	.	PUNCT
ejpam-3478	31	1	l	l	NOUN
ejpam-3478	31	2	is	be	AUX
ejpam-3478	31	3	made	make	VERB
ejpam-3478	31	4	up	up	ADP
ejpam-3478	31	5	of	of	ADP
ejpam-3478	31	6	the	the	DET
ejpam-3478	31	7	risky	risky	ADJ
ejpam-3478	31	8	insurance	insurance	NOUN
ejpam-3478	31	9	liability	liability	NOUN
ejpam-3478	31	10	ul	ul	NOUN
ejpam-3478	31	11	and	and	CCONJ
ejpam-3478	31	12	riskless	riskless	NOUN
ejpam-3478	31	13	liability	liability	NOUN
ejpam-3478	31	14	(	(	PUNCT
ejpam-3478	31	15	1−	1−	NUM
ejpam-3478	31	16	u)l	u)l	X
ejpam-3478	31	17	.	.	PUNCT
ejpam-3478	32	1	the	the	DET
ejpam-3478	32	2	risky	risky	ADJ
ejpam-3478	32	3	insurance	insurance	NOUN
ejpam-3478	32	4	liability	liability	NOUN
ejpam-3478	32	5	comes	come	VERB
ejpam-3478	32	6	from	from	ADP
ejpam-3478	32	7	the	the	DET
ejpam-3478	32	8	stochastic	stochastic	ADJ
ejpam-3478	32	9	nature	nature	NOUN
ejpam-3478	32	10	of	of	ADP
ejpam-3478	32	11	the	the	DET
ejpam-3478	32	12	benefits	benefit	NOUN
ejpam-3478	32	13	outgo	outgo	NOUN
ejpam-3478	32	14	(	(	PUNCT
ejpam-3478	32	15	claims	claim	NOUN
ejpam-3478	32	16	payment	payment	NOUN
ejpam-3478	32	17	,	,	PUNCT
ejpam-3478	32	18	surrender	surrender	NOUN
ejpam-3478	32	19	,	,	PUNCT
ejpam-3478	32	20	and	and	CCONJ
ejpam-3478	32	21	maturity	maturity	NOUN
ejpam-3478	32	22	benefits	benefit	NOUN
ejpam-3478	32	23	)	)	PUNCT
ejpam-3478	32	24	.	.	PUNCT
ejpam-3478	33	1	the	the	DET
ejpam-3478	33	2	riskless	riskless	NOUN
ejpam-3478	33	3	liability	liability	NOUN
ejpam-3478	33	4	is	be	AUX
ejpam-3478	33	5	defined	define	VERB
ejpam-3478	33	6	to	to	PART
ejpam-3478	33	7	be	be	AUX
ejpam-3478	33	8	liabilities	liability	NOUN
ejpam-3478	33	9	that	that	PRON
ejpam-3478	33	10	are	be	AUX
ejpam-3478	33	11	deterministic	deterministic	ADJ
ejpam-3478	33	12	in	in	ADP
ejpam-3478	33	13	value	value	NOUN
ejpam-3478	33	14	such	such	ADJ
ejpam-3478	33	15	as	as	ADP
ejpam-3478	33	16	debt	debt	NOUN
ejpam-3478	33	17	issued	issue	VERB
ejpam-3478	33	18	by	by	ADP
ejpam-3478	33	19	the	the	DET
ejpam-3478	33	20	company	company	NOUN
ejpam-3478	33	21	.	.	PUNCT
ejpam-3478	34	1	suppose	suppose	VERB
ejpam-3478	34	2	that	that	SCONJ
ejpam-3478	34	3	we	we	PRON
ejpam-3478	34	4	assume	assume	VERB
ejpam-3478	34	5	that	that	SCONJ
ejpam-3478	34	6	the	the	DET
ejpam-3478	34	7	liability	liability	NOUN
ejpam-3478	34	8	of	of	ADP
ejpam-3478	34	9	a	a	DET
ejpam-3478	34	10	life	life	NOUN
ejpam-3478	34	11	insurance	insurance	NOUN
ejpam-3478	34	12	company	company	NOUN
ejpam-3478	34	13	evolves	evolve	VERB
ejpam-3478	34	14	according	accord	VERB
ejpam-3478	34	15	to	to	ADP
ejpam-3478	34	16	the	the	DET
ejpam-3478	34	17	stochastic	stochastic	ADJ
ejpam-3478	34	18	differential	differential	ADJ
ejpam-3478	34	19	equation	equation	NOUN
ejpam-3478	34	20	dlt	dlt	PROPN
ejpam-3478	35	1	=	=	SYM
ejpam-3478	35	2	(	(	PUNCT
ejpam-3478	35	3	cult	cult	NOUN
ejpam-3478	35	4	−mult	−mult	NOUN
ejpam-3478	35	5	+	+	CCONJ
ejpam-3478	35	6	(	(	PUNCT
ejpam-3478	35	7	1−	1−	NUM
ejpam-3478	35	8	u)ltrl)dt−	u)ltrl)dt−	ADJ
ejpam-3478	35	9	qltudz	qltudz	NOUN
ejpam-3478	35	10	(	(	PUNCT
ejpam-3478	35	11	t	t	NOUN
ejpam-3478	35	12	)	)	PUNCT
ejpam-3478	35	13	(	(	PUNCT
ejpam-3478	35	14	1	1	X
ejpam-3478	35	15	)	)	PUNCT
ejpam-3478	35	16	where	where	SCONJ
ejpam-3478	35	17	lt	lt	NOUN
ejpam-3478	35	18	is	be	AUX
ejpam-3478	35	19	the	the	DET
ejpam-3478	35	20	liability	liability	NOUN
ejpam-3478	35	21	at	at	ADP
ejpam-3478	35	22	time	time	NOUN
ejpam-3478	35	23	t	t	PROPN
ejpam-3478	35	24	,	,	PUNCT
ejpam-3478	35	25	c	c	PROPN
ejpam-3478	35	26	(	(	PUNCT
ejpam-3478	35	27	orm	orm	NOUN
ejpam-3478	35	28	)	)	PUNCT
ejpam-3478	35	29	represents	represent	VERB
ejpam-3478	35	30	the	the	DET
ejpam-3478	35	31	exponential	exponential	ADJ
ejpam-3478	35	32	growth	growth	NOUN
ejpam-3478	35	33	(	(	PUNCT
ejpam-3478	35	34	or	or	CCONJ
ejpam-3478	35	35	decay	decay	NOUN
ejpam-3478	35	36	)	)	PUNCT
ejpam-3478	35	37	rate	rate	NOUN
ejpam-3478	35	38	in	in	ADP
ejpam-3478	35	39	l	l	NOUN
ejpam-3478	35	40	,	,	PUNCT
ejpam-3478	35	41	qdz	qdz	PROPN
ejpam-3478	35	42	is	be	AUX
ejpam-3478	35	43	the	the	DET
ejpam-3478	35	44	stochastic	stochastic	ADJ
ejpam-3478	35	45	component	component	NOUN
ejpam-3478	35	46	which	which	PRON
ejpam-3478	35	47	represents	represent	VERB
ejpam-3478	35	48	the	the	DET
ejpam-3478	35	49	random	random	ADJ
ejpam-3478	35	50	nature	nature	NOUN
ejpam-3478	35	51	of	of	ADP
ejpam-3478	35	52	insurance	insurance	NOUN
ejpam-3478	35	53	,	,	PUNCT
ejpam-3478	35	54	dz	dz	X
ejpam-3478	35	55	is	be	AUX
ejpam-3478	35	56	an	an	DET
ejpam-3478	35	57	infinitesimal	infinitesimal	ADJ
ejpam-3478	35	58	wiener	wiener	NOUN
ejpam-3478	35	59	increment	increment	NOUN
ejpam-3478	35	60	.	.	PUNCT
ejpam-3478	36	1	the	the	DET
ejpam-3478	36	2	stochastic	stochastic	ADJ
ejpam-3478	36	3	term	term	NOUN
ejpam-3478	36	4	−qltdz	−qltdz	NOUN
ejpam-3478	36	5	(	(	PUNCT
ejpam-3478	36	6	t	t	NOUN
ejpam-3478	36	7	)	)	PUNCT
ejpam-3478	36	8	can	can	AUX
ejpam-3478	36	9	increase	increase	VERB
ejpam-3478	36	10	or	or	CCONJ
ejpam-3478	36	11	decrease	decrease	VERB
ejpam-3478	36	12	the	the	DET
ejpam-3478	36	13	liability	liability	NOUN
ejpam-3478	36	14	of	of	ADP
ejpam-3478	36	15	the	the	DET
ejpam-3478	36	16	insurance	insurance	NOUN
ejpam-3478	36	17	company	company	NOUN
ejpam-3478	36	18	.	.	PUNCT
ejpam-3478	37	1	the	the	DET
ejpam-3478	37	2	variable	variable	NOUN
ejpam-3478	37	3	rl	rl	X
ejpam-3478	37	4	represents	represent	VERB
ejpam-3478	37	5	the	the	DET
ejpam-3478	37	6	interest	interest	NOUN
ejpam-3478	37	7	rate	rate	NOUN
ejpam-3478	37	8	at	at	ADP
ejpam-3478	37	9	which	which	PRON
ejpam-3478	37	10	the	the	DET
ejpam-3478	37	11	riskless	riskless	NOUN
ejpam-3478	37	12	liability	liability	NOUN
ejpam-3478	37	13	grows	grow	VERB
ejpam-3478	37	14	;	;	PUNCT
ejpam-3478	37	15	equivalently	equivalently	ADV
ejpam-3478	37	16	this	this	PRON
ejpam-3478	37	17	is	be	AUX
ejpam-3478	37	18	the	the	DET
ejpam-3478	37	19	same	same	ADJ
ejpam-3478	37	20	as	as	ADP
ejpam-3478	37	21	the	the	DET
ejpam-3478	37	22	interest	interest	NOUN
ejpam-3478	37	23	rate	rate	NOUN
ejpam-3478	37	24	charged	charge	VERB
ejpam-3478	37	25	for	for	ADP
ejpam-3478	37	26	a	a	DET
ejpam-3478	37	27	loan	loan	NOUN
ejpam-3478	37	28	.	.	PUNCT
ejpam-3478	38	1	the	the	DET
ejpam-3478	38	2	control	control	PROPN
ejpam-3478	38	3	variable	variable	NOUN
ejpam-3478	38	4	u	u	PROPN
ejpam-3478	38	5	allows	allow	VERB
ejpam-3478	38	6	the	the	DET
ejpam-3478	38	7	management	management	NOUN
ejpam-3478	38	8	to	to	PART
ejpam-3478	38	9	vary	vary	VERB
ejpam-3478	38	10	the	the	DET
ejpam-3478	38	11	proportion	proportion	NOUN
ejpam-3478	38	12	of	of	ADP
ejpam-3478	38	13	the	the	DET
ejpam-3478	38	14	policyholder	policyholder	NOUN
ejpam-3478	38	15	’s	’s	PART
ejpam-3478	38	16	liability	liability	NOUN
ejpam-3478	38	17	between	between	ADP
ejpam-3478	38	18	the	the	DET
ejpam-3478	38	19	deterministic	deterministic	ADJ
ejpam-3478	38	20	(	(	PUNCT
ejpam-3478	38	21	riskless	riskless	NOUN
ejpam-3478	38	22	)	)	PUNCT
ejpam-3478	38	23	liability	liability	NOUN
ejpam-3478	38	24	which	which	PRON
ejpam-3478	38	25	grows	grow	VERB
ejpam-3478	38	26	at	at	ADP
ejpam-3478	38	27	the	the	DET
ejpam-3478	38	28	rate	rate	NOUN
ejpam-3478	38	29	rl	rl	NOUN
ejpam-3478	38	30	and	and	CCONJ
ejpam-3478	38	31	the	the	DET
ejpam-3478	38	32	stochastic	stochastic	ADJ
ejpam-3478	38	33	(	(	PUNCT
ejpam-3478	38	34	risky	risky	ADJ
ejpam-3478	38	35	)	)	PUNCT
ejpam-3478	38	36	liability	liability	NOUN
ejpam-3478	38	37	with	with	ADP
ejpam-3478	38	38	some	some	DET
ejpam-3478	38	39	known	know	VERB
ejpam-3478	38	40	probability	probability	NOUN
ejpam-3478	38	41	distribution	distribution	NOUN
ejpam-3478	38	42	.	.	PUNCT
ejpam-3478	39	1	†life	†life	NOUN
ejpam-3478	39	2	insurance	insurance	NOUN
ejpam-3478	39	3	products	product	NOUN
ejpam-3478	39	4	have	have	VERB
ejpam-3478	39	5	vastly	vastly	ADV
ejpam-3478	39	6	different	different	ADJ
ejpam-3478	39	7	risk	risk	NOUN
ejpam-3478	39	8	profiles	profile	NOUN
ejpam-3478	39	9	.	.	PUNCT
ejpam-3478	40	1	the	the	DET
ejpam-3478	40	2	decision	decision	NOUN
ejpam-3478	40	3	to	to	PART
ejpam-3478	40	4	market	market	VERB
ejpam-3478	40	5	a	a	DET
ejpam-3478	40	6	particular	particular	ADJ
ejpam-3478	40	7	product	product	NOUN
ejpam-3478	40	8	should	should	AUX
ejpam-3478	40	9	be	be	AUX
ejpam-3478	40	10	based	base	VERB
ejpam-3478	40	11	on	on	ADP
ejpam-3478	40	12	the	the	DET
ejpam-3478	40	13	ability	ability	NOUN
ejpam-3478	40	14	to	to	PART
ejpam-3478	40	15	find	find	VERB
ejpam-3478	40	16	suitable	suitable	ADJ
ejpam-3478	40	17	assets	asset	NOUN
ejpam-3478	40	18	to	to	PART
ejpam-3478	40	19	invest	invest	VERB
ejpam-3478	40	20	in	in	ADP
ejpam-3478	40	21	.	.	PUNCT
ejpam-3478	41	1	c.	c.	PROPN
ejpam-3478	41	2	atkinson	atkinson	PROPN
ejpam-3478	41	3	,	,	PUNCT
ejpam-3478	41	4	s.	s.	PROPN
ejpam-3478	41	5	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	41	6	,	,	PUNCT
ejpam-3478	41	7	p.	p.	PROPN
ejpam-3478	41	8	ingpochai	ingpochai	PROPN
ejpam-3478	41	9	/	/	SYM
ejpam-3478	41	10	eur	eur	PROPN
ejpam-3478	41	11	.	.	PUNCT
ejpam-3478	42	1	j.	j.	PROPN
ejpam-3478	42	2	pure	pure	PROPN
ejpam-3478	42	3	appl	appl	PROPN
ejpam-3478	42	4	.	.	PROPN
ejpam-3478	42	5	math	math	PROPN
ejpam-3478	42	6	,	,	PUNCT
ejpam-3478	42	7	12	12	NUM
ejpam-3478	42	8	(	(	PUNCT
ejpam-3478	42	9	3	3	NUM
ejpam-3478	42	10	)	)	PUNCT
ejpam-3478	42	11	(	(	PUNCT
ejpam-3478	42	12	2019	2019	NUM
ejpam-3478	42	13	)	)	PUNCT
ejpam-3478	42	14	,	,	PUNCT
ejpam-3478	42	15	1315	1315	NUM
ejpam-3478	42	16	-	-	SYM
ejpam-3478	42	17	1336	1336	NUM
ejpam-3478	42	18	1317	1317	NUM
ejpam-3478	42	19	figure	figure	NOUN
ejpam-3478	42	20	1	1	NUM
ejpam-3478	42	21	:	:	PUNCT
ejpam-3478	42	22	illustration	illustration	NOUN
ejpam-3478	42	23	of	of	ADP
ejpam-3478	42	24	the	the	DET
ejpam-3478	42	25	insurer	insurer	NOUN
ejpam-3478	42	26	’s	’s	PART
ejpam-3478	42	27	balance	balance	NOUN
ejpam-3478	42	28	sheet	sheet	NOUN
ejpam-3478	42	29	and	and	CCONJ
ejpam-3478	42	30	the	the	DET
ejpam-3478	42	31	associated	associated	ADJ
ejpam-3478	42	32	control	control	NOUN
ejpam-3478	42	33	variables	variable	NOUN
ejpam-3478	42	34	w	w	VERB
ejpam-3478	42	35	and	and	CCONJ
ejpam-3478	42	36	u.	u.	VERB
ejpam-3478	42	37	in	in	ADP
ejpam-3478	42	38	reality	reality	NOUN
ejpam-3478	42	39	,	,	PUNCT
ejpam-3478	42	40	this	this	PRON
ejpam-3478	42	41	can	can	AUX
ejpam-3478	42	42	be	be	AUX
ejpam-3478	42	43	done	do	VERB
ejpam-3478	42	44	through	through	ADP
ejpam-3478	42	45	risk	risk	NOUN
ejpam-3478	42	46	transfer	transfer	NOUN
ejpam-3478	42	47	techniques	technique	NOUN
ejpam-3478	42	48	such	such	ADJ
ejpam-3478	42	49	as	as	ADP
ejpam-3478	42	50	reinsurance	reinsurance	NOUN
ejpam-3478	42	51	or	or	CCONJ
ejpam-3478	42	52	hedging	hedging	NOUN
ejpam-3478	42	53	with	with	ADP
ejpam-3478	42	54	swaps	swap	NOUN
ejpam-3478	42	55	.	.	PUNCT
ejpam-3478	43	1	intuitively	intuitively	ADV
ejpam-3478	43	2	,	,	PUNCT
ejpam-3478	43	3	suppose	suppose	VERB
ejpam-3478	43	4	that	that	SCONJ
ejpam-3478	43	5	there	there	PRON
ejpam-3478	43	6	is	be	VERB
ejpam-3478	43	7	a	a	DET
ejpam-3478	43	8	death	death	NOUN
ejpam-3478	43	9	claim	claim	NOUN
ejpam-3478	43	10	then	then	ADV
ejpam-3478	43	11	the	the	DET
ejpam-3478	43	12	company	company	NOUN
ejpam-3478	43	13	’s	’s	PART
ejpam-3478	43	14	liability	liability	NOUN
ejpam-3478	43	15	decreases	decrease	NOUN
ejpam-3478	43	16	(	(	PUNCT
ejpam-3478	43	17	i.e.	i.e.	X
ejpam-3478	43	18	once	once	SCONJ
ejpam-3478	43	19	the	the	DET
ejpam-3478	43	20	company	company	NOUN
ejpam-3478	43	21	has	have	AUX
ejpam-3478	43	22	paid	pay	VERB
ejpam-3478	43	23	out	out	ADP
ejpam-3478	43	24	the	the	DET
ejpam-3478	43	25	claim	claim	NOUN
ejpam-3478	43	26	of	of	ADP
ejpam-3478	43	27	this	this	DET
ejpam-3478	43	28	particular	particular	ADJ
ejpam-3478	43	29	policy	policy	NOUN
ejpam-3478	43	30	,	,	PUNCT
ejpam-3478	43	31	the	the	DET
ejpam-3478	43	32	contract	contract	NOUN
ejpam-3478	43	33	is	be	AUX
ejpam-3478	43	34	terminated	terminate	VERB
ejpam-3478	43	35	)	)	PUNCT
ejpam-3478	43	36	.	.	PUNCT
ejpam-3478	44	1	also	also	ADV
ejpam-3478	44	2	,	,	PUNCT
ejpam-3478	44	3	the	the	DET
ejpam-3478	44	4	liability	liability	NOUN
ejpam-3478	44	5	can	can	AUX
ejpam-3478	44	6	increase	increase	VERB
ejpam-3478	44	7	if	if	SCONJ
ejpam-3478	44	8	the	the	DET
ejpam-3478	44	9	actuary	actuary	NOUN
ejpam-3478	44	10	decides	decide	VERB
ejpam-3478	44	11	to	to	PART
ejpam-3478	44	12	strengthen	strengthen	VERB
ejpam-3478	44	13	the	the	DET
ejpam-3478	44	14	reserve	reserve	NOUN
ejpam-3478	44	15	.	.	PUNCT
ejpam-3478	45	1	2.2	2.2	NUM
ejpam-3478	45	2	.	.	PUNCT
ejpam-3478	45	3	evolution	evolution	NOUN
ejpam-3478	45	4	of	of	ADP
ejpam-3478	45	5	the	the	DET
ejpam-3478	45	6	total	total	ADJ
ejpam-3478	45	7	asset	asset	NOUN
ejpam-3478	46	1	w	w	NOUN
ejpam-3478	46	2	let	let	VERB
ejpam-3478	46	3	us	we	PRON
ejpam-3478	46	4	assume	assume	VERB
ejpam-3478	46	5	that	that	SCONJ
ejpam-3478	46	6	the	the	DET
ejpam-3478	46	7	company	company	NOUN
ejpam-3478	46	8	’s	’s	PART
ejpam-3478	46	9	assets	asset	NOUN
ejpam-3478	46	10	are	be	AUX
ejpam-3478	46	11	comprised	comprise	VERB
ejpam-3478	46	12	of	of	ADP
ejpam-3478	46	13	the	the	DET
ejpam-3478	46	14	risky	risky	ADJ
ejpam-3478	46	15	asset	asset	NOUN
ejpam-3478	46	16	,	,	PUNCT
ejpam-3478	46	17	s1	s1	PROPN
ejpam-3478	46	18	(=	(=	ADV
ejpam-3478	46	19	ww	ww	PROPN
ejpam-3478	46	20	)	)	PUNCT
ejpam-3478	46	21	and	and	CCONJ
ejpam-3478	46	22	the	the	DET
ejpam-3478	46	23	risk	risk	NOUN
ejpam-3478	46	24	-	-	PUNCT
ejpam-3478	46	25	free	free	ADJ
ejpam-3478	46	26	asset	asset	NOUN
ejpam-3478	46	27	s0	s0	NOUN
ejpam-3478	47	1	(=	(=	X
ejpam-3478	47	2	(	(	PUNCT
ejpam-3478	47	3	1−	1−	NUM
ejpam-3478	47	4	w)w	w)w	X
ejpam-3478	47	5	)	)	PUNCT
ejpam-3478	47	6	with	with	ADP
ejpam-3478	47	7	ds1	ds1	PROPN
ejpam-3478	47	8	=	=	SYM
ejpam-3478	47	9	αs1dt+	αs1dt+	X
ejpam-3478	47	10	σs1dx	σs1dx	NOUN
ejpam-3478	47	11	(	(	PUNCT
ejpam-3478	47	12	2	2	NUM
ejpam-3478	47	13	)	)	PUNCT
ejpam-3478	47	14	ds0	ds0	NOUN
ejpam-3478	48	1	=	=	PUNCT
ejpam-3478	48	2	ras0dt	ras0dt	X
ejpam-3478	48	3	(	(	PUNCT
ejpam-3478	48	4	3	3	NUM
ejpam-3478	48	5	)	)	PUNCT
ejpam-3478	48	6	then	then	ADV
ejpam-3478	48	7	we	we	PRON
ejpam-3478	48	8	can	can	AUX
ejpam-3478	48	9	write	write	VERB
ejpam-3478	48	10	dw	dw	NOUN
ejpam-3478	49	1	=	=	PUNCT
ejpam-3478	50	1	[	[	X
ejpam-3478	50	2	w	w	X
ejpam-3478	50	3	(	(	PUNCT
ejpam-3478	50	4	α−	α−	ADP
ejpam-3478	50	5	ra	ra	NOUN
ejpam-3478	50	6	)	)	PUNCT
ejpam-3478	50	7	+	+	CCONJ
ejpam-3478	51	1	ra]wdt+	ra]wdt+	ADP
ejpam-3478	51	2	wwσdx	wwσdx	NOUN
ejpam-3478	51	3	(	(	PUNCT
ejpam-3478	51	4	4	4	NUM
ejpam-3478	51	5	)	)	PUNCT
ejpam-3478	51	6	where	where	SCONJ
ejpam-3478	51	7	dx	dx	PROPN
ejpam-3478	51	8	is	be	AUX
ejpam-3478	51	9	an	an	DET
ejpam-3478	51	10	infinitesimal	infinitesimal	ADJ
ejpam-3478	51	11	wiener	wiener	NOUN
ejpam-3478	51	12	increment	increment	NOUN
ejpam-3478	51	13	.	.	PUNCT
ejpam-3478	52	1	the	the	DET
ejpam-3478	52	2	total	total	ADJ
ejpam-3478	52	3	asset	asset	NOUN
ejpam-3478	52	4	of	of	ADP
ejpam-3478	52	5	the	the	DET
ejpam-3478	52	6	company	company	NOUN
ejpam-3478	52	7	w	w	NOUN
ejpam-3478	52	8	is	be	AUX
ejpam-3478	52	9	by	by	ADP
ejpam-3478	52	10	definition	definition	NOUN
ejpam-3478	52	11	w	w	PROPN
ejpam-3478	52	12	≡	≡	PROPN
ejpam-3478	52	13	l+	l+	X
ejpam-3478	52	14	e	e	X
ejpam-3478	52	15	(	(	PUNCT
ejpam-3478	52	16	5	5	NUM
ejpam-3478	52	17	)	)	PUNCT
ejpam-3478	52	18	where	where	SCONJ
ejpam-3478	52	19	e	e	NOUN
ejpam-3478	52	20	stands	stand	VERB
ejpam-3478	52	21	for	for	ADP
ejpam-3478	52	22	equity	equity	NOUN
ejpam-3478	52	23	and	and	CCONJ
ejpam-3478	52	24	represents	represent	VERB
ejpam-3478	52	25	the	the	DET
ejpam-3478	52	26	portion	portion	NOUN
ejpam-3478	52	27	of	of	ADP
ejpam-3478	52	28	assets	asset	NOUN
ejpam-3478	52	29	owned	own	VERB
ejpam-3478	52	30	by	by	ADP
ejpam-3478	52	31	the	the	DET
ejpam-3478	52	32	shareholders	shareholder	NOUN
ejpam-3478	52	33	once	once	ADV
ejpam-3478	52	34	all	all	DET
ejpam-3478	52	35	the	the	DET
ejpam-3478	52	36	liabilities	liability	NOUN
ejpam-3478	52	37	have	have	AUX
ejpam-3478	52	38	been	be	AUX
ejpam-3478	52	39	paid	pay	VERB
ejpam-3478	52	40	out	out	ADP
ejpam-3478	52	41	.	.	PUNCT
ejpam-3478	53	1	the	the	DET
ejpam-3478	53	2	illustration	illustration	NOUN
ejpam-3478	53	3	of	of	ADP
ejpam-3478	53	4	the	the	DET
ejpam-3478	53	5	insurer	insurer	NOUN
ejpam-3478	53	6	’s	’s	PART
ejpam-3478	53	7	balance	balance	NOUN
ejpam-3478	53	8	sheet	sheet	NOUN
ejpam-3478	53	9	is	be	AUX
ejpam-3478	53	10	shown	show	VERB
ejpam-3478	53	11	in	in	ADP
ejpam-3478	53	12	figure	figure	NOUN
ejpam-3478	53	13	(	(	PUNCT
ejpam-3478	53	14	1	1	NUM
ejpam-3478	53	15	)	)	PUNCT
ejpam-3478	53	16	.	.	PUNCT
ejpam-3478	54	1	then	then	ADV
ejpam-3478	54	2	de	de	PROPN
ejpam-3478	54	3	=	=	PROPN
ejpam-3478	54	4	dw	dw	PROPN
ejpam-3478	54	5	−	−	PROPN
ejpam-3478	54	6	dl	dl	PROPN
ejpam-3478	54	7	(	(	PUNCT
ejpam-3478	54	8	6	6	NUM
ejpam-3478	54	9	)	)	PUNCT
ejpam-3478	54	10	c.	c.	PROPN
ejpam-3478	54	11	atkinson	atkinson	PROPN
ejpam-3478	54	12	,	,	PUNCT
ejpam-3478	54	13	s.	s.	PROPN
ejpam-3478	54	14	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	54	15	,	,	PUNCT
ejpam-3478	54	16	p.	p.	PROPN
ejpam-3478	54	17	ingpochai	ingpochai	PROPN
ejpam-3478	54	18	/	/	SYM
ejpam-3478	54	19	eur	eur	PROPN
ejpam-3478	54	20	.	.	PUNCT
ejpam-3478	55	1	j.	j.	PROPN
ejpam-3478	55	2	pure	pure	PROPN
ejpam-3478	55	3	appl	appl	PROPN
ejpam-3478	55	4	.	.	PROPN
ejpam-3478	55	5	math	math	PROPN
ejpam-3478	55	6	,	,	PUNCT
ejpam-3478	55	7	12	12	NUM
ejpam-3478	55	8	(	(	PUNCT
ejpam-3478	55	9	3	3	NUM
ejpam-3478	55	10	)	)	PUNCT
ejpam-3478	55	11	(	(	PUNCT
ejpam-3478	55	12	2019	2019	NUM
ejpam-3478	55	13	)	)	PUNCT
ejpam-3478	55	14	,	,	PUNCT
ejpam-3478	55	15	1315	1315	NUM
ejpam-3478	55	16	-	-	SYM
ejpam-3478	55	17	1336	1336	NUM
ejpam-3478	55	18	1318	1318	NUM
ejpam-3478	55	19	=	=	SYM
ejpam-3478	55	20	{	{	PUNCT
ejpam-3478	56	1	[	[	X
ejpam-3478	56	2	w	w	X
ejpam-3478	56	3	(	(	PUNCT
ejpam-3478	56	4	α−	α−	ADP
ejpam-3478	56	5	ra	ra	NOUN
ejpam-3478	56	6	)	)	PUNCT
ejpam-3478	56	7	+	+	CCONJ
ejpam-3478	56	8	ra]w	ra]w	NOUN
ejpam-3478	56	9	−	−	PROPN
ejpam-3478	56	10	cult	cult	NOUN
ejpam-3478	56	11	−	−	PROPN
ejpam-3478	56	12	(	(	PUNCT
ejpam-3478	56	13	(	(	PUNCT
ejpam-3478	56	14	1−	1−	NUM
ejpam-3478	56	15	u	u	NOUN
ejpam-3478	56	16	)	)	PUNCT
ejpam-3478	56	17	rl	rl	ADP
ejpam-3478	56	18	−mu)lt	−mu)lt	NOUN
ejpam-3478	56	19	}	}	PUNCT
ejpam-3478	56	20	dt	dt	PUNCT
ejpam-3478	57	1	+	+	CCONJ
ejpam-3478	57	2	qltudz	qltudz	ADJ
ejpam-3478	57	3	+	+	CCONJ
ejpam-3478	57	4	wwσdx	wwσdx	NOUN
ejpam-3478	57	5	(	(	PUNCT
ejpam-3478	57	6	7	7	NUM
ejpam-3478	57	7	)	)	PUNCT
ejpam-3478	57	8	the	the	DET
ejpam-3478	57	9	problem	problem	NOUN
ejpam-3478	57	10	for	for	ADP
ejpam-3478	57	11	choosing	choose	VERB
ejpam-3478	57	12	the	the	DET
ejpam-3478	57	13	strategic	strategic	ADJ
ejpam-3478	57	14	asset	asset	NOUN
ejpam-3478	57	15	allocation	allocation	NOUN
ejpam-3478	57	16	and	and	CCONJ
ejpam-3478	57	17	insurance	insurance	NOUN
ejpam-3478	57	18	product	product	NOUN
ejpam-3478	57	19	mix	mix	NOUN
ejpam-3478	57	20	strategy	strategy	NOUN
ejpam-3478	57	21	is	be	AUX
ejpam-3478	57	22	formulated	formulate	VERB
ejpam-3478	57	23	as	as	SCONJ
ejpam-3478	57	24	follows	follow	VERB
ejpam-3478	57	25	;	;	PUNCT
ejpam-3478	57	26	maxe	maxe	NOUN
ejpam-3478	57	27	{	{	PUNCT
ejpam-3478	57	28	∫	∫	PROPN
ejpam-3478	57	29	t	t	PROPN
ejpam-3478	57	30	0	0	NUM
ejpam-3478	57	31	u	u	NOUN
ejpam-3478	58	1	[	[	X
ejpam-3478	58	2	w	w	X
ejpam-3478	58	3	(	(	PUNCT
ejpam-3478	58	4	t	t	PROPN
ejpam-3478	58	5	)	)	PUNCT
ejpam-3478	58	6	,	,	PUNCT
ejpam-3478	58	7	l	l	X
ejpam-3478	58	8	(	(	PUNCT
ejpam-3478	58	9	t	t	PROPN
ejpam-3478	58	10	)	)	PUNCT
ejpam-3478	58	11	]	]	PUNCT
ejpam-3478	59	1	dt+b	dt+b	PROPN
ejpam-3478	59	2	[	[	X
ejpam-3478	59	3	w	w	X
ejpam-3478	59	4	(	(	PUNCT
ejpam-3478	59	5	t	t	PROPN
ejpam-3478	59	6	)	)	PUNCT
ejpam-3478	59	7	,	,	PUNCT
ejpam-3478	59	8	l	l	X
ejpam-3478	59	9	(	(	PUNCT
ejpam-3478	59	10	t	t	PROPN
ejpam-3478	59	11	)	)	PUNCT
ejpam-3478	59	12	,	,	PUNCT
ejpam-3478	59	13	t	t	X
ejpam-3478	59	14	]	]	PUNCT
ejpam-3478	59	15	}	}	PUNCT
ejpam-3478	59	16	subject	subject	ADJ
ejpam-3478	59	17	to	to	ADP
ejpam-3478	59	18	the	the	DET
ejpam-3478	59	19	budget	budget	NOUN
ejpam-3478	59	20	equation	equation	NOUN
ejpam-3478	59	21	(	(	PUNCT
ejpam-3478	59	22	4	4	NUM
ejpam-3478	59	23	)	)	PUNCT
ejpam-3478	59	24	,	,	PUNCT
ejpam-3478	59	25	and	and	CCONJ
ejpam-3478	59	26	w	w	PROPN
ejpam-3478	59	27	(	(	PUNCT
ejpam-3478	59	28	t	t	PROPN
ejpam-3478	59	29	)	)	PUNCT
ejpam-3478	59	30	>	>	X
ejpam-3478	59	31	0;w	0;w	PUNCT
ejpam-3478	60	1	(	(	PUNCT
ejpam-3478	60	2	0	0	NUM
ejpam-3478	60	3	)	)	PUNCT
ejpam-3478	60	4	=	=	NOUN
ejpam-3478	60	5	w0	w0	PROPN
ejpam-3478	60	6	>	>	X
ejpam-3478	60	7	0	0	X
ejpam-3478	60	8	.	.	PUNCT
ejpam-3478	61	1	let	let	VERB
ejpam-3478	61	2	us	we	PRON
ejpam-3478	61	3	assume	assume	VERB
ejpam-3478	61	4	u	u	PROPN
ejpam-3478	61	5	(	(	PUNCT
ejpam-3478	61	6	w	w	PROPN
ejpam-3478	61	7	,	,	PUNCT
ejpam-3478	61	8	l	l	NOUN
ejpam-3478	61	9	)	)	PUNCT
ejpam-3478	61	10	to	to	PART
ejpam-3478	61	11	be	be	AUX
ejpam-3478	61	12	a	a	DET
ejpam-3478	61	13	strictly	strictly	ADV
ejpam-3478	61	14	concave	concave	VERB
ejpam-3478	61	15	utility	utility	NOUN
ejpam-3478	61	16	function	function	NOUN
ejpam-3478	61	17	and	and	CCONJ
ejpam-3478	62	1	b	b	X
ejpam-3478	62	2	[	[	X
ejpam-3478	62	3	w	w	X
ejpam-3478	62	4	(	(	PUNCT
ejpam-3478	62	5	t	t	PROPN
ejpam-3478	62	6	)	)	PUNCT
ejpam-3478	62	7	,	,	PUNCT
ejpam-3478	62	8	t	t	PROPN
ejpam-3478	62	9	]	]	PUNCT
ejpam-3478	62	10	is	be	AUX
ejpam-3478	62	11	a	a	DET
ejpam-3478	62	12	specified	specified	ADJ
ejpam-3478	62	13	bequest	bequ	ADJ
ejpam-3478	62	14	valuation	valuation	NOUN
ejpam-3478	62	15	function	function	NOUN
ejpam-3478	62	16	.	.	PUNCT
ejpam-3478	63	1	more	more	ADJ
ejpam-3478	63	2	details	detail	NOUN
ejpam-3478	63	3	on	on	ADP
ejpam-3478	63	4	the	the	DET
ejpam-3478	63	5	bequest	bequest	NOUN
ejpam-3478	63	6	valuation	valuation	NOUN
ejpam-3478	63	7	function	function	NOUN
ejpam-3478	63	8	can	can	AUX
ejpam-3478	63	9	be	be	AUX
ejpam-3478	63	10	found	find	VERB
ejpam-3478	63	11	in	in	ADP
ejpam-3478	63	12	merton	merton	NOUN
ejpam-3478	63	13	(	(	PUNCT
ejpam-3478	63	14	1969	1969	NUM
ejpam-3478	63	15	)	)	PUNCT
ejpam-3478	63	16	.	.	PUNCT
ejpam-3478	64	1	here	here	ADV
ejpam-3478	64	2	e	e	X
ejpam-3478	64	3	is	be	AUX
ejpam-3478	64	4	short	short	ADJ
ejpam-3478	64	5	for	for	ADP
ejpam-3478	64	6	e	e	X
ejpam-3478	64	7	(	(	PUNCT
ejpam-3478	64	8	0	0	NUM
ejpam-3478	64	9	)	)	PUNCT
ejpam-3478	64	10	,	,	PUNCT
ejpam-3478	64	11	the	the	DET
ejpam-3478	64	12	conditional	conditional	ADJ
ejpam-3478	64	13	expectation	expectation	NOUN
ejpam-3478	64	14	operator	operator	NOUN
ejpam-3478	64	15	given	give	VERB
ejpam-3478	64	16	w0	w0	PROPN
ejpam-3478	64	17	is	be	AUX
ejpam-3478	64	18	known	know	VERB
ejpam-3478	64	19	.	.	PUNCT
ejpam-3478	65	1	the	the	DET
ejpam-3478	65	2	differential	differential	ADJ
ejpam-3478	65	3	equations	equation	NOUN
ejpam-3478	65	4	governing	govern	VERB
ejpam-3478	65	5	the	the	DET
ejpam-3478	65	6	optimal	optimal	ADJ
ejpam-3478	65	7	solution	solution	NOUN
ejpam-3478	65	8	of	of	ADP
ejpam-3478	65	9	this	this	DET
ejpam-3478	65	10	stochastic	stochastic	ADJ
ejpam-3478	65	11	control	control	NOUN
ejpam-3478	65	12	problem	problem	NOUN
ejpam-3478	65	13	for	for	ADP
ejpam-3478	65	14	the	the	DET
ejpam-3478	65	15	portfolio	portfolio	NOUN
ejpam-3478	65	16	selection	selection	NOUN
ejpam-3478	65	17	(	(	PUNCT
ejpam-3478	65	18	w	w	NOUN
ejpam-3478	65	19	is	be	AUX
ejpam-3478	65	20	the	the	DET
ejpam-3478	65	21	weight	weight	NOUN
ejpam-3478	65	22	of	of	ADP
ejpam-3478	65	23	risky	risky	ADJ
ejpam-3478	65	24	investment	investment	NOUN
ejpam-3478	65	25	)	)	PUNCT
ejpam-3478	65	26	and	and	CCONJ
ejpam-3478	65	27	liability	liability	NOUN
ejpam-3478	65	28	mix	mix	NOUN
ejpam-3478	65	29	(	(	PUNCT
ejpam-3478	65	30	u	u	NOUN
ejpam-3478	65	31	is	be	AUX
ejpam-3478	65	32	the	the	DET
ejpam-3478	65	33	weight	weight	NOUN
ejpam-3478	65	34	of	of	ADP
ejpam-3478	65	35	the	the	DET
ejpam-3478	65	36	risky	risky	ADJ
ejpam-3478	65	37	insurance	insurance	NOUN
ejpam-3478	65	38	liability	liability	NOUN
ejpam-3478	65	39	)	)	PUNCT
ejpam-3478	65	40	can	can	AUX
ejpam-3478	65	41	be	be	AUX
ejpam-3478	65	42	derived	derive	VERB
ejpam-3478	65	43	by	by	ADP
ejpam-3478	65	44	the	the	DET
ejpam-3478	65	45	methods	method	NOUN
ejpam-3478	65	46	of	of	ADP
ejpam-3478	65	47	stochastic	stochastic	ADJ
ejpam-3478	65	48	dynamic	dynamic	ADJ
ejpam-3478	65	49	programming	programming	NOUN
ejpam-3478	65	50	see	see	VERB
ejpam-3478	65	51	e.g.	e.g.	ADV
ejpam-3478	65	52	merton	merton	X
ejpam-3478	65	53	(	(	PUNCT
ejpam-3478	65	54	1990	1990	NUM
ejpam-3478	65	55	)	)	PUNCT
ejpam-3478	65	56	.	.	PUNCT
ejpam-3478	66	1	define	define	VERB
ejpam-3478	66	2	the	the	DET
ejpam-3478	66	3	value	value	NOUN
ejpam-3478	66	4	function	function	NOUN
ejpam-3478	66	5	j	j	PROPN
ejpam-3478	66	6	(	(	PUNCT
ejpam-3478	66	7	w	w	PROPN
ejpam-3478	66	8	(	(	PUNCT
ejpam-3478	66	9	t	t	PROPN
ejpam-3478	66	10	)	)	PUNCT
ejpam-3478	66	11	,	,	PUNCT
ejpam-3478	66	12	l	l	X
ejpam-3478	66	13	(	(	PUNCT
ejpam-3478	66	14	t	t	PROPN
ejpam-3478	66	15	)	)	PUNCT
ejpam-3478	66	16	,	,	PUNCT
ejpam-3478	66	17	t	t	PROPN
ejpam-3478	66	18	)	)	PUNCT
ejpam-3478	66	19	by	by	ADP
ejpam-3478	66	20	j	j	PROPN
ejpam-3478	66	21	=	=	SYM
ejpam-3478	66	22	maxet	maxet	PROPN
ejpam-3478	66	23	{	{	PUNCT
ejpam-3478	66	24	∫	∫	PROPN
ejpam-3478	66	25	t	t	PROPN
ejpam-3478	66	26	t	t	PROPN
ejpam-3478	66	27	u	u	PROPN
ejpam-3478	66	28	(	(	PUNCT
ejpam-3478	66	29	w	w	PROPN
ejpam-3478	66	30	(	(	PUNCT
ejpam-3478	66	31	t	t	PROPN
ejpam-3478	66	32	)	)	PUNCT
ejpam-3478	66	33	,	,	PUNCT
ejpam-3478	66	34	l	l	X
ejpam-3478	66	35	(	(	PUNCT
ejpam-3478	66	36	t	t	PROPN
ejpam-3478	66	37	)	)	PUNCT
ejpam-3478	66	38	)	)	PUNCT
ejpam-3478	67	1	dt+b	dt+b	NOUN
ejpam-3478	67	2	(	(	PUNCT
ejpam-3478	67	3	w	w	PROPN
ejpam-3478	67	4	(	(	PUNCT
ejpam-3478	67	5	t	t	PROPN
ejpam-3478	67	6	)	)	PUNCT
ejpam-3478	67	7	,	,	PUNCT
ejpam-3478	67	8	l	l	X
ejpam-3478	67	9	(	(	PUNCT
ejpam-3478	67	10	t	t	PROPN
ejpam-3478	67	11	)	)	PUNCT
ejpam-3478	67	12	,	,	PUNCT
ejpam-3478	67	13	t	t	NOUN
ejpam-3478	67	14	)	)	PUNCT
ejpam-3478	67	15	}	}	PUNCT
ejpam-3478	67	16	=	=	SYM
ejpam-3478	67	17	maxet	maxet	X
ejpam-3478	67	18	{	{	PUNCT
ejpam-3478	67	19	∫	∫	PROPN
ejpam-3478	67	20	t+δt	t+δt	PROPN
ejpam-3478	67	21	t	t	PROPN
ejpam-3478	67	22	u	u	PROPN
ejpam-3478	67	23	(	(	PUNCT
ejpam-3478	67	24	w	w	PROPN
ejpam-3478	67	25	(	(	PUNCT
ejpam-3478	67	26	t	t	PROPN
ejpam-3478	67	27	)	)	PUNCT
ejpam-3478	67	28	,	,	PUNCT
ejpam-3478	67	29	l	l	X
ejpam-3478	67	30	(	(	PUNCT
ejpam-3478	67	31	t	t	PROPN
ejpam-3478	67	32	)	)	PUNCT
ejpam-3478	67	33	)	)	PUNCT
ejpam-3478	67	34	dt	dt	PUNCT
ejpam-3478	68	1	+	+	NOUN
ejpam-3478	68	2	j	j	PROPN
ejpam-3478	68	3	(	(	PUNCT
ejpam-3478	68	4	w	w	PROPN
ejpam-3478	68	5	(	(	PUNCT
ejpam-3478	68	6	t+	t+	NOUN
ejpam-3478	68	7	δt	δt	NOUN
ejpam-3478	68	8	)	)	PUNCT
ejpam-3478	68	9	,	,	PUNCT
ejpam-3478	68	10	l	l	NOUN
ejpam-3478	68	11	(	(	PUNCT
ejpam-3478	68	12	t+	t+	NOUN
ejpam-3478	68	13	δt	δt	NOUN
ejpam-3478	68	14	)	)	PUNCT
ejpam-3478	68	15	,	,	PUNCT
ejpam-3478	68	16	t+	t+	X
ejpam-3478	68	17	δt	δt	NOUN
ejpam-3478	68	18	)	)	PUNCT
ejpam-3478	68	19	}	}	PUNCT
ejpam-3478	68	20	(	(	PUNCT
ejpam-3478	68	21	8)	8)	NUM
ejpam-3478	68	22	where	where	SCONJ
ejpam-3478	68	23	et	et	PROPN
ejpam-3478	68	24	is	be	AUX
ejpam-3478	68	25	the	the	DET
ejpam-3478	68	26	conditional	conditional	ADJ
ejpam-3478	68	27	expectation	expectation	NOUN
ejpam-3478	68	28	operator	operator	NOUN
ejpam-3478	68	29	given	give	VERB
ejpam-3478	68	30	w	w	PROPN
ejpam-3478	68	31	(	(	PUNCT
ejpam-3478	68	32	t	t	PROPN
ejpam-3478	68	33	)	)	PUNCT
ejpam-3478	68	34	is	be	AUX
ejpam-3478	68	35	known	know	VERB
ejpam-3478	68	36	.	.	PUNCT
ejpam-3478	69	1	if	if	SCONJ
ejpam-3478	69	2	one	one	NUM
ejpam-3478	69	3	now	now	ADV
ejpam-3478	69	4	expands	expand	VERB
ejpam-3478	69	5	the	the	DET
ejpam-3478	69	6	term	term	NOUN
ejpam-3478	69	7	in	in	ADP
ejpam-3478	69	8	j	j	PROPN
ejpam-3478	69	9	on	on	ADP
ejpam-3478	69	10	the	the	DET
ejpam-3478	69	11	right	right	ADJ
ejpam-3478	69	12	hand	hand	NOUN
ejpam-3478	69	13	side	side	NOUN
ejpam-3478	69	14	of	of	ADP
ejpam-3478	69	15	(	(	PUNCT
ejpam-3478	69	16	8)	8)	NUM
ejpam-3478	69	17	by	by	ADP
ejpam-3478	69	18	taylor	taylor	PROPN
ejpam-3478	69	19	’s	’s	PART
ejpam-3478	69	20	series	series	NOUN
ejpam-3478	69	21	using	use	VERB
ejpam-3478	69	22	equations	equation	NOUN
ejpam-3478	69	23	(	(	PUNCT
ejpam-3478	69	24	1	1	NUM
ejpam-3478	69	25	)	)	PUNCT
ejpam-3478	69	26	and	and	CCONJ
ejpam-3478	69	27	(	(	PUNCT
ejpam-3478	69	28	4	4	NUM
ejpam-3478	69	29	)	)	PUNCT
ejpam-3478	69	30	,	,	PUNCT
ejpam-3478	69	31	apply	apply	VERB
ejpam-3478	69	32	ito	ito	PROPN
ejpam-3478	69	33	’s	’s	PART
ejpam-3478	69	34	lemma	lemma	PROPN
ejpam-3478	69	35	,	,	PUNCT
ejpam-3478	69	36	and	and	CCONJ
ejpam-3478	69	37	then	then	ADV
ejpam-3478	69	38	take	take	VERB
ejpam-3478	69	39	the	the	DET
ejpam-3478	69	40	limit	limit	NOUN
ejpam-3478	69	41	as	as	SCONJ
ejpam-3478	69	42	δt	δt	PRON
ejpam-3478	69	43	tends	tend	VERB
ejpam-3478	69	44	to	to	AUX
ejpam-3478	69	45	zero	zero	NUM
ejpam-3478	69	46	one	one	NUM
ejpam-3478	69	47	arrives	arrive	VERB
ejpam-3478	69	48	at	at	ADP
ejpam-3478	69	49	the	the	DET
ejpam-3478	69	50	hamiltonjacobi	hamiltonjacobi	ADJ
ejpam-3478	69	51	equation	equation	NOUN
ejpam-3478	69	52	for	for	ADP
ejpam-3478	69	53	the	the	DET
ejpam-3478	69	54	value	value	NOUN
ejpam-3478	69	55	function	function	NOUN
ejpam-3478	69	56	given	give	VERB
ejpam-3478	69	57	by	by	ADP
ejpam-3478	69	58	0	0	NUM
ejpam-3478	69	59	=	=	SYM
ejpam-3478	69	60	φ	φ	PROPN
ejpam-3478	70	1	[	[	X
ejpam-3478	70	2	w∗	w∗	NOUN
ejpam-3478	70	3	,	,	PUNCT
ejpam-3478	70	4	u∗;w	u∗;w	PROPN
ejpam-3478	70	5	,	,	PUNCT
ejpam-3478	70	6	l	l	PROPN
ejpam-3478	70	7	,	,	PUNCT
ejpam-3478	70	8	t	t	PROPN
ejpam-3478	70	9	]	]	X
ejpam-3478	70	10	≡	≡	PROPN
ejpam-3478	70	11	max	max	PROPN
ejpam-3478	70	12	{	{	PUNCT
ejpam-3478	70	13	u	u	PROPN
ejpam-3478	70	14	,	,	PUNCT
ejpam-3478	70	15	w	w	NOUN
ejpam-3478	70	16	}	}	PUNCT
ejpam-3478	70	17	{	{	PUNCT
ejpam-3478	70	18	u	u	NOUN
ejpam-3478	70	19	(	(	PUNCT
ejpam-3478	70	20	w	w	PROPN
ejpam-3478	70	21	,	,	PUNCT
ejpam-3478	70	22	l	l	NOUN
ejpam-3478	70	23	)	)	PUNCT
ejpam-3478	71	1	+	+	PUNCT
ejpam-3478	72	1	∂j	∂j	PROPN
ejpam-3478	72	2	∂t	∂t	NOUN
ejpam-3478	73	1	+	+	CCONJ
ejpam-3478	74	1	[	[	X
ejpam-3478	74	2	w	w	X
ejpam-3478	74	3	(	(	PUNCT
ejpam-3478	74	4	α−	α−	ADP
ejpam-3478	74	5	ra	ra	NOUN
ejpam-3478	74	6	)	)	PUNCT
ejpam-3478	75	1	+	+	CCONJ
ejpam-3478	75	2	ra]w	ra]w	NOUN
ejpam-3478	75	3	∂j	∂j	NOUN
ejpam-3478	76	1	∂w	∂w	NOUN
ejpam-3478	77	1	+	+	CCONJ
ejpam-3478	77	2	1	1	NUM
ejpam-3478	77	3	2	2	NUM
ejpam-3478	77	4	σ2w2w	σ2w2w	SYM
ejpam-3478	77	5	2	2	NUM
ejpam-3478	77	6	∂	∂	NUM
ejpam-3478	77	7	2j	2j	X
ejpam-3478	77	8	∂w	∂w	PROPN
ejpam-3478	77	9	2	2	NUM
ejpam-3478	77	10	+	+	CCONJ
ejpam-3478	77	11	{	{	PUNCT
ejpam-3478	77	12	cu−mu+	cu−mu+	X
ejpam-3478	77	13	(	(	PUNCT
ejpam-3478	77	14	1−	1−	NUM
ejpam-3478	77	15	u	u	NOUN
ejpam-3478	77	16	)	)	PUNCT
ejpam-3478	77	17	rl}l	rl}l	PROPN
ejpam-3478	78	1	∂j	∂j	PROPN
ejpam-3478	79	1	∂l	∂l	NOUN
ejpam-3478	80	1	+	+	ADV
ejpam-3478	80	2	qlwuwσρ	qlwuwσρ	ADJ
ejpam-3478	80	3	∂2j	∂2j	PROPN
ejpam-3478	80	4	∂l∂w	∂l∂w	NOUN
ejpam-3478	80	5	+	+	CCONJ
ejpam-3478	80	6	1	1	NUM
ejpam-3478	80	7	2	2	NUM
ejpam-3478	80	8	q2l2u2	q2l2u2	NOUN
ejpam-3478	80	9	∂2j	∂2j	NOUN
ejpam-3478	80	10	∂l2	∂l2	PROPN
ejpam-3478	80	11	}	}	PUNCT
ejpam-3478	80	12	(	(	PUNCT
ejpam-3478	80	13	9	9	X
ejpam-3478	80	14	)	)	PUNCT
ejpam-3478	80	15	the	the	DET
ejpam-3478	80	16	optimality	optimality	NOUN
ejpam-3478	80	17	condition	condition	NOUN
ejpam-3478	80	18	may	may	AUX
ejpam-3478	80	19	be	be	AUX
ejpam-3478	80	20	rewritten	rewrite	VERB
ejpam-3478	80	21	as	as	ADP
ejpam-3478	80	22	φ	φ	PROPN
ejpam-3478	80	23	[	[	X
ejpam-3478	80	24	w∗	w∗	PROPN
ejpam-3478	80	25	,	,	PUNCT
ejpam-3478	80	26	u∗;w	u∗;w	PROPN
ejpam-3478	80	27	,	,	PUNCT
ejpam-3478	80	28	l	l	PROPN
ejpam-3478	80	29	,	,	PUNCT
ejpam-3478	80	30	t	t	X
ejpam-3478	80	31	]	]	X
ejpam-3478	80	32	=	=	SYM
ejpam-3478	80	33	0	0	NUM
ejpam-3478	80	34	,	,	PUNCT
ejpam-3478	80	35	(	(	PUNCT
ejpam-3478	80	36	10	10	NUM
ejpam-3478	80	37	)	)	PUNCT
ejpam-3478	80	38	for	for	ADP
ejpam-3478	80	39	fixed	fix	VERB
ejpam-3478	80	40	w	w	PROPN
ejpam-3478	80	41	and	and	CCONJ
ejpam-3478	80	42	l	l	NOUN
ejpam-3478	80	43	at	at	ADP
ejpam-3478	80	44	anytime	anytime	ADV
ejpam-3478	80	45	t.	t.	X
ejpam-3478	80	46	the	the	DET
ejpam-3478	80	47	optimal	optimal	ADJ
ejpam-3478	80	48	strategy	strategy	NOUN
ejpam-3478	80	49	of	of	ADP
ejpam-3478	80	50	(	(	PUNCT
ejpam-3478	80	51	9	9	NUM
ejpam-3478	80	52	)	)	PUNCT
ejpam-3478	80	53	is	be	AUX
ejpam-3478	80	54	given	give	VERB
ejpam-3478	80	55	by	by	ADP
ejpam-3478	80	56	w∗and	w∗and	PROPN
ejpam-3478	80	57	u∗.	u∗.	PROPN
ejpam-3478	80	58	we	we	PRON
ejpam-3478	80	59	differentiate	differentiate	VERB
ejpam-3478	80	60	(	(	PUNCT
ejpam-3478	80	61	10	10	NUM
ejpam-3478	80	62	)	)	PUNCT
ejpam-3478	80	63	with	with	ADP
ejpam-3478	80	64	respect	respect	NOUN
ejpam-3478	80	65	to	to	ADP
ejpam-3478	80	66	w	w	NOUN
ejpam-3478	80	67	and	and	CCONJ
ejpam-3478	80	68	u	u	PRON
ejpam-3478	80	69	and	and	CCONJ
ejpam-3478	80	70	set	set	VERB
ejpam-3478	80	71	to	to	ADP
ejpam-3478	80	72	zero	zero	NUM
ejpam-3478	80	73	to	to	PART
ejpam-3478	80	74	find	find	VERB
ejpam-3478	80	75	the	the	DET
ejpam-3478	80	76	interior	interior	ADJ
ejpam-3478	80	77	maximum	maximum	NOUN
ejpam-3478	80	78	.	.	PUNCT
ejpam-3478	81	1	c.	c.	PROPN
ejpam-3478	81	2	atkinson	atkinson	PROPN
ejpam-3478	81	3	,	,	PUNCT
ejpam-3478	81	4	s.	s.	PROPN
ejpam-3478	81	5	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	81	6	,	,	PUNCT
ejpam-3478	81	7	p.	p.	PROPN
ejpam-3478	81	8	ingpochai	ingpochai	PROPN
ejpam-3478	81	9	/	/	SYM
ejpam-3478	81	10	eur	eur	PROPN
ejpam-3478	81	11	.	.	PUNCT
ejpam-3478	82	1	j.	j.	PROPN
ejpam-3478	82	2	pure	pure	PROPN
ejpam-3478	82	3	appl	appl	PROPN
ejpam-3478	82	4	.	.	PROPN
ejpam-3478	82	5	math	math	PROPN
ejpam-3478	82	6	,	,	PUNCT
ejpam-3478	82	7	12	12	NUM
ejpam-3478	82	8	(	(	PUNCT
ejpam-3478	82	9	3	3	NUM
ejpam-3478	82	10	)	)	PUNCT
ejpam-3478	82	11	(	(	PUNCT
ejpam-3478	82	12	2019	2019	NUM
ejpam-3478	82	13	)	)	PUNCT
ejpam-3478	82	14	,	,	PUNCT
ejpam-3478	82	15	1315	1315	NUM
ejpam-3478	82	16	-	-	SYM
ejpam-3478	82	17	1336	1336	NUM
ejpam-3478	82	18	1319	1319	NUM
ejpam-3478	82	19	this	this	PRON
ejpam-3478	82	20	gives	give	VERB
ejpam-3478	82	21	(	(	PUNCT
ejpam-3478	82	22	α−	α−	ADP
ejpam-3478	82	23	ra)w	ra)w	NOUN
ejpam-3478	82	24	∂j	∂j	NOUN
ejpam-3478	83	1	∂w	∂w	NOUN
ejpam-3478	84	1	+	+	CCONJ
ejpam-3478	84	2	σ2ww	σ2ww	PROPN
ejpam-3478	84	3	2	2	NUM
ejpam-3478	84	4	∂	∂	NUM
ejpam-3478	84	5	2j	2j	X
ejpam-3478	84	6	∂w	∂w	PROPN
ejpam-3478	84	7	2	2	NUM
ejpam-3478	84	8	+	+	NUM
ejpam-3478	84	9	qlwuσρ	qlwuσρ	PROPN
ejpam-3478	84	10	∂2j	∂2j	PROPN
ejpam-3478	84	11	∂l∂w	∂l∂w	NOUN
ejpam-3478	84	12	=	=	SYM
ejpam-3478	84	13	0	0	NUM
ejpam-3478	84	14	(	(	PUNCT
ejpam-3478	84	15	11	11	NUM
ejpam-3478	84	16	)	)	PUNCT
ejpam-3478	84	17	and	and	CCONJ
ejpam-3478	84	18	{	{	PUNCT
ejpam-3478	84	19	c−m−	c−m−	PROPN
ejpam-3478	84	20	rl}l	rl}l	PROPN
ejpam-3478	85	1	∂j	∂j	PROPN
ejpam-3478	86	1	∂l	∂l	NOUN
ejpam-3478	86	2	+	+	CCONJ
ejpam-3478	86	3	qlwwσρ	qlwwσρ	ADJ
ejpam-3478	86	4	∂2j	∂2j	PROPN
ejpam-3478	86	5	∂l∂w	∂l∂w	NOUN
ejpam-3478	86	6	+	+	CCONJ
ejpam-3478	86	7	uq2l2	uq2l2	PROPN
ejpam-3478	86	8	∂	∂	NOUN
ejpam-3478	86	9	2j	2j	X
ejpam-3478	86	10	∂l2	∂l2	X
ejpam-3478	86	11	=	=	SYM
ejpam-3478	86	12	0	0	NUM
ejpam-3478	87	1	(	(	PUNCT
ejpam-3478	87	2	12	12	NUM
ejpam-3478	87	3	)	)	PUNCT
ejpam-3478	87	4	note	note	NOUN
ejpam-3478	87	5	that	that	SCONJ
ejpam-3478	87	6	w	w	PROPN
ejpam-3478	87	7	∂φ	∂φ	PROPN
ejpam-3478	88	1	∂w	∂w	PROPN
ejpam-3478	89	1	+	+	NUM
ejpam-3478	89	2	u∂φ∂u	u∂φ∂u	PROPN
ejpam-3478	89	3	gives	give	VERB
ejpam-3478	89	4	1	1	NUM
ejpam-3478	89	5	2	2	NUM
ejpam-3478	89	6	σ2w2w	σ2w2w	SYM
ejpam-3478	89	7	2	2	NUM
ejpam-3478	89	8	∂	∂	NUM
ejpam-3478	89	9	2j	2j	X
ejpam-3478	90	1	∂w	∂w	PROPN
ejpam-3478	90	2	2	2	NUM
ejpam-3478	90	3	+	+	CCONJ
ejpam-3478	90	4	1	1	NUM
ejpam-3478	90	5	2	2	NUM
ejpam-3478	90	6	u2q2l2	u2q2l2	PROPN
ejpam-3478	90	7	∂	∂	NUM
ejpam-3478	90	8	2j	2j	X
ejpam-3478	90	9	∂l2	∂l2	PROPN
ejpam-3478	90	10	+	+	CCONJ
ejpam-3478	90	11	qlwwuσρ	qlwwuσρ	NOUN
ejpam-3478	90	12	∂2j	∂2j	PROPN
ejpam-3478	90	13	∂l∂w	∂l∂w	NOUN
ejpam-3478	90	14	=	=	SYM
ejpam-3478	90	15	1	1	NUM
ejpam-3478	90	16	2	2	NUM
ejpam-3478	90	17	{	{	PUNCT
ejpam-3478	90	18	−{c−m−	−{c−m−	NOUN
ejpam-3478	90	19	rl}ul	rl}ul	PROPN
ejpam-3478	90	20	∂j	∂j	PROPN
ejpam-3478	91	1	∂l	∂l	NOUN
ejpam-3478	92	1	−	−	PROPN
ejpam-3478	92	2	(	(	PUNCT
ejpam-3478	92	3	α−	α−	ADP
ejpam-3478	92	4	ra)ww	ra)ww	PROPN
ejpam-3478	92	5	∂j	∂j	NOUN
ejpam-3478	92	6	∂w	∂w	PROPN
ejpam-3478	92	7	}	}	PUNCT
ejpam-3478	92	8	(	(	PUNCT
ejpam-3478	92	9	13	13	NUM
ejpam-3478	92	10	)	)	PUNCT
ejpam-3478	92	11	substituting	substitute	VERB
ejpam-3478	92	12	this	this	PRON
ejpam-3478	92	13	into	into	ADP
ejpam-3478	92	14	φ	φ	PROPN
ejpam-3478	92	15	=	=	SYM
ejpam-3478	92	16	0	0	NUM
ejpam-3478	92	17	gives	give	VERB
ejpam-3478	92	18	0	0	NUM
ejpam-3478	93	1	=	=	SYM
ejpam-3478	93	2	max	max	PROPN
ejpam-3478	93	3	{	{	PUNCT
ejpam-3478	93	4	u	u	NOUN
ejpam-3478	93	5	,	,	PUNCT
ejpam-3478	93	6	w	w	NOUN
ejpam-3478	93	7	}	}	PUNCT
ejpam-3478	93	8	{	{	PUNCT
ejpam-3478	93	9	u	u	NOUN
ejpam-3478	93	10	(	(	PUNCT
ejpam-3478	93	11	w	w	PROPN
ejpam-3478	93	12	,	,	PUNCT
ejpam-3478	93	13	l	l	NOUN
ejpam-3478	93	14	)	)	PUNCT
ejpam-3478	94	1	+	+	PUNCT
ejpam-3478	95	1	∂j	∂j	PROPN
ejpam-3478	95	2	∂t	∂t	NOUN
ejpam-3478	96	1	+	+	CCONJ
ejpam-3478	96	2	[	[	PUNCT
ejpam-3478	96	3	1	1	NUM
ejpam-3478	96	4	2	2	NUM
ejpam-3478	96	5	w	w	NOUN
ejpam-3478	96	6	(	(	PUNCT
ejpam-3478	96	7	α−	α−	ADP
ejpam-3478	96	8	ra	ra	NOUN
ejpam-3478	96	9	)	)	PUNCT
ejpam-3478	97	1	+	+	CCONJ
ejpam-3478	97	2	ra	ra	X
ejpam-3478	97	3	]	]	PUNCT
ejpam-3478	98	1	w	w	PROPN
ejpam-3478	98	2	∂j	∂j	PROPN
ejpam-3478	98	3	∂w	∂w	PROPN
ejpam-3478	98	4	+	+	CCONJ
ejpam-3478	98	5	{	{	PUNCT
ejpam-3478	98	6	1	1	NUM
ejpam-3478	98	7	2	2	NUM
ejpam-3478	98	8	cu−	cu−	NUM
ejpam-3478	98	9	1	1	NUM
ejpam-3478	98	10	2	2	NUM
ejpam-3478	98	11	mu+	mu+	NOUN
ejpam-3478	98	12	(	(	PUNCT
ejpam-3478	98	13	1−	1−	NUM
ejpam-3478	98	14	1	1	NUM
ejpam-3478	98	15	2	2	NUM
ejpam-3478	98	16	u	u	NOUN
ejpam-3478	98	17	)	)	PUNCT
ejpam-3478	98	18	rl	rl	ADP
ejpam-3478	98	19	}	}	PUNCT
ejpam-3478	98	20	l	l	NOUN
ejpam-3478	98	21	∂j	∂j	NOUN
ejpam-3478	99	1	∂l	∂l	NOUN
ejpam-3478	99	2	}	}	PUNCT
ejpam-3478	99	3	(	(	PUNCT
ejpam-3478	99	4	14	14	NUM
ejpam-3478	99	5	)	)	PUNCT
ejpam-3478	99	6	subject	subject	NOUN
ejpam-3478	99	7	to	to	ADP
ejpam-3478	99	8	the	the	DET
ejpam-3478	99	9	terminal	terminal	ADJ
ejpam-3478	99	10	condition	condition	NOUN
ejpam-3478	99	11	j	j	PROPN
ejpam-3478	100	1	[	[	X
ejpam-3478	100	2	w	w	X
ejpam-3478	100	3	(	(	PUNCT
ejpam-3478	100	4	t	t	PROPN
ejpam-3478	100	5	)	)	PUNCT
ejpam-3478	100	6	,	,	PUNCT
ejpam-3478	100	7	l	l	X
ejpam-3478	100	8	(	(	PUNCT
ejpam-3478	100	9	t	t	PROPN
ejpam-3478	100	10	)	)	PUNCT
ejpam-3478	100	11	,	,	PUNCT
ejpam-3478	100	12	t	t	X
ejpam-3478	100	13	]	]	PUNCT
ejpam-3478	101	1	=	=	PUNCT
ejpam-3478	101	2	b	b	X
ejpam-3478	102	1	[	[	X
ejpam-3478	102	2	w	w	X
ejpam-3478	102	3	(	(	PUNCT
ejpam-3478	102	4	t	t	PROPN
ejpam-3478	102	5	)	)	PUNCT
ejpam-3478	102	6	,	,	PUNCT
ejpam-3478	102	7	l	l	X
ejpam-3478	102	8	(	(	PUNCT
ejpam-3478	102	9	t	t	PROPN
ejpam-3478	102	10	)	)	PUNCT
ejpam-3478	102	11	,	,	PUNCT
ejpam-3478	102	12	t	t	X
ejpam-3478	102	13	]	]	PUNCT
ejpam-3478	102	14	and	and	CCONJ
ejpam-3478	102	15	the	the	DET
ejpam-3478	102	16	solution	solution	NOUN
ejpam-3478	102	17	being	be	AUX
ejpam-3478	102	18	feasible	feasible	ADJ
ejpam-3478	102	19	.	.	PUNCT
ejpam-3478	103	1	3	3	X
ejpam-3478	103	2	.	.	X
ejpam-3478	103	3	utility	utility	NOUN
ejpam-3478	103	4	u	u	NOUN
ejpam-3478	103	5	(	(	PUNCT
ejpam-3478	103	6	w	w	PROPN
ejpam-3478	103	7	)	)	PUNCT
ejpam-3478	103	8	=	=	PUNCT
ejpam-3478	103	9	w	w	PROPN
ejpam-3478	103	10	γ	γ	X
ejpam-3478	103	11	γ	γ	X
ejpam-3478	103	12	for	for	ADP
ejpam-3478	103	13	this	this	DET
ejpam-3478	103	14	particular	particular	ADJ
ejpam-3478	103	15	case	case	NOUN
ejpam-3478	103	16	,	,	PUNCT
ejpam-3478	103	17	the	the	DET
ejpam-3478	103	18	utility	utility	NOUN
ejpam-3478	103	19	function	function	NOUN
ejpam-3478	103	20	is	be	AUX
ejpam-3478	103	21	a	a	DET
ejpam-3478	103	22	function	function	NOUN
ejpam-3478	103	23	of	of	ADP
ejpam-3478	103	24	w	w	NOUN
ejpam-3478	103	25	only	only	ADV
ejpam-3478	103	26	.	.	PUNCT
ejpam-3478	104	1	this	this	PRON
ejpam-3478	104	2	suggests	suggest	VERB
ejpam-3478	104	3	that	that	SCONJ
ejpam-3478	104	4	the	the	DET
ejpam-3478	104	5	management	management	NOUN
ejpam-3478	104	6	is	be	AUX
ejpam-3478	104	7	most	most	ADV
ejpam-3478	104	8	interested	interested	ADJ
ejpam-3478	104	9	in	in	ADP
ejpam-3478	104	10	maximising	maximise	VERB
ejpam-3478	104	11	the	the	DET
ejpam-3478	104	12	firm	firm	NOUN
ejpam-3478	104	13	’s	’s	PART
ejpam-3478	104	14	total	total	ADJ
ejpam-3478	104	15	asset	asset	NOUN
ejpam-3478	104	16	.	.	PUNCT
ejpam-3478	105	1	this	this	PRON
ejpam-3478	105	2	is	be	AUX
ejpam-3478	105	3	not	not	PART
ejpam-3478	105	4	as	as	ADV
ejpam-3478	105	5	nonsensical	nonsensical	ADJ
ejpam-3478	105	6	as	as	SCONJ
ejpam-3478	105	7	it	it	PRON
ejpam-3478	105	8	may	may	AUX
ejpam-3478	105	9	first	first	ADV
ejpam-3478	105	10	seem	seem	VERB
ejpam-3478	105	11	as	as	SCONJ
ejpam-3478	105	12	financial	financial	ADJ
ejpam-3478	105	13	institutions	institution	NOUN
ejpam-3478	105	14	are	be	AUX
ejpam-3478	105	15	constantly	constantly	ADV
ejpam-3478	105	16	seeking	seek	VERB
ejpam-3478	105	17	to	to	PART
ejpam-3478	105	18	reduce	reduce	VERB
ejpam-3478	105	19	their	their	PRON
ejpam-3478	105	20	expense	expense	NOUN
ejpam-3478	105	21	ratio	ratio	NOUN
ejpam-3478	105	22	;	;	PUNCT
ejpam-3478	105	23	increasing	increase	VERB
ejpam-3478	105	24	the	the	DET
ejpam-3478	105	25	size	size	NOUN
ejpam-3478	105	26	of	of	ADP
ejpam-3478	105	27	the	the	DET
ejpam-3478	105	28	asset	asset	NOUN
ejpam-3478	105	29	under	under	ADP
ejpam-3478	105	30	management	management	NOUN
ejpam-3478	105	31	is	be	AUX
ejpam-3478	105	32	one	one	NUM
ejpam-3478	105	33	way	way	NOUN
ejpam-3478	105	34	of	of	ADP
ejpam-3478	105	35	achieving	achieve	VERB
ejpam-3478	105	36	this	this	PRON
ejpam-3478	105	37	.	.	PUNCT
ejpam-3478	106	1	suppose	suppose	VERB
ejpam-3478	106	2	that	that	SCONJ
ejpam-3478	106	3	u	u	PROPN
ejpam-3478	106	4	(	(	PUNCT
ejpam-3478	106	5	w	w	PROPN
ejpam-3478	106	6	)	)	PUNCT
ejpam-3478	106	7	=	=	PUNCT
ejpam-3478	106	8	w	w	PROPN
ejpam-3478	106	9	γ	γ	X
ejpam-3478	106	10	γ	γ	X
ejpam-3478	106	11	and	and	CCONJ
ejpam-3478	106	12	assume	assume	VERB
ejpam-3478	106	13	that	that	SCONJ
ejpam-3478	106	14	the	the	DET
ejpam-3478	106	15	value	value	NOUN
ejpam-3478	106	16	function	function	NOUN
ejpam-3478	106	17	has	have	VERB
ejpam-3478	106	18	the	the	DET
ejpam-3478	106	19	form	form	NOUN
ejpam-3478	106	20	j	j	NOUN
ejpam-3478	107	1	=	=	PUNCT
ejpam-3478	107	2	w	w	PROPN
ejpam-3478	107	3	γf	γf	PROPN
ejpam-3478	107	4	(	(	PUNCT
ejpam-3478	107	5	l	l	NOUN
ejpam-3478	107	6	,	,	PUNCT
ejpam-3478	107	7	t	t	PROPN
ejpam-3478	107	8	)	)	PUNCT
ejpam-3478	107	9	,	,	PUNCT
ejpam-3478	107	10	where	where	SCONJ
ejpam-3478	107	11	f	f	PROPN
ejpam-3478	107	12	(	(	PUNCT
ejpam-3478	107	13	l	l	PROPN
ejpam-3478	107	14	,	,	PUNCT
ejpam-3478	107	15	t	t	PROPN
ejpam-3478	107	16	)	)	PUNCT
ejpam-3478	107	17	is	be	AUX
ejpam-3478	107	18	an	an	DET
ejpam-3478	107	19	arbitrary	arbitrary	ADJ
ejpam-3478	107	20	function	function	NOUN
ejpam-3478	107	21	independent	independent	ADJ
ejpam-3478	107	22	of	of	ADP
ejpam-3478	107	23	w	w	PROPN
ejpam-3478	107	24	,	,	PUNCT
ejpam-3478	107	25	then	then	ADV
ejpam-3478	107	26	the	the	DET
ejpam-3478	107	27	optimality	optimality	NOUN
ejpam-3478	107	28	conditions	condition	NOUN
ejpam-3478	107	29	for	for	ADP
ejpam-3478	107	30	w	w	NOUN
ejpam-3478	107	31	and	and	CCONJ
ejpam-3478	107	32	u	u	NOUN
ejpam-3478	107	33	in	in	ADP
ejpam-3478	107	34	equations	equation	NOUN
ejpam-3478	107	35	(	(	PUNCT
ejpam-3478	107	36	11	11	NUM
ejpam-3478	107	37	)	)	PUNCT
ejpam-3478	107	38	and	and	CCONJ
ejpam-3478	107	39	(	(	PUNCT
ejpam-3478	107	40	12	12	NUM
ejpam-3478	107	41	)	)	PUNCT
ejpam-3478	107	42	become	become	VERB
ejpam-3478	107	43	(	(	PUNCT
ejpam-3478	107	44	α−	α−	ADP
ejpam-3478	107	45	ra)f	ra)f	PROPN
ejpam-3478	107	46	+	+	PROPN
ejpam-3478	108	1	σ2w(γ	σ2w(γ	PROPN
ejpam-3478	108	2	−	−	PROPN
ejpam-3478	108	3	1)f	1)f	NUM
ejpam-3478	109	1	+	+	NUM
ejpam-3478	109	2	qluσρ	qluσρ	NOUN
ejpam-3478	109	3	∂f	∂f	PROPN
ejpam-3478	109	4	∂l	∂l	NOUN
ejpam-3478	109	5	=	=	SYM
ejpam-3478	109	6	0	0	NUM
ejpam-3478	109	7	(	(	PUNCT
ejpam-3478	109	8	15	15	NUM
ejpam-3478	109	9	)	)	PUNCT
ejpam-3478	109	10	and	and	CCONJ
ejpam-3478	109	11	(	(	PUNCT
ejpam-3478	109	12	c−m−	c−m−	PROPN
ejpam-3478	109	13	rl	rl	VERB
ejpam-3478	109	14	+	+	PUNCT
ejpam-3478	109	15	qwσργ	qwσργ	ADJ
ejpam-3478	109	16	)	)	PUNCT
ejpam-3478	109	17	∂f	∂f	PROPN
ejpam-3478	109	18	∂l	∂l	NOUN
ejpam-3478	110	1	+	+	CCONJ
ejpam-3478	110	2	uq2l	uq2l	PROPN
ejpam-3478	110	3	∂2f	∂2f	VERB
ejpam-3478	110	4	∂l2	∂l2	NOUN
ejpam-3478	110	5	=	=	NOUN
ejpam-3478	110	6	0	0	NUM
ejpam-3478	110	7	.	.	PUNCT
ejpam-3478	111	1	(	(	PUNCT
ejpam-3478	111	2	16	16	NUM
ejpam-3478	111	3	)	)	PUNCT
ejpam-3478	111	4	the	the	DET
ejpam-3478	111	5	value	value	NOUN
ejpam-3478	111	6	function	function	NOUN
ejpam-3478	111	7	as	as	SCONJ
ejpam-3478	111	8	given	give	VERB
ejpam-3478	111	9	in	in	ADP
ejpam-3478	111	10	(	(	PUNCT
ejpam-3478	111	11	9	9	NUM
ejpam-3478	111	12	)	)	PUNCT
ejpam-3478	111	13	becomes	become	VERB
ejpam-3478	111	14	0	0	NUM
ejpam-3478	111	15	=	=	SYM
ejpam-3478	111	16	φ	φ	PROPN
ejpam-3478	112	1	[	[	X
ejpam-3478	112	2	w∗	w∗	NOUN
ejpam-3478	112	3	,	,	PUNCT
ejpam-3478	112	4	u∗;w	u∗;w	PROPN
ejpam-3478	112	5	,	,	PUNCT
ejpam-3478	112	6	l	l	PROPN
ejpam-3478	112	7	,	,	PUNCT
ejpam-3478	112	8	t	t	PROPN
ejpam-3478	112	9	]	]	X
ejpam-3478	112	10	≡	≡	PROPN
ejpam-3478	112	11	max	max	PROPN
ejpam-3478	112	12	{	{	PUNCT
ejpam-3478	112	13	u(s),w(s	u(s),w(s	PROPN
ejpam-3478	112	14	)	)	PUNCT
ejpam-3478	112	15	}	}	PUNCT
ejpam-3478	112	16	{	{	PUNCT
ejpam-3478	112	17	1	1	NUM
ejpam-3478	112	18	γ	γ	X
ejpam-3478	112	19	+	+	CCONJ
ejpam-3478	112	20	∂f	∂f	PROPN
ejpam-3478	112	21	∂t	∂t	PROPN
ejpam-3478	112	22	c.	c.	PROPN
ejpam-3478	112	23	atkinson	atkinson	PROPN
ejpam-3478	112	24	,	,	PUNCT
ejpam-3478	112	25	s.	s.	PROPN
ejpam-3478	112	26	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	112	27	,	,	PUNCT
ejpam-3478	112	28	p.	p.	PROPN
ejpam-3478	112	29	ingpochai	ingpochai	PROPN
ejpam-3478	112	30	/	/	SYM
ejpam-3478	112	31	eur	eur	PROPN
ejpam-3478	112	32	.	.	PUNCT
ejpam-3478	113	1	j.	j.	PROPN
ejpam-3478	113	2	pure	pure	PROPN
ejpam-3478	113	3	appl	appl	PROPN
ejpam-3478	113	4	.	.	PROPN
ejpam-3478	113	5	math	math	PROPN
ejpam-3478	113	6	,	,	PUNCT
ejpam-3478	113	7	12	12	NUM
ejpam-3478	113	8	(	(	PUNCT
ejpam-3478	113	9	3	3	NUM
ejpam-3478	113	10	)	)	PUNCT
ejpam-3478	113	11	(	(	PUNCT
ejpam-3478	113	12	2019	2019	NUM
ejpam-3478	113	13	)	)	PUNCT
ejpam-3478	113	14	,	,	PUNCT
ejpam-3478	113	15	1315	1315	NUM
ejpam-3478	113	16	-	-	SYM
ejpam-3478	113	17	1336	1336	NUM
ejpam-3478	113	18	1320	1320	NUM
ejpam-3478	113	19	+	+	CCONJ
ejpam-3478	113	20	(	(	PUNCT
ejpam-3478	113	21	w	w	X
ejpam-3478	113	22	(	(	PUNCT
ejpam-3478	113	23	α−	α−	ADP
ejpam-3478	113	24	ra	ra	NOUN
ejpam-3478	113	25	)	)	PUNCT
ejpam-3478	114	1	+	+	CCONJ
ejpam-3478	114	2	ra	ra	PROPN
ejpam-3478	115	1	+	+	NOUN
ejpam-3478	115	2	1	1	NUM
ejpam-3478	115	3	2	2	NUM
ejpam-3478	115	4	σ2w2(γ	σ2w2(γ	PROPN
ejpam-3478	115	5	−	−	PROPN
ejpam-3478	115	6	1	1	NUM
ejpam-3478	115	7	)	)	PUNCT
ejpam-3478	115	8	)	)	PUNCT
ejpam-3478	116	1	γf	γf	PROPN
ejpam-3478	117	1	+	+	CCONJ
ejpam-3478	117	2	(	(	PUNCT
ejpam-3478	117	3	cu−mu+	cu−mu+	X
ejpam-3478	117	4	(	(	PUNCT
ejpam-3478	117	5	1−	1−	NUM
ejpam-3478	117	6	u	u	NOUN
ejpam-3478	117	7	)	)	PUNCT
ejpam-3478	117	8	rl	rl	VERB
ejpam-3478	117	9	+	+	ADJ
ejpam-3478	117	10	quwσργ)l	quwσργ)l	PROPN
ejpam-3478	118	1	∂f	∂f	PROPN
ejpam-3478	118	2	∂l	∂l	PROPN
ejpam-3478	119	1	+	+	CCONJ
ejpam-3478	119	2	1	1	NUM
ejpam-3478	119	3	2	2	NUM
ejpam-3478	119	4	q2u2l2∂	q2u2l2∂	NOUN
ejpam-3478	119	5	2f	2f	NUM
ejpam-3478	119	6	∂l2	∂l2	PROPN
ejpam-3478	119	7	}	}	PUNCT
ejpam-3478	119	8	.	.	PUNCT
ejpam-3478	120	1	(	(	PUNCT
ejpam-3478	120	2	17	17	NUM
ejpam-3478	120	3	)	)	PUNCT
ejpam-3478	120	4	3.1	3.1	NUM
ejpam-3478	120	5	.	.	NOUN
ejpam-3478	120	6	zero	zero	NUM
ejpam-3478	120	7	correlation	correlation	NOUN
ejpam-3478	120	8	case	case	NOUN
ejpam-3478	120	9	in	in	ADP
ejpam-3478	120	10	this	this	DET
ejpam-3478	120	11	particular	particular	ADJ
ejpam-3478	120	12	scenario	scenario	NOUN
ejpam-3478	120	13	,	,	PUNCT
ejpam-3478	120	14	we	we	PRON
ejpam-3478	120	15	assume	assume	VERB
ejpam-3478	120	16	that	that	SCONJ
ejpam-3478	120	17	the	the	DET
ejpam-3478	120	18	correlation	correlation	NOUN
ejpam-3478	120	19	between	between	ADP
ejpam-3478	120	20	the	the	DET
ejpam-3478	120	21	risky	risky	ADJ
ejpam-3478	120	22	asset	asset	NOUN
ejpam-3478	120	23	and	and	CCONJ
ejpam-3478	120	24	the	the	DET
ejpam-3478	120	25	risky	risky	ADJ
ejpam-3478	120	26	liability	liability	NOUN
ejpam-3478	120	27	is	be	AUX
ejpam-3478	120	28	zero	zero	NUM
ejpam-3478	120	29	.	.	PUNCT
ejpam-3478	121	1	note	note	VERB
ejpam-3478	121	2	that	that	SCONJ
ejpam-3478	121	3	if	if	SCONJ
ejpam-3478	121	4	ρ	ρ	PROPN
ejpam-3478	121	5	=	=	SYM
ejpam-3478	121	6	0	0	PUNCT
ejpam-3478	121	7	then	then	ADV
ejpam-3478	121	8	from	from	ADP
ejpam-3478	121	9	(	(	PUNCT
ejpam-3478	121	10	15	15	NUM
ejpam-3478	121	11	)	)	PUNCT
ejpam-3478	121	12	and	and	CCONJ
ejpam-3478	121	13	(	(	PUNCT
ejpam-3478	121	14	16	16	NUM
ejpam-3478	121	15	)	)	PUNCT
ejpam-3478	121	16	we	we	PRON
ejpam-3478	121	17	obtain	obtain	VERB
ejpam-3478	121	18	w∗	w∗	NOUN
ejpam-3478	121	19	=	=	SYM
ejpam-3478	121	20	(	(	PUNCT
ejpam-3478	121	21	α−	α−	ADP
ejpam-3478	121	22	ra	ra	NOUN
ejpam-3478	121	23	)	)	PUNCT
ejpam-3478	121	24	σ2(1−	σ2(1−	PROPN
ejpam-3478	121	25	γ	γ	PROPN
ejpam-3478	121	26	)	)	PUNCT
ejpam-3478	121	27	(	(	PUNCT
ejpam-3478	121	28	18	18	NUM
ejpam-3478	121	29	)	)	PUNCT
ejpam-3478	121	30	and	and	CCONJ
ejpam-3478	121	31	u∗	u∗	NOUN
ejpam-3478	121	32	=	=	PUNCT
ejpam-3478	121	33	(	(	PUNCT
ejpam-3478	121	34	−	−	X
ejpam-3478	121	35	(	(	PUNCT
ejpam-3478	121	36	c−m−	c−m−	PROPN
ejpam-3478	121	37	rl	rl	PROPN
ejpam-3478	121	38	)	)	PUNCT
ejpam-3478	121	39	∂f∂l	∂f∂l	VERB
ejpam-3478	121	40	q2l∂	q2l∂	ADP
ejpam-3478	121	41	2f	2f	NUM
ejpam-3478	121	42	∂l2	∂l2	PROPN
ejpam-3478	121	43	)	)	PUNCT
ejpam-3478	121	44	(	(	PUNCT
ejpam-3478	121	45	19	19	NUM
ejpam-3478	121	46	)	)	PUNCT
ejpam-3478	121	47	then	then	ADV
ejpam-3478	121	48	from	from	ADP
ejpam-3478	121	49	(	(	PUNCT
ejpam-3478	121	50	17	17	NUM
ejpam-3478	121	51	)	)	PUNCT
ejpam-3478	121	52	0	0	NUM
ejpam-3478	122	1	=	=	SYM
ejpam-3478	122	2	1	1	NUM
ejpam-3478	122	3	γ	γ	X
ejpam-3478	122	4	+	+	X
ejpam-3478	122	5	∂f	∂f	PROPN
ejpam-3478	122	6	∂t	∂t	PROPN
ejpam-3478	123	1	+	+	CCONJ
ejpam-3478	123	2	(	(	PUNCT
ejpam-3478	123	3	ra	ra	PROPN
ejpam-3478	123	4	+	+	NOUN
ejpam-3478	123	5	1	1	NUM
ejpam-3478	123	6	(	(	PUNCT
ejpam-3478	123	7	α−	α−	ADP
ejpam-3478	123	8	ra)2	ra)2	NOUN
ejpam-3478	123	9	2σ2	2σ2	NUM
ejpam-3478	123	10	(	(	PUNCT
ejpam-3478	123	11	1−	1−	NUM
ejpam-3478	123	12	γ	γ	NOUN
ejpam-3478	123	13	)	)	PUNCT
ejpam-3478	123	14	)	)	PUNCT
ejpam-3478	124	1	γf	γf	INTJ
ejpam-3478	125	1	+	+	CCONJ
ejpam-3478	125	2	(	(	PUNCT
ejpam-3478	125	3	rl	rl	INTJ
ejpam-3478	125	4	−	−	PROPN
ejpam-3478	125	5	(	(	PUNCT
ejpam-3478	125	6	c−m−	c−m−	PROPN
ejpam-3478	125	7	rl)2	rl)2	PROPN
ejpam-3478	125	8	∂f∂l	∂f∂l	VERB
ejpam-3478	125	9	2q2l∂	2q2l∂	NUM
ejpam-3478	125	10	2f	2f	NUM
ejpam-3478	125	11	∂l2	∂l2	NUM
ejpam-3478	125	12	)	)	PUNCT
ejpam-3478	126	1	l	l	NOUN
ejpam-3478	126	2	∂f	∂f	PROPN
ejpam-3478	126	3	∂l	∂l	NOUN
ejpam-3478	126	4	(	(	PUNCT
ejpam-3478	126	5	20	20	NUM
ejpam-3478	126	6	)	)	PUNCT
ejpam-3478	126	7	if	if	SCONJ
ejpam-3478	126	8	we	we	PRON
ejpam-3478	126	9	choose	choose	VERB
ejpam-3478	126	10	f	f	PROPN
ejpam-3478	126	11	(	(	PUNCT
ejpam-3478	126	12	l	l	PROPN
ejpam-3478	126	13	,	,	PUNCT
ejpam-3478	126	14	t	t	PROPN
ejpam-3478	126	15	)	)	PUNCT
ejpam-3478	126	16	=	=	SYM
ejpam-3478	127	1	a	a	PRON
ejpam-3478	127	2	(	(	PUNCT
ejpam-3478	127	3	t)lλ	t)lλ	PROPN
ejpam-3478	127	4	+	+	PROPN
ejpam-3478	127	5	b	b	PROPN
ejpam-3478	127	6	(	(	PUNCT
ejpam-3478	127	7	t	t	PROPN
ejpam-3478	127	8	)	)	PUNCT
ejpam-3478	127	9	,	,	PUNCT
ejpam-3478	127	10	(	(	PUNCT
ejpam-3478	127	11	21	21	NUM
ejpam-3478	127	12	)	)	PUNCT
ejpam-3478	127	13	then	then	ADV
ejpam-3478	127	14	∂f	∂f	PROPN
ejpam-3478	127	15	∂l	∂l	PROPN
ejpam-3478	128	1	=	=	PUNCT
ejpam-3478	128	2	a	a	PRON
ejpam-3478	128	3	(	(	PUNCT
ejpam-3478	128	4	t)λlλ−1	t)λlλ−1	PROPN
ejpam-3478	128	5	,	,	PUNCT
ejpam-3478	128	6	∂2f	∂2f	VERB
ejpam-3478	128	7	∂l2	∂l2	NOUN
ejpam-3478	128	8	=	=	PUNCT
ejpam-3478	128	9	a	a	PRON
ejpam-3478	128	10	(	(	PUNCT
ejpam-3478	128	11	t)λ	t)λ	X
ejpam-3478	128	12	(	(	PUNCT
ejpam-3478	128	13	λ−	λ−	PROPN
ejpam-3478	128	14	1)lλ−2	1)lλ−2	NUM
ejpam-3478	128	15	,	,	PUNCT
ejpam-3478	128	16	∂f∂t	∂f∂t	PROPN
ejpam-3478	128	17	=	=	SYM
ejpam-3478	128	18	ȧ	ȧ	PROPN
ejpam-3478	128	19	(	(	PUNCT
ejpam-3478	128	20	t)lλ	t)lλ	PROPN
ejpam-3478	128	21	+	+	CCONJ
ejpam-3478	128	22	ḃ	ḃ	PROPN
ejpam-3478	128	23	(	(	PUNCT
ejpam-3478	128	24	t	t	PROPN
ejpam-3478	128	25	)	)	PUNCT
ejpam-3478	128	26	.	.	PUNCT
ejpam-3478	129	1	substituting	substitute	VERB
ejpam-3478	129	2	this	this	PRON
ejpam-3478	129	3	into	into	ADP
ejpam-3478	129	4	(	(	PUNCT
ejpam-3478	129	5	20	20	NUM
ejpam-3478	129	6	)	)	PUNCT
ejpam-3478	129	7	gives	give	VERB
ejpam-3478	129	8	0	0	NUM
ejpam-3478	130	1	=	=	SYM
ejpam-3478	130	2	1	1	NUM
ejpam-3478	130	3	γ	γ	X
ejpam-3478	130	4	+	+	X
ejpam-3478	130	5	ȧ	ȧ	PROPN
ejpam-3478	130	6	(	(	PUNCT
ejpam-3478	130	7	t)lλ	t)lλ	PROPN
ejpam-3478	130	8	+	+	CCONJ
ejpam-3478	130	9	ḃ	ḃ	PROPN
ejpam-3478	130	10	(	(	PUNCT
ejpam-3478	130	11	t	t	PROPN
ejpam-3478	130	12	)	)	PUNCT
ejpam-3478	130	13	+	+	CCONJ
ejpam-3478	130	14	(	(	PUNCT
ejpam-3478	130	15	ra	ra	PROPN
ejpam-3478	130	16	+	+	NOUN
ejpam-3478	130	17	1	1	NUM
ejpam-3478	130	18	2	2	NUM
ejpam-3478	130	19	(	(	PUNCT
ejpam-3478	130	20	α−	α−	ADP
ejpam-3478	130	21	ra)2	ra)2	PROPN
ejpam-3478	130	22	σ2(1−	σ2(1−	NOUN
ejpam-3478	130	23	γ	γ	PROPN
ejpam-3478	130	24	)	)	PUNCT
ejpam-3478	130	25	)	)	PUNCT
ejpam-3478	130	26	γ	γ	PROPN
ejpam-3478	130	27	(	(	PUNCT
ejpam-3478	130	28	a	a	PRON
ejpam-3478	130	29	(	(	PUNCT
ejpam-3478	130	30	t)lλ	t)lλ	PROPN
ejpam-3478	130	31	+	+	PROPN
ejpam-3478	130	32	b	b	PROPN
ejpam-3478	130	33	(	(	PUNCT
ejpam-3478	130	34	t	t	PROPN
ejpam-3478	130	35	)	)	PUNCT
ejpam-3478	130	36	)	)	PUNCT
ejpam-3478	131	1	+	+	CCONJ
ejpam-3478	131	2	(	(	PUNCT
ejpam-3478	131	3	rl	rl	INTJ
ejpam-3478	131	4	−	−	PROPN
ejpam-3478	131	5	(	(	PUNCT
ejpam-3478	131	6	c−m−	c−m−	PROPN
ejpam-3478	131	7	rl)2	rl)2	PROPN
ejpam-3478	131	8	2q2	2q2	NUM
ejpam-3478	131	9	(	(	PUNCT
ejpam-3478	131	10	λ−	λ−	PROPN
ejpam-3478	131	11	1	1	NUM
ejpam-3478	131	12	)	)	PUNCT
ejpam-3478	131	13	)	)	PUNCT
ejpam-3478	131	14	aλlλ	aλlλ	VERB
ejpam-3478	131	15	.	.	PUNCT
ejpam-3478	132	1	(	(	PUNCT
ejpam-3478	132	2	22	22	NUM
ejpam-3478	132	3	)	)	PUNCT
ejpam-3478	132	4	this	this	PRON
ejpam-3478	132	5	implies	imply	VERB
ejpam-3478	132	6	that	that	SCONJ
ejpam-3478	132	7	0	0	NUM
ejpam-3478	132	8	=	=	SYM
ejpam-3478	132	9	1	1	NUM
ejpam-3478	132	10	γ	γ	X
ejpam-3478	132	11	+	+	CCONJ
ejpam-3478	132	12	ḃ	ḃ	PROPN
ejpam-3478	132	13	(	(	PUNCT
ejpam-3478	132	14	t	t	PROPN
ejpam-3478	132	15	)	)	PUNCT
ejpam-3478	132	16	+	+	CCONJ
ejpam-3478	133	1	(	(	PUNCT
ejpam-3478	133	2	ra	ra	PROPN
ejpam-3478	133	3	+	+	NOUN
ejpam-3478	133	4	1	1	NUM
ejpam-3478	133	5	2	2	NUM
ejpam-3478	133	6	(	(	PUNCT
ejpam-3478	133	7	α−	α−	ADP
ejpam-3478	133	8	ra)2	ra)2	PROPN
ejpam-3478	133	9	σ2(1−	σ2(1−	NOUN
ejpam-3478	133	10	γ	γ	PROPN
ejpam-3478	133	11	)	)	PUNCT
ejpam-3478	133	12	)	)	PUNCT
ejpam-3478	133	13	γb	γb	NOUN
ejpam-3478	133	14	(	(	PUNCT
ejpam-3478	133	15	t	t	NOUN
ejpam-3478	133	16	)	)	PUNCT
ejpam-3478	133	17	(	(	PUNCT
ejpam-3478	133	18	23	23	NUM
ejpam-3478	133	19	)	)	PUNCT
ejpam-3478	133	20	and	and	CCONJ
ejpam-3478	133	21	0	0	X
ejpam-3478	134	1	=	=	SYM
ejpam-3478	134	2	ȧ	ȧ	PROPN
ejpam-3478	134	3	(	(	PUNCT
ejpam-3478	134	4	t	t	PROPN
ejpam-3478	134	5	)	)	PUNCT
ejpam-3478	134	6	+	+	CCONJ
ejpam-3478	134	7	(	(	PUNCT
ejpam-3478	134	8	ra	ra	PROPN
ejpam-3478	134	9	+	+	NOUN
ejpam-3478	134	10	1	1	NUM
ejpam-3478	134	11	2	2	NUM
ejpam-3478	134	12	(	(	PUNCT
ejpam-3478	134	13	α−	α−	ADP
ejpam-3478	134	14	ra)2	ra)2	PROPN
ejpam-3478	134	15	σ2(1−	σ2(1−	NOUN
ejpam-3478	134	16	γ	γ	PROPN
ejpam-3478	134	17	)	)	PUNCT
ejpam-3478	134	18	)	)	PUNCT
ejpam-3478	134	19	γa	γa	PROPN
ejpam-3478	134	20	(	(	PUNCT
ejpam-3478	134	21	t	t	PROPN
ejpam-3478	134	22	)	)	PUNCT
ejpam-3478	134	23	c.	c.	PROPN
ejpam-3478	134	24	atkinson	atkinson	PROPN
ejpam-3478	134	25	,	,	PUNCT
ejpam-3478	134	26	s.	s.	PROPN
ejpam-3478	134	27	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	134	28	,	,	PUNCT
ejpam-3478	134	29	p.	p.	PROPN
ejpam-3478	134	30	ingpochai	ingpochai	PROPN
ejpam-3478	134	31	/	/	SYM
ejpam-3478	134	32	eur	eur	PROPN
ejpam-3478	134	33	.	.	PUNCT
ejpam-3478	135	1	j.	j.	PROPN
ejpam-3478	135	2	pure	pure	PROPN
ejpam-3478	135	3	appl	appl	PROPN
ejpam-3478	135	4	.	.	PROPN
ejpam-3478	135	5	math	math	PROPN
ejpam-3478	135	6	,	,	PUNCT
ejpam-3478	135	7	12	12	NUM
ejpam-3478	135	8	(	(	PUNCT
ejpam-3478	135	9	3	3	NUM
ejpam-3478	135	10	)	)	PUNCT
ejpam-3478	135	11	(	(	PUNCT
ejpam-3478	135	12	2019	2019	NUM
ejpam-3478	135	13	)	)	PUNCT
ejpam-3478	135	14	,	,	PUNCT
ejpam-3478	135	15	1315	1315	NUM
ejpam-3478	135	16	-	-	SYM
ejpam-3478	135	17	1336	1336	NUM
ejpam-3478	135	18	1321	1321	NUM
ejpam-3478	135	19	+	+	CCONJ
ejpam-3478	135	20	(	(	PUNCT
ejpam-3478	135	21	rl	rl	ADP
ejpam-3478	135	22	−	−	PROPN
ejpam-3478	135	23	(	(	PUNCT
ejpam-3478	135	24	c−m−	c−m−	PROPN
ejpam-3478	135	25	rl)2	rl)2	PROPN
ejpam-3478	135	26	2q2	2q2	NUM
ejpam-3478	135	27	(	(	PUNCT
ejpam-3478	135	28	γ	γ	PROPN
ejpam-3478	135	29	−	−	PROPN
ejpam-3478	135	30	1	1	NUM
ejpam-3478	135	31	)	)	PUNCT
ejpam-3478	135	32	)	)	PUNCT
ejpam-3478	136	1	λa	λa	X
ejpam-3478	136	2	(	(	PUNCT
ejpam-3478	136	3	t	t	PROPN
ejpam-3478	136	4	)	)	PUNCT
ejpam-3478	136	5	.	.	PUNCT
ejpam-3478	137	1	(	(	PUNCT
ejpam-3478	137	2	24	24	NUM
ejpam-3478	137	3	)	)	PUNCT
ejpam-3478	137	4	therefore	therefore	ADV
ejpam-3478	137	5	,	,	PUNCT
ejpam-3478	137	6	a	a	DET
ejpam-3478	137	7	(	(	PUNCT
ejpam-3478	137	8	t	t	NOUN
ejpam-3478	137	9	)	)	PUNCT
ejpam-3478	137	10	=	=	PROPN
ejpam-3478	137	11	a0	a0	PROPN
ejpam-3478	137	12	exp	exp	NOUN
ejpam-3478	137	13	[	[	PUNCT
ejpam-3478	137	14	−	−	PROPN
ejpam-3478	137	15	(	(	PUNCT
ejpam-3478	137	16	raγ	raγ	NOUN
ejpam-3478	138	1	+	+	CCONJ
ejpam-3478	138	2	1	1	NUM
ejpam-3478	138	3	2	2	NUM
ejpam-3478	138	4	(	(	PUNCT
ejpam-3478	138	5	α−	α−	ADP
ejpam-3478	138	6	ra)2	ra)2	NOUN
ejpam-3478	138	7	γ	γ	PROPN
ejpam-3478	138	8	σ2(1−	σ2(1−	PROPN
ejpam-3478	138	9	γ	γ	PROPN
ejpam-3478	138	10	)	)	PUNCT
ejpam-3478	138	11	+	+	NUM
ejpam-3478	138	12	rlλ−	rlλ−	NOUN
ejpam-3478	138	13	(	(	PUNCT
ejpam-3478	138	14	c−m−	c−m−	PROPN
ejpam-3478	138	15	rl)2	rl)2	PROPN
ejpam-3478	138	16	λ	λ	PROPN
ejpam-3478	138	17	2q2	2q2	NUM
ejpam-3478	138	18	(	(	PUNCT
ejpam-3478	138	19	λ−	λ−	PROPN
ejpam-3478	138	20	1	1	NUM
ejpam-3478	138	21	)	)	PUNCT
ejpam-3478	138	22	)	)	PUNCT
ejpam-3478	139	1	t	t	NOUN
ejpam-3478	139	2	]	]	PUNCT
ejpam-3478	139	3	.	.	PUNCT
ejpam-3478	140	1	(	(	PUNCT
ejpam-3478	140	2	25	25	NUM
ejpam-3478	140	3	)	)	PUNCT
ejpam-3478	140	4	we	we	PRON
ejpam-3478	140	5	now	now	ADV
ejpam-3478	140	6	solve	solve	VERB
ejpam-3478	140	7	for	for	ADP
ejpam-3478	140	8	a	a	DET
ejpam-3478	140	9	(	(	PUNCT
ejpam-3478	140	10	t	t	NOUN
ejpam-3478	140	11	)	)	PUNCT
ejpam-3478	140	12	and	and	CCONJ
ejpam-3478	140	13	b	b	PROPN
ejpam-3478	140	14	(	(	PUNCT
ejpam-3478	140	15	t	t	PROPN
ejpam-3478	140	16	)	)	PUNCT
ejpam-3478	140	17	with	with	ADP
ejpam-3478	140	18	the	the	DET
ejpam-3478	140	19	terminal	terminal	ADJ
ejpam-3478	140	20	condition	condition	NOUN
ejpam-3478	140	21	f	f	X
ejpam-3478	140	22	(	(	PUNCT
ejpam-3478	140	23	l	l	PROPN
ejpam-3478	140	24	,	,	PUNCT
ejpam-3478	140	25	t	t	NOUN
ejpam-3478	140	26	)	)	PUNCT
ejpam-3478	141	1	=	=	PUNCT
ejpam-3478	141	2	a	a	DET
ejpam-3478	141	3	(	(	PUNCT
ejpam-3478	141	4	t	t	NOUN
ejpam-3478	141	5	)	)	PUNCT
ejpam-3478	141	6	l2	l2	VERB
ejpam-3478	141	7	+	+	NOUN
ejpam-3478	141	8	b	b	PROPN
ejpam-3478	141	9	(	(	PUNCT
ejpam-3478	141	10	t	t	PROPN
ejpam-3478	141	11	)	)	PUNCT
ejpam-3478	141	12	,	,	PUNCT
ejpam-3478	141	13	with	with	ADP
ejpam-3478	141	14	a(t	a(t	NOUN
ejpam-3478	141	15	)	)	PUNCT
ejpam-3478	141	16	given	give	VERB
ejpam-3478	141	17	in	in	ADP
ejpam-3478	141	18	(	(	PUNCT
ejpam-3478	141	19	25	25	NUM
ejpam-3478	141	20	)	)	PUNCT
ejpam-3478	141	21	then	then	ADV
ejpam-3478	141	22	u∗	u∗	ADV
ejpam-3478	142	1	=	=	PUNCT
ejpam-3478	142	2	c−m−	c−m−	PROPN
ejpam-3478	142	3	rl	rl	PROPN
ejpam-3478	142	4	q2	q2	NOUN
ejpam-3478	142	5	(	(	PUNCT
ejpam-3478	142	6	1−	1−	NUM
ejpam-3478	142	7	λ	λ	NOUN
ejpam-3478	142	8	)	)	PUNCT
ejpam-3478	142	9	.	.	PUNCT
ejpam-3478	143	1	(	(	PUNCT
ejpam-3478	143	2	26	26	NUM
ejpam-3478	143	3	)	)	PUNCT
ejpam-3478	143	4	if	if	SCONJ
ejpam-3478	143	5	this	this	DET
ejpam-3478	143	6	final	final	ADJ
ejpam-3478	143	7	condition	condition	NOUN
ejpam-3478	143	8	is	be	AUX
ejpam-3478	143	9	f	f	PROPN
ejpam-3478	143	10	(	(	PUNCT
ejpam-3478	143	11	l	l	PROPN
ejpam-3478	143	12	,	,	PUNCT
ejpam-3478	143	13	t	t	NOUN
ejpam-3478	143	14	)	)	PUNCT
ejpam-3478	143	15	=	=	PUNCT
ejpam-3478	144	1	0	0	PUNCT
ejpam-3478	144	2	then	then	ADV
ejpam-3478	144	3	from	from	ADP
ejpam-3478	144	4	(	(	PUNCT
ejpam-3478	144	5	21	21	NUM
ejpam-3478	144	6	)	)	PUNCT
ejpam-3478	144	7	we	we	PRON
ejpam-3478	144	8	obtain	obtain	VERB
ejpam-3478	144	9	b	b	X
ejpam-3478	144	10	(	(	PUNCT
ejpam-3478	144	11	t	t	PROPN
ejpam-3478	144	12	)	)	PUNCT
ejpam-3478	144	13	=	=	SYM
ejpam-3478	144	14	0	0	NUM
ejpam-3478	144	15	and	and	CCONJ
ejpam-3478	144	16	a	a	DET
ejpam-3478	144	17	(	(	PUNCT
ejpam-3478	144	18	t	t	NOUN
ejpam-3478	144	19	)	)	PUNCT
ejpam-3478	144	20	=	=	SYM
ejpam-3478	144	21	0	0	PUNCT
ejpam-3478	145	1	and	and	CCONJ
ejpam-3478	145	2	then	then	ADV
ejpam-3478	145	3	b	b	X
ejpam-3478	145	4	(	(	PUNCT
ejpam-3478	145	5	t	t	PROPN
ejpam-3478	145	6	)	)	PUNCT
ejpam-3478	145	7	=	=	SYM
ejpam-3478	145	8	1	1	NUM
ejpam-3478	145	9	γ2	γ2	NOUN
ejpam-3478	145	10	(	(	PUNCT
ejpam-3478	145	11	ra	ra	PROPN
ejpam-3478	146	1	+	+	CCONJ
ejpam-3478	146	2	1	1	NUM
ejpam-3478	146	3	2	2	NUM
ejpam-3478	146	4	(	(	PUNCT
ejpam-3478	146	5	α−	α−	ADP
ejpam-3478	146	6	ra)2	ra)2	PROPN
ejpam-3478	146	7	σ2	σ2	PROPN
ejpam-3478	146	8	(	(	PUNCT
ejpam-3478	146	9	1−	1−	NUM
ejpam-3478	146	10	γ	γ	NOUN
ejpam-3478	146	11	)	)	PUNCT
ejpam-3478	146	12	)	)	PUNCT
ejpam-3478	146	13	(	(	PUNCT
ejpam-3478	146	14	exp	exp	X
ejpam-3478	146	15	[	[	PUNCT
ejpam-3478	146	16	−	−	PROPN
ejpam-3478	146	17	{	{	PUNCT
ejpam-3478	146	18	ra	ra	PROPN
ejpam-3478	146	19	+	+	CCONJ
ejpam-3478	146	20	1	1	NUM
ejpam-3478	146	21	2	2	NUM
ejpam-3478	146	22	(	(	PUNCT
ejpam-3478	146	23	α−	α−	ADP
ejpam-3478	146	24	ra)2	ra)2	PROPN
ejpam-3478	146	25	σ2	σ2	PROPN
ejpam-3478	146	26	(	(	PUNCT
ejpam-3478	146	27	1−	1−	NUM
ejpam-3478	146	28	γ	γ	NOUN
ejpam-3478	146	29	)	)	PUNCT
ejpam-3478	146	30	}	}	PUNCT
ejpam-3478	146	31	γ	γ	X
ejpam-3478	146	32	(	(	PUNCT
ejpam-3478	146	33	t−	t−	PROPN
ejpam-3478	146	34	t	t	PROPN
ejpam-3478	146	35	)	)	PUNCT
ejpam-3478	146	36	]	]	PUNCT
ejpam-3478	146	37	−	−	PROPN
ejpam-3478	147	1	1	1	X
ejpam-3478	147	2	)	)	PUNCT
ejpam-3478	147	3	a	a	DET
ejpam-3478	147	4	(	(	PUNCT
ejpam-3478	147	5	t	t	NOUN
ejpam-3478	147	6	)	)	PUNCT
ejpam-3478	147	7	≡	≡	PROPN
ejpam-3478	147	8	0	0	PUNCT
ejpam-3478	147	9	.	.	PUNCT
ejpam-3478	148	1	hence	hence	ADV
ejpam-3478	148	2	the	the	DET
ejpam-3478	148	3	solution	solution	NOUN
ejpam-3478	148	4	is	be	AUX
ejpam-3478	148	5	independent	independent	ADJ
ejpam-3478	148	6	of	of	ADP
ejpam-3478	148	7	u.	u.	PROPN
ejpam-3478	148	8	this	this	PRON
ejpam-3478	148	9	is	be	AUX
ejpam-3478	148	10	aligned	align	VERB
ejpam-3478	148	11	with	with	ADP
ejpam-3478	148	12	our	our	PRON
ejpam-3478	148	13	intuition	intuition	NOUN
ejpam-3478	148	14	that	that	SCONJ
ejpam-3478	148	15	if	if	SCONJ
ejpam-3478	148	16	the	the	DET
ejpam-3478	148	17	utility	utility	NOUN
ejpam-3478	148	18	depends	depend	VERB
ejpam-3478	148	19	only	only	ADV
ejpam-3478	148	20	on	on	ADP
ejpam-3478	148	21	w	w	NOUN
ejpam-3478	148	22	and	and	CCONJ
ejpam-3478	148	23	that	that	SCONJ
ejpam-3478	148	24	the	the	DET
ejpam-3478	148	25	risky	risky	ADJ
ejpam-3478	148	26	insurance	insurance	NOUN
ejpam-3478	148	27	liability	liability	NOUN
ejpam-3478	148	28	is	be	AUX
ejpam-3478	148	29	not	not	PART
ejpam-3478	148	30	related	relate	VERB
ejpam-3478	148	31	to	to	ADP
ejpam-3478	148	32	the	the	DET
ejpam-3478	148	33	risky	risky	ADJ
ejpam-3478	148	34	asset	asset	NOUN
ejpam-3478	148	35	then	then	ADV
ejpam-3478	148	36	we	we	PRON
ejpam-3478	148	37	would	would	AUX
ejpam-3478	148	38	expect	expect	VERB
ejpam-3478	148	39	to	to	PART
ejpam-3478	148	40	find	find	VERB
ejpam-3478	148	41	that	that	SCONJ
ejpam-3478	148	42	the	the	DET
ejpam-3478	148	43	strategic	strategic	ADJ
ejpam-3478	148	44	allocation	allocation	NOUN
ejpam-3478	148	45	of	of	ADP
ejpam-3478	148	46	the	the	DET
ejpam-3478	148	47	risky	risky	ADJ
ejpam-3478	148	48	asset	asset	NOUN
ejpam-3478	148	49	,	,	PUNCT
ejpam-3478	148	50	w	w	PROPN
ejpam-3478	148	51	,	,	PUNCT
ejpam-3478	148	52	is	be	AUX
ejpam-3478	148	53	the	the	DET
ejpam-3478	148	54	same	same	ADJ
ejpam-3478	148	55	as	as	ADP
ejpam-3478	148	56	merton	merton	NOUN
ejpam-3478	148	57	’s	’s	PART
ejpam-3478	148	58	solution	solution	NOUN
ejpam-3478	148	59	and	and	CCONJ
ejpam-3478	148	60	the	the	DET
ejpam-3478	148	61	optimal	optimal	ADJ
ejpam-3478	148	62	product	product	NOUN
ejpam-3478	148	63	mix	mix	NOUN
ejpam-3478	148	64	u	u	NOUN
ejpam-3478	148	65	can	can	AUX
ejpam-3478	148	66	take	take	VERB
ejpam-3478	148	67	on	on	ADP
ejpam-3478	148	68	any	any	DET
ejpam-3478	148	69	value	value	NOUN
ejpam-3478	148	70	.	.	PUNCT
ejpam-3478	149	1	4	4	X
ejpam-3478	149	2	.	.	X
ejpam-3478	149	3	utility	utility	NOUN
ejpam-3478	149	4	u	u	NOUN
ejpam-3478	149	5	(	(	PUNCT
ejpam-3478	149	6	w	w	PROPN
ejpam-3478	149	7	,	,	PUNCT
ejpam-3478	149	8	l	l	NOUN
ejpam-3478	149	9	)	)	PUNCT
ejpam-3478	149	10	=	=	SYM
ejpam-3478	149	11	(	(	PUNCT
ejpam-3478	149	12	w−l)γ	w−l)γ	PROPN
ejpam-3478	149	13	γ	γ	X
ejpam-3478	149	14	the	the	DET
ejpam-3478	149	15	power	power	NOUN
ejpam-3478	149	16	utility	utility	NOUN
ejpam-3478	149	17	function	function	NOUN
ejpam-3478	149	18	assumed	assume	VERB
ejpam-3478	149	19	in	in	ADP
ejpam-3478	149	20	this	this	DET
ejpam-3478	149	21	paper	paper	NOUN
ejpam-3478	149	22	belongs	belong	VERB
ejpam-3478	149	23	to	to	ADP
ejpam-3478	149	24	the	the	DET
ejpam-3478	149	25	class	class	NOUN
ejpam-3478	149	26	of	of	ADP
ejpam-3478	149	27	utility	utility	NOUN
ejpam-3478	149	28	functions	function	NOUN
ejpam-3478	149	29	known	know	VERB
ejpam-3478	149	30	as	as	ADP
ejpam-3478	149	31	constant	constant	ADJ
ejpam-3478	149	32	relative	relative	ADJ
ejpam-3478	149	33	risk	risk	NOUN
ejpam-3478	149	34	aversion	aversion	NOUN
ejpam-3478	149	35	(	(	PUNCT
ejpam-3478	149	36	crra	crra	NOUN
ejpam-3478	149	37	)	)	PUNCT
ejpam-3478	149	38	.	.	PUNCT
ejpam-3478	150	1	utility	utility	NOUN
ejpam-3478	150	2	of	of	ADP
ejpam-3478	150	3	this	this	DET
ejpam-3478	150	4	class	class	NOUN
ejpam-3478	150	5	are	be	AUX
ejpam-3478	150	6	sensible	sensible	ADJ
ejpam-3478	150	7	because	because	SCONJ
ejpam-3478	150	8	we	we	PRON
ejpam-3478	150	9	observe	observe	VERB
ejpam-3478	150	10	that	that	SCONJ
ejpam-3478	150	11	companies	company	NOUN
ejpam-3478	150	12	strive	strive	VERB
ejpam-3478	150	13	to	to	PART
ejpam-3478	150	14	link	link	VERB
ejpam-3478	150	15	the	the	DET
ejpam-3478	150	16	size	size	NOUN
ejpam-3478	150	17	of	of	ADP
ejpam-3478	150	18	the	the	DET
ejpam-3478	150	19	risk	risk	NOUN
ejpam-3478	150	20	that	that	PRON
ejpam-3478	150	21	they	they	PRON
ejpam-3478	150	22	take	take	VERB
ejpam-3478	150	23	to	to	ADP
ejpam-3478	150	24	their	their	PRON
ejpam-3478	150	25	capacity	capacity	NOUN
ejpam-3478	150	26	for	for	ADP
ejpam-3478	150	27	risk	risk	NOUN
ejpam-3478	150	28	absorption	absorption	NOUN
ejpam-3478	150	29	.	.	PUNCT
ejpam-3478	151	1	4.1	4.1	NUM
ejpam-3478	151	2	.	.	PUNCT
ejpam-3478	151	3	non	non	ADJ
ejpam-3478	151	4	-	-	ADJ
ejpam-3478	151	5	zero	zero	NUM
ejpam-3478	151	6	correlation	correlation	NOUN
ejpam-3478	151	7	and	and	CCONJ
ejpam-3478	151	8	ra	ra	NOUN
ejpam-3478	151	9	=	=	NOUN
ejpam-3478	151	10	rl	rl	VERB
ejpam-3478	151	11	by	by	ADP
ejpam-3478	151	12	setting	set	VERB
ejpam-3478	151	13	the	the	DET
ejpam-3478	151	14	utility	utility	NOUN
ejpam-3478	151	15	of	of	ADP
ejpam-3478	151	16	the	the	DET
ejpam-3478	151	17	form	form	NOUN
ejpam-3478	151	18	(	(	PUNCT
ejpam-3478	151	19	w−l)γ	w−l)γ	NOUN
ejpam-3478	151	20	γ	γ	X
ejpam-3478	151	21	,	,	PUNCT
ejpam-3478	151	22	we	we	PRON
ejpam-3478	151	23	are	be	AUX
ejpam-3478	151	24	assuming	assume	VERB
ejpam-3478	151	25	that	that	SCONJ
ejpam-3478	151	26	the	the	DET
ejpam-3478	151	27	management	management	NOUN
ejpam-3478	151	28	is	be	AUX
ejpam-3478	151	29	interested	interested	ADJ
ejpam-3478	151	30	in	in	ADP
ejpam-3478	151	31	maximising	maximise	VERB
ejpam-3478	151	32	the	the	DET
ejpam-3478	151	33	utility	utility	NOUN
ejpam-3478	151	34	based	base	VERB
ejpam-3478	151	35	on	on	ADP
ejpam-3478	151	36	shareholder	shareholder	NOUN
ejpam-3478	151	37	’s	’s	PART
ejpam-3478	151	38	equity	equity	NOUN
ejpam-3478	151	39	.	.	PUNCT
ejpam-3478	152	1	it	it	PRON
ejpam-3478	152	2	can	can	AUX
ejpam-3478	152	3	be	be	AUX
ejpam-3478	152	4	argued	argue	VERB
ejpam-3478	152	5	that	that	SCONJ
ejpam-3478	152	6	a	a	DET
ejpam-3478	152	7	utility	utility	NOUN
ejpam-3478	152	8	function	function	NOUN
ejpam-3478	152	9	that	that	PRON
ejpam-3478	152	10	depends	depend	VERB
ejpam-3478	152	11	on	on	ADP
ejpam-3478	152	12	the	the	DET
ejpam-3478	152	13	shareholder	shareholder	NOUN
ejpam-3478	152	14	’s	’s	PART
ejpam-3478	152	15	equity	equity	NOUN
ejpam-3478	152	16	is	be	AUX
ejpam-3478	152	17	more	more	ADV
ejpam-3478	152	18	sensible	sensible	ADJ
ejpam-3478	152	19	than	than	ADP
ejpam-3478	152	20	a	a	DET
ejpam-3478	152	21	utility	utility	NOUN
ejpam-3478	152	22	which	which	PRON
ejpam-3478	152	23	depends	depend	VERB
ejpam-3478	152	24	solely	solely	ADV
ejpam-3478	152	25	on	on	ADP
ejpam-3478	152	26	the	the	DET
ejpam-3478	152	27	size	size	NOUN
ejpam-3478	152	28	of	of	ADP
ejpam-3478	152	29	the	the	DET
ejpam-3478	152	30	company	company	NOUN
ejpam-3478	152	31	as	as	SCONJ
ejpam-3478	152	32	shown	show	VERB
ejpam-3478	152	33	in	in	ADP
ejpam-3478	152	34	the	the	DET
ejpam-3478	152	35	earlier	early	ADJ
ejpam-3478	152	36	example	example	NOUN
ejpam-3478	152	37	.	.	PUNCT
ejpam-3478	153	1	suppose	suppose	VERB
ejpam-3478	153	2	that	that	SCONJ
ejpam-3478	153	3	the	the	DET
ejpam-3478	153	4	utility	utility	NOUN
ejpam-3478	153	5	function	function	NOUN
ejpam-3478	153	6	has	have	VERB
ejpam-3478	153	7	the	the	DET
ejpam-3478	153	8	form	form	NOUN
ejpam-3478	153	9	u	u	NOUN
ejpam-3478	153	10	(	(	PUNCT
ejpam-3478	153	11	e	e	NOUN
ejpam-3478	153	12	)	)	PUNCT
ejpam-3478	153	13	=	=	PUNCT
ejpam-3478	153	14	eγ	eγ	ADP
ejpam-3478	153	15	γ	γ	X
ejpam-3478	153	16	=	=	SYM
ejpam-3478	153	17	(	(	PUNCT
ejpam-3478	153	18	w−l)γ	w−l)γ	PROPN
ejpam-3478	153	19	γ	γ	X
ejpam-3478	154	1	and	and	CCONJ
ejpam-3478	154	2	we	we	PRON
ejpam-3478	154	3	seek	seek	VERB
ejpam-3478	154	4	the	the	DET
ejpam-3478	154	5	solution	solution	NOUN
ejpam-3478	154	6	to	to	ADP
ejpam-3478	154	7	the	the	DET
ejpam-3478	154	8	value	value	NOUN
ejpam-3478	154	9	function	function	NOUN
ejpam-3478	154	10	of	of	ADP
ejpam-3478	154	11	the	the	DET
ejpam-3478	154	12	form	form	NOUN
ejpam-3478	154	13	j	j	PROPN
ejpam-3478	154	14	(	(	PUNCT
ejpam-3478	154	15	w	w	PROPN
ejpam-3478	154	16	,	,	PUNCT
ejpam-3478	154	17	l	l	PROPN
ejpam-3478	154	18	,	,	PUNCT
ejpam-3478	154	19	t	t	PROPN
ejpam-3478	154	20	)	)	PUNCT
ejpam-3478	154	21	=	=	SYM
ejpam-3478	154	22	a	a	DET
ejpam-3478	154	23	(	(	PUNCT
ejpam-3478	154	24	t	t	NOUN
ejpam-3478	154	25	)	)	PUNCT
ejpam-3478	154	26	(	(	PUNCT
ejpam-3478	154	27	w−l)γ	w−l)γ	NOUN
ejpam-3478	154	28	γ	γ	X
ejpam-3478	154	29	thus	thus	ADV
ejpam-3478	154	30	from	from	ADP
ejpam-3478	154	31	(	(	PUNCT
ejpam-3478	154	32	11	11	NUM
ejpam-3478	154	33	)	)	PUNCT
ejpam-3478	154	34	and	and	CCONJ
ejpam-3478	154	35	(	(	PUNCT
ejpam-3478	154	36	12	12	NUM
ejpam-3478	154	37	)	)	PUNCT
ejpam-3478	154	38	we	we	PRON
ejpam-3478	154	39	have	have	VERB
ejpam-3478	154	40	σ2ww	σ2ww	X
ejpam-3478	154	41	(	(	PUNCT
ejpam-3478	154	42	γ	γ	PROPN
ejpam-3478	154	43	−	−	PROPN
ejpam-3478	154	44	1)−	1)−	PROPN
ejpam-3478	154	45	qulσρ	qulσρ	PROPN
ejpam-3478	154	46	(	(	PUNCT
ejpam-3478	154	47	γ	γ	PROPN
ejpam-3478	154	48	−	−	PROPN
ejpam-3478	154	49	1	1	NUM
ejpam-3478	154	50	)	)	PUNCT
ejpam-3478	154	51	=	=	SYM
ejpam-3478	155	1	−	−	PROPN
ejpam-3478	155	2	(	(	PUNCT
ejpam-3478	155	3	α−	α−	ADP
ejpam-3478	155	4	ra	ra	NOUN
ejpam-3478	155	5	)	)	PUNCT
ejpam-3478	155	6	(	(	PUNCT
ejpam-3478	155	7	w	w	PROPN
ejpam-3478	155	8	−	−	PROPN
ejpam-3478	155	9	l	l	NOUN
ejpam-3478	155	10	)	)	PUNCT
ejpam-3478	155	11	(	(	PUNCT
ejpam-3478	155	12	27	27	NUM
ejpam-3478	155	13	)	)	PUNCT
ejpam-3478	155	14	c.	c.	PROPN
ejpam-3478	155	15	atkinson	atkinson	PROPN
ejpam-3478	155	16	,	,	PUNCT
ejpam-3478	155	17	s.	s.	PROPN
ejpam-3478	155	18	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	155	19	,	,	PUNCT
ejpam-3478	155	20	p.	p.	PROPN
ejpam-3478	155	21	ingpochai	ingpochai	PROPN
ejpam-3478	155	22	/	/	SYM
ejpam-3478	155	23	eur	eur	PROPN
ejpam-3478	155	24	.	.	PUNCT
ejpam-3478	156	1	j.	j.	PROPN
ejpam-3478	156	2	pure	pure	PROPN
ejpam-3478	156	3	appl	appl	PROPN
ejpam-3478	156	4	.	.	PROPN
ejpam-3478	156	5	math	math	PROPN
ejpam-3478	156	6	,	,	PUNCT
ejpam-3478	156	7	12	12	NUM
ejpam-3478	156	8	(	(	PUNCT
ejpam-3478	156	9	3	3	NUM
ejpam-3478	156	10	)	)	PUNCT
ejpam-3478	156	11	(	(	PUNCT
ejpam-3478	156	12	2019	2019	NUM
ejpam-3478	156	13	)	)	PUNCT
ejpam-3478	156	14	,	,	PUNCT
ejpam-3478	156	15	1315	1315	NUM
ejpam-3478	156	16	-	-	SYM
ejpam-3478	156	17	1336	1336	NUM
ejpam-3478	156	18	1322	1322	NUM
ejpam-3478	156	19	and	and	CCONJ
ejpam-3478	156	20	−qwwσρ	−qwwσρ	PROPN
ejpam-3478	156	21	(	(	PUNCT
ejpam-3478	156	22	γ	γ	X
ejpam-3478	156	23	−	−	PROPN
ejpam-3478	156	24	1	1	NUM
ejpam-3478	156	25	)	)	PUNCT
ejpam-3478	156	26	+	+	CCONJ
ejpam-3478	156	27	q2ul	q2ul	X
ejpam-3478	156	28	(	(	PUNCT
ejpam-3478	156	29	γ	γ	NOUN
ejpam-3478	156	30	−	−	PROPN
ejpam-3478	156	31	1	1	NUM
ejpam-3478	156	32	)	)	PUNCT
ejpam-3478	156	33	=	=	PRON
ejpam-3478	156	34	{	{	PUNCT
ejpam-3478	156	35	c−m−	c−m−	PROPN
ejpam-3478	156	36	rl	rl	X
ejpam-3478	156	37	}	}	PUNCT
ejpam-3478	156	38	(	(	PUNCT
ejpam-3478	156	39	w	w	PROPN
ejpam-3478	156	40	−	−	PROPN
ejpam-3478	156	41	l	l	NOUN
ejpam-3478	156	42	)	)	PUNCT
ejpam-3478	156	43	(	(	PUNCT
ejpam-3478	156	44	28	28	NUM
ejpam-3478	156	45	)	)	PUNCT
ejpam-3478	156	46	which	which	PRON
ejpam-3478	156	47	can	can	AUX
ejpam-3478	156	48	be	be	AUX
ejpam-3478	156	49	rewritten	rewrite	VERB
ejpam-3478	156	50	as	as	ADP
ejpam-3478	156	51	(	(	PUNCT
ejpam-3478	156	52	σ2	σ2	PROPN
ejpam-3478	156	53	(	(	PUNCT
ejpam-3478	156	54	γ	γ	PROPN
ejpam-3478	156	55	−	−	PROPN
ejpam-3478	156	56	1	1	NUM
ejpam-3478	156	57	)	)	PUNCT
ejpam-3478	156	58	−qσρ	−qσρ	NUM
ejpam-3478	156	59	(	(	PUNCT
ejpam-3478	156	60	γ	γ	X
ejpam-3478	156	61	−	−	PROPN
ejpam-3478	156	62	1	1	NUM
ejpam-3478	156	63	)	)	PUNCT
ejpam-3478	156	64	−qσρ	−qσρ	NUM
ejpam-3478	156	65	(	(	PUNCT
ejpam-3478	156	66	γ	γ	X
ejpam-3478	156	67	−	−	PROPN
ejpam-3478	156	68	1	1	NUM
ejpam-3478	156	69	)	)	PUNCT
ejpam-3478	156	70	q2	q2	NOUN
ejpam-3478	156	71	(	(	PUNCT
ejpam-3478	156	72	γ	γ	NOUN
ejpam-3478	156	73	−	−	PROPN
ejpam-3478	156	74	1	1	NUM
ejpam-3478	156	75	)	)	PUNCT
ejpam-3478	156	76	)	)	PUNCT
ejpam-3478	157	1	(	(	PUNCT
ejpam-3478	157	2	ww	ww	PROPN
ejpam-3478	157	3	ul	ul	INTJ
ejpam-3478	157	4	)	)	PUNCT
ejpam-3478	157	5	=	=	PUNCT
ejpam-3478	158	1	(	(	PUNCT
ejpam-3478	158	2	−	−	X
ejpam-3478	158	3	(	(	PUNCT
ejpam-3478	158	4	α−	α−	ADP
ejpam-3478	158	5	ra	ra	NOUN
ejpam-3478	158	6	)	)	PUNCT
ejpam-3478	158	7	(	(	PUNCT
ejpam-3478	158	8	w	w	PROPN
ejpam-3478	158	9	−	−	PROPN
ejpam-3478	158	10	l	l	NOUN
ejpam-3478	158	11	)	)	PUNCT
ejpam-3478	158	12	{	{	PUNCT
ejpam-3478	158	13	c−m−	c−m−	PROPN
ejpam-3478	158	14	rl	rl	X
ejpam-3478	158	15	}	}	PUNCT
ejpam-3478	158	16	(	(	PUNCT
ejpam-3478	158	17	w	w	PROPN
ejpam-3478	158	18	−	−	PROPN
ejpam-3478	158	19	l	l	NOUN
ejpam-3478	158	20	)	)	PUNCT
ejpam-3478	158	21	)	)	PUNCT
ejpam-3478	158	22	.	.	PUNCT
ejpam-3478	159	1	(	(	PUNCT
ejpam-3478	159	2	29	29	NUM
ejpam-3478	159	3	)	)	PUNCT
ejpam-3478	159	4	the	the	DET
ejpam-3478	159	5	equation	equation	NOUN
ejpam-3478	159	6	(	(	PUNCT
ejpam-3478	159	7	29	29	NUM
ejpam-3478	159	8	)	)	PUNCT
ejpam-3478	159	9	can	can	AUX
ejpam-3478	159	10	then	then	ADV
ejpam-3478	159	11	be	be	AUX
ejpam-3478	159	12	solved	solve	VERB
ejpam-3478	159	13	to	to	PART
ejpam-3478	159	14	give	give	VERB
ejpam-3478	159	15	ww	ww	PROPN
ejpam-3478	159	16	=	=	PROPN
ejpam-3478	159	17	q1	q1	PROPN
ejpam-3478	159	18	(	(	PUNCT
ejpam-3478	159	19	w	w	PROPN
ejpam-3478	159	20	−	−	PROPN
ejpam-3478	159	21	l	l	NOUN
ejpam-3478	159	22	)	)	PUNCT
ejpam-3478	159	23	(	(	PUNCT
ejpam-3478	159	24	30	30	NUM
ejpam-3478	159	25	)	)	PUNCT
ejpam-3478	159	26	ul	ul	NOUN
ejpam-3478	159	27	=	=	PROPN
ejpam-3478	159	28	q2	q2	PROPN
ejpam-3478	159	29	(	(	PUNCT
ejpam-3478	159	30	w	w	PROPN
ejpam-3478	159	31	−	−	PROPN
ejpam-3478	159	32	l	l	NOUN
ejpam-3478	159	33	)	)	PUNCT
ejpam-3478	159	34	(	(	PUNCT
ejpam-3478	159	35	31	31	NUM
ejpam-3478	159	36	)	)	PUNCT
ejpam-3478	159	37	where	where	SCONJ
ejpam-3478	159	38	q1	q1	NOUN
ejpam-3478	159	39	=	=	PROPN
ejpam-3478	160	1	−	−	PROPN
ejpam-3478	161	1	(	(	PUNCT
ejpam-3478	161	2	α−	α−	ADP
ejpam-3478	161	3	ra	ra	NOUN
ejpam-3478	161	4	)	)	PUNCT
ejpam-3478	161	5	q2	q2	NOUN
ejpam-3478	161	6	+	+	CCONJ
ejpam-3478	161	7	qσρ	qσρ	NOUN
ejpam-3478	161	8	(	(	PUNCT
ejpam-3478	161	9	c−m−	c−m−	PROPN
ejpam-3478	161	10	rl	rl	PROPN
ejpam-3478	161	11	)	)	PUNCT
ejpam-3478	161	12	σ2q2	σ2q2	NOUN
ejpam-3478	161	13	(	(	PUNCT
ejpam-3478	161	14	γ	γ	PROPN
ejpam-3478	161	15	−	−	PROPN
ejpam-3478	161	16	1	1	NUM
ejpam-3478	161	17	)	)	PUNCT
ejpam-3478	161	18	(	(	PUNCT
ejpam-3478	161	19	1−	1−	NUM
ejpam-3478	161	20	ρ2	ρ2	NOUN
ejpam-3478	161	21	)	)	PUNCT
ejpam-3478	161	22	(	(	PUNCT
ejpam-3478	161	23	32	32	NUM
ejpam-3478	161	24	)	)	PUNCT
ejpam-3478	161	25	and	and	CCONJ
ejpam-3478	161	26	q2	q2	NOUN
ejpam-3478	161	27	=	=	SYM
ejpam-3478	161	28	−qσρ	−qσρ	PROPN
ejpam-3478	161	29	(	(	PUNCT
ejpam-3478	161	30	α−	α−	ADP
ejpam-3478	161	31	ra	ra	PROPN
ejpam-3478	161	32	)	)	PUNCT
ejpam-3478	162	1	+	+	CCONJ
ejpam-3478	162	2	σ2	σ2	NOUN
ejpam-3478	162	3	(	(	PUNCT
ejpam-3478	162	4	c−m−	c−m−	PROPN
ejpam-3478	162	5	rl	rl	PROPN
ejpam-3478	162	6	)	)	PUNCT
ejpam-3478	162	7	σ2q2	σ2q2	NOUN
ejpam-3478	162	8	(	(	PUNCT
ejpam-3478	162	9	γ	γ	PROPN
ejpam-3478	162	10	−	−	PROPN
ejpam-3478	162	11	1	1	NUM
ejpam-3478	162	12	)	)	PUNCT
ejpam-3478	162	13	(	(	PUNCT
ejpam-3478	162	14	1−	1−	NUM
ejpam-3478	162	15	ρ2	ρ2	NOUN
ejpam-3478	162	16	)	)	PUNCT
ejpam-3478	162	17	.	.	PUNCT
ejpam-3478	163	1	(	(	PUNCT
ejpam-3478	163	2	33	33	NUM
ejpam-3478	163	3	)	)	PUNCT
ejpam-3478	163	4	note	note	NOUN
ejpam-3478	163	5	that	that	SCONJ
ejpam-3478	163	6	the	the	DET
ejpam-3478	163	7	weights	weight	NOUN
ejpam-3478	163	8	w	w	NOUN
ejpam-3478	163	9	and	and	CCONJ
ejpam-3478	163	10	u	u	NOUN
ejpam-3478	163	11	are	be	AUX
ejpam-3478	163	12	time	time	NOUN
ejpam-3478	163	13	independent	independent	ADJ
ejpam-3478	163	14	depending	depend	VERB
ejpam-3478	163	15	on	on	ADP
ejpam-3478	163	16	the	the	DET
ejpam-3478	163	17	parameters	parameter	NOUN
ejpam-3478	163	18	α	α	NOUN
ejpam-3478	163	19	,	,	PUNCT
ejpam-3478	163	20	ra	ra	PROPN
ejpam-3478	163	21	,	,	PUNCT
ejpam-3478	163	22	rl	rl	X
ejpam-3478	163	23	,	,	PUNCT
ejpam-3478	163	24	q	q	X
ejpam-3478	163	25	,	,	PUNCT
ejpam-3478	163	26	γ	γ	PROPN
ejpam-3478	163	27	,	,	PUNCT
ejpam-3478	163	28	σ	σ	PROPN
ejpam-3478	163	29	,	,	PUNCT
ejpam-3478	163	30	ρ	ρ	PROPN
ejpam-3478	163	31	,	,	PUNCT
ejpam-3478	163	32	c	c	NOUN
ejpam-3478	163	33	,	,	PUNCT
ejpam-3478	163	34	m.	m.	NOUN
ejpam-3478	163	35	and	and	CCONJ
ejpam-3478	163	36	also	also	ADV
ejpam-3478	163	37	on	on	ADP
ejpam-3478	163	38	the	the	DET
ejpam-3478	163	39	ratio	ratio	NOUN
ejpam-3478	163	40	e	e	PROPN
ejpam-3478	163	41	w	w	PROPN
ejpam-3478	163	42	.	.	PUNCT
ejpam-3478	164	1	also	also	ADV
ejpam-3478	164	2	these	these	DET
ejpam-3478	164	3	weights	weight	NOUN
ejpam-3478	164	4	involve	involve	VERB
ejpam-3478	164	5	both	both	DET
ejpam-3478	164	6	rα	rα	ADJ
ejpam-3478	164	7	and	and	CCONJ
ejpam-3478	164	8	rl	rl	INTJ
ejpam-3478	164	9	and	and	CCONJ
ejpam-3478	164	10	they	they	PRON
ejpam-3478	164	11	have	have	AUX
ejpam-3478	164	12	only	only	ADV
ejpam-3478	164	13	been	be	AUX
ejpam-3478	164	14	assumed	assume	VERB
ejpam-3478	164	15	equal	equal	ADJ
ejpam-3478	164	16	to	to	PART
ejpam-3478	164	17	solve	solve	VERB
ejpam-3478	164	18	the	the	DET
ejpam-3478	164	19	full	full	ADJ
ejpam-3478	164	20	hamilton	hamilton	PROPN
ejpam-3478	164	21	-	-	PUNCT
ejpam-3478	164	22	jacobi	jacobi	PROPN
ejpam-3478	164	23	equation	equation	NOUN
ejpam-3478	164	24	to	to	ADP
ejpam-3478	164	25	this	this	DET
ejpam-3478	164	26	order	order	NOUN
ejpam-3478	164	27	.	.	PUNCT
ejpam-3478	165	1	when	when	SCONJ
ejpam-3478	165	2	we	we	PRON
ejpam-3478	165	3	go	go	VERB
ejpam-3478	165	4	to	to	ADP
ejpam-3478	165	5	the	the	DET
ejpam-3478	165	6	next	next	ADJ
ejpam-3478	165	7	order	order	NOUN
ejpam-3478	165	8	,	,	PUNCT
ejpam-3478	165	9	order	order	NOUN
ejpam-3478	165	10	ε	ε	PROPN
ejpam-3478	165	11	,	,	PUNCT
ejpam-3478	165	12	we	we	PRON
ejpam-3478	165	13	must	must	AUX
ejpam-3478	165	14	keep	keep	VERB
ejpam-3478	165	15	ra	ra	PROPN
ejpam-3478	165	16	and	and	CCONJ
ejpam-3478	165	17	rl	rl	VERB
ejpam-3478	165	18	in	in	ADP
ejpam-3478	165	19	the	the	DET
ejpam-3478	165	20	above	above	ADJ
ejpam-3478	165	21	equations	equation	NOUN
ejpam-3478	165	22	.	.	PUNCT
ejpam-3478	166	1	with	with	ADP
ejpam-3478	166	2	the	the	DET
ejpam-3478	166	3	value	value	NOUN
ejpam-3478	166	4	function	function	NOUN
ejpam-3478	166	5	of	of	ADP
ejpam-3478	166	6	the	the	DET
ejpam-3478	166	7	form	form	NOUN
ejpam-3478	166	8	j	j	PROPN
ejpam-3478	166	9	(	(	PUNCT
ejpam-3478	166	10	w	w	PROPN
ejpam-3478	166	11	,	,	PUNCT
ejpam-3478	166	12	l	l	PROPN
ejpam-3478	166	13	,	,	PUNCT
ejpam-3478	166	14	t	t	PROPN
ejpam-3478	166	15	)	)	PUNCT
ejpam-3478	166	16	=	=	SYM
ejpam-3478	166	17	a	a	DET
ejpam-3478	166	18	(	(	PUNCT
ejpam-3478	166	19	t	t	NOUN
ejpam-3478	166	20	)	)	PUNCT
ejpam-3478	166	21	(	(	PUNCT
ejpam-3478	166	22	w−l)γ	w−l)γ	NOUN
ejpam-3478	166	23	γ	γ	NOUN
ejpam-3478	166	24	and	and	CCONJ
ejpam-3478	166	25	its	its	PRON
ejpam-3478	166	26	respective	respective	ADJ
ejpam-3478	166	27	derivatives	derivative	NOUN
ejpam-3478	166	28	,	,	PUNCT
ejpam-3478	166	29	we	we	PRON
ejpam-3478	166	30	can	can	AUX
ejpam-3478	166	31	substitute	substitute	VERB
ejpam-3478	166	32	(	(	PUNCT
ejpam-3478	166	33	30	30	NUM
ejpam-3478	166	34	)	)	PUNCT
ejpam-3478	166	35	and	and	CCONJ
ejpam-3478	166	36	(	(	PUNCT
ejpam-3478	166	37	31	31	NUM
ejpam-3478	166	38	)	)	PUNCT
ejpam-3478	166	39	into	into	ADP
ejpam-3478	166	40	(	(	PUNCT
ejpam-3478	166	41	9	9	NUM
ejpam-3478	166	42	)	)	PUNCT
ejpam-3478	166	43	,	,	PUNCT
ejpam-3478	166	44	which	which	PRON
ejpam-3478	166	45	gives	give	VERB
ejpam-3478	166	46	0	0	NUM
ejpam-3478	166	47	=	=	SYM
ejpam-3478	166	48	{	{	PUNCT
ejpam-3478	166	49	(	(	PUNCT
ejpam-3478	166	50	w	w	NOUN
ejpam-3478	166	51	−	−	PROPN
ejpam-3478	166	52	l)γ	l)γ	NOUN
ejpam-3478	167	1	γ	γ	X
ejpam-3478	167	2	+	+	PROPN
ejpam-3478	167	3	a′	a′	PROPN
ejpam-3478	167	4	(	(	PUNCT
ejpam-3478	167	5	w	w	NOUN
ejpam-3478	167	6	−	−	PROPN
ejpam-3478	167	7	l)γ	l)γ	NOUN
ejpam-3478	167	8	γ	γ	X
ejpam-3478	167	9	+	+	X
ejpam-3478	167	10	(	(	PUNCT
ejpam-3478	167	11	α−	α−	ADP
ejpam-3478	167	12	ra)q1a	ra)q1a	NOUN
ejpam-3478	167	13	(	(	PUNCT
ejpam-3478	167	14	w	w	NOUN
ejpam-3478	167	15	−	−	NOUN
ejpam-3478	167	16	l)γ	l)γ	NOUN
ejpam-3478	167	17	+	+	CCONJ
ejpam-3478	167	18	1	1	NUM
ejpam-3478	167	19	2	2	NUM
ejpam-3478	167	20	σ2q2	σ2q2	NOUN
ejpam-3478	167	21	1	1	NUM
ejpam-3478	167	22	(	(	PUNCT
ejpam-3478	167	23	γ	γ	PROPN
ejpam-3478	167	24	−	−	PROPN
ejpam-3478	167	25	1)a	1)a	NUM
ejpam-3478	167	26	(	(	PUNCT
ejpam-3478	167	27	w	w	NOUN
ejpam-3478	167	28	−	−	PROPN
ejpam-3478	167	29	l)γ	l)γ	NOUN
ejpam-3478	167	30	−{c−m−	−{c−m−	NOUN
ejpam-3478	168	1	rl}q2a	rl}q2a	NOUN
ejpam-3478	168	2	(	(	PUNCT
ejpam-3478	168	3	w	w	NOUN
ejpam-3478	168	4	−	−	NOUN
ejpam-3478	168	5	l)γ	l)γ	NOUN
ejpam-3478	168	6	+	+	CCONJ
ejpam-3478	168	7	rawa	rawa	PROPN
ejpam-3478	168	8	(	(	PUNCT
ejpam-3478	168	9	w	w	PROPN
ejpam-3478	168	10	−	−	PROPN
ejpam-3478	168	11	l)γ−1	l)γ−1	NOUN
ejpam-3478	168	12	−	−	PROPN
ejpam-3478	168	13	rlla	rlla	NOUN
ejpam-3478	168	14	(	(	PUNCT
ejpam-3478	168	15	w	w	NOUN
ejpam-3478	168	16	−	−	PROPN
ejpam-3478	168	17	l)γ−1	l)γ−1	PROPN
ejpam-3478	168	18	−qσρq1q2	−qσρq1q2	PROPN
ejpam-3478	168	19	(	(	PUNCT
ejpam-3478	168	20	γ	γ	PROPN
ejpam-3478	168	21	−	−	PROPN
ejpam-3478	168	22	1)a	1)a	NUM
ejpam-3478	168	23	(	(	PUNCT
ejpam-3478	168	24	w	w	NOUN
ejpam-3478	168	25	−	−	NOUN
ejpam-3478	168	26	l)γ	l)γ	NOUN
ejpam-3478	168	27	+	+	CCONJ
ejpam-3478	168	28	1	1	NUM
ejpam-3478	168	29	2	2	NUM
ejpam-3478	168	30	q2q2	q2q2	ADP
ejpam-3478	168	31	2	2	NUM
ejpam-3478	168	32	(	(	PUNCT
ejpam-3478	168	33	γ	γ	PROPN
ejpam-3478	168	34	−	−	PROPN
ejpam-3478	168	35	1)a	1)a	NUM
ejpam-3478	168	36	(	(	PUNCT
ejpam-3478	168	37	w	w	NOUN
ejpam-3478	168	38	−	−	PROPN
ejpam-3478	168	39	l)γ	l)γ	NOUN
ejpam-3478	168	40	}	}	PUNCT
ejpam-3478	168	41	(	(	PUNCT
ejpam-3478	168	42	34	34	NUM
ejpam-3478	168	43	)	)	PUNCT
ejpam-3478	168	44	dividing	dividing	NOUN
ejpam-3478	168	45	(	(	PUNCT
ejpam-3478	168	46	34	34	NUM
ejpam-3478	168	47	)	)	PUNCT
ejpam-3478	168	48	by	by	ADP
ejpam-3478	168	49	(	(	PUNCT
ejpam-3478	168	50	w	w	NOUN
ejpam-3478	168	51	−	−	PROPN
ejpam-3478	168	52	l)γ	l)γ	NOUN
ejpam-3478	168	53	gives	give	VERB
ejpam-3478	168	54	0	0	NUM
ejpam-3478	169	1	=	=	SYM
ejpam-3478	169	2	{	{	PUNCT
ejpam-3478	169	3	1	1	NUM
ejpam-3478	169	4	γ	γ	X
ejpam-3478	169	5	+	+	PROPN
ejpam-3478	169	6	a′	a′	PROPN
ejpam-3478	169	7	γ	γ	X
ejpam-3478	169	8	+	+	X
ejpam-3478	169	9	(	(	PUNCT
ejpam-3478	169	10	(	(	PUNCT
ejpam-3478	169	11	α−	α−	ADP
ejpam-3478	169	12	ra)q1	ra)q1	ADJ
ejpam-3478	169	13	+	+	CCONJ
ejpam-3478	169	14	1	1	NUM
ejpam-3478	169	15	2	2	NUM
ejpam-3478	169	16	σ2q2	σ2q2	NOUN
ejpam-3478	169	17	1	1	NUM
ejpam-3478	169	18	(	(	PUNCT
ejpam-3478	169	19	γ	γ	PROPN
ejpam-3478	169	20	−	−	PROPN
ejpam-3478	169	21	1)−	1)−	PROPN
ejpam-3478	169	22	{	{	PUNCT
ejpam-3478	169	23	c−m−	c−m−	PROPN
ejpam-3478	169	24	rl}q2	rl}q2	PROPN
ejpam-3478	169	25	−qσρq1q2	−qσρq1q2	PROPN
ejpam-3478	169	26	(	(	PUNCT
ejpam-3478	169	27	γ	γ	PROPN
ejpam-3478	169	28	−	−	PROPN
ejpam-3478	169	29	1	1	NUM
ejpam-3478	169	30	)	)	PUNCT
ejpam-3478	169	31	+	+	CCONJ
ejpam-3478	169	32	1	1	NUM
ejpam-3478	169	33	2	2	NUM
ejpam-3478	169	34	q2q2	q2q2	ADP
ejpam-3478	169	35	2	2	NUM
ejpam-3478	169	36	(	(	PUNCT
ejpam-3478	169	37	γ	γ	NOUN
ejpam-3478	169	38	−	−	PROPN
ejpam-3478	169	39	1	1	NUM
ejpam-3478	169	40	)	)	PUNCT
ejpam-3478	169	41	)	)	PUNCT
ejpam-3478	170	1	a	a	DET
ejpam-3478	170	2	+	+	ADJ
ejpam-3478	170	3	(	(	PUNCT
ejpam-3478	170	4	raw	raw	ADJ
ejpam-3478	170	5	−	−	NOUN
ejpam-3478	170	6	rll)a	rll)a	PROPN
ejpam-3478	170	7	(	(	PUNCT
ejpam-3478	170	8	w	w	PROPN
ejpam-3478	170	9	−	−	PROPN
ejpam-3478	170	10	l	l	NOUN
ejpam-3478	170	11	)	)	PUNCT
ejpam-3478	170	12	}	}	PUNCT
ejpam-3478	170	13	.	.	PUNCT
ejpam-3478	171	1	(	(	PUNCT
ejpam-3478	171	2	35	35	NUM
ejpam-3478	171	3	)	)	PUNCT
ejpam-3478	171	4	c.	c.	PROPN
ejpam-3478	171	5	atkinson	atkinson	PROPN
ejpam-3478	171	6	,	,	PUNCT
ejpam-3478	171	7	s.	s.	PROPN
ejpam-3478	171	8	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	171	9	,	,	PUNCT
ejpam-3478	171	10	p.	p.	PROPN
ejpam-3478	171	11	ingpochai	ingpochai	PROPN
ejpam-3478	171	12	/	/	SYM
ejpam-3478	171	13	eur	eur	PROPN
ejpam-3478	171	14	.	.	PUNCT
ejpam-3478	172	1	j.	j.	PROPN
ejpam-3478	172	2	pure	pure	PROPN
ejpam-3478	172	3	appl	appl	PROPN
ejpam-3478	172	4	.	.	PROPN
ejpam-3478	172	5	math	math	PROPN
ejpam-3478	172	6	,	,	PUNCT
ejpam-3478	172	7	12	12	NUM
ejpam-3478	172	8	(	(	PUNCT
ejpam-3478	172	9	3	3	NUM
ejpam-3478	172	10	)	)	PUNCT
ejpam-3478	172	11	(	(	PUNCT
ejpam-3478	172	12	2019	2019	NUM
ejpam-3478	172	13	)	)	PUNCT
ejpam-3478	172	14	,	,	PUNCT
ejpam-3478	172	15	1315	1315	NUM
ejpam-3478	172	16	-	-	SYM
ejpam-3478	172	17	1336	1336	NUM
ejpam-3478	172	18	1323	1323	NUM
ejpam-3478	172	19	4.1.1	4.1.1	NUM
ejpam-3478	172	20	.	.	PUNCT
ejpam-3478	173	1	case	case	NOUN
ejpam-3478	173	2	:	:	PUNCT
ejpam-3478	173	3	ra	ra	PROPN
ejpam-3478	173	4	≡	≡	PROPN
ejpam-3478	173	5	rl	rl	VERB
ejpam-3478	173	6	the	the	DET
ejpam-3478	173	7	equation	equation	NOUN
ejpam-3478	173	8	above	above	ADV
ejpam-3478	173	9	has	have	VERB
ejpam-3478	173	10	a	a	DET
ejpam-3478	173	11	special	special	ADJ
ejpam-3478	173	12	solution	solution	NOUN
ejpam-3478	173	13	when	when	SCONJ
ejpam-3478	173	14	ra	ra	PROPN
ejpam-3478	173	15	≡	≡	PROPN
ejpam-3478	173	16	rl	rl	PROPN
ejpam-3478	173	17	.	.	PUNCT
ejpam-3478	174	1	in	in	ADP
ejpam-3478	174	2	this	this	DET
ejpam-3478	174	3	particular	particular	ADJ
ejpam-3478	174	4	case	case	NOUN
ejpam-3478	174	5	,	,	PUNCT
ejpam-3478	174	6	we	we	PRON
ejpam-3478	174	7	can	can	AUX
ejpam-3478	174	8	cancel	cancel	VERB
ejpam-3478	174	9	out	out	ADP
ejpam-3478	174	10	w−l	w−l	NOUN
ejpam-3478	174	11	and	and	CCONJ
ejpam-3478	174	12	solve	solve	VERB
ejpam-3478	174	13	for	for	ADP
ejpam-3478	174	14	a	a	DET
ejpam-3478	174	15	(	(	PUNCT
ejpam-3478	174	16	t	t	PROPN
ejpam-3478	174	17	)	)	PUNCT
ejpam-3478	174	18	.	.	PUNCT
ejpam-3478	175	1	from	from	ADP
ejpam-3478	175	2	a	a	DET
ejpam-3478	175	3	practical	practical	ADJ
ejpam-3478	175	4	perspective	perspective	NOUN
ejpam-3478	175	5	,	,	PUNCT
ejpam-3478	175	6	equating	equate	VERB
ejpam-3478	175	7	ra	ra	PROPN
ejpam-3478	175	8	to	to	PART
ejpam-3478	175	9	rl	rl	PROPN
ejpam-3478	175	10	implies	imply	VERB
ejpam-3478	175	11	that	that	SCONJ
ejpam-3478	175	12	the	the	DET
ejpam-3478	175	13	risk	risk	NOUN
ejpam-3478	175	14	-	-	PUNCT
ejpam-3478	175	15	free	free	ADJ
ejpam-3478	175	16	interest	interest	NOUN
ejpam-3478	175	17	rate	rate	NOUN
ejpam-3478	175	18	on	on	ADP
ejpam-3478	175	19	the	the	DET
ejpam-3478	175	20	asset	asset	NOUN
ejpam-3478	175	21	side	side	NOUN
ejpam-3478	175	22	is	be	AUX
ejpam-3478	175	23	assumed	assume	VERB
ejpam-3478	175	24	to	to	PART
ejpam-3478	175	25	be	be	AUX
ejpam-3478	175	26	the	the	DET
ejpam-3478	175	27	same	same	ADJ
ejpam-3478	175	28	as	as	ADP
ejpam-3478	175	29	the	the	DET
ejpam-3478	175	30	borrowing	borrowing	NOUN
ejpam-3478	175	31	rate	rate	NOUN
ejpam-3478	175	32	on	on	ADP
ejpam-3478	175	33	the	the	DET
ejpam-3478	175	34	liability	liability	NOUN
ejpam-3478	175	35	side	side	NOUN
ejpam-3478	175	36	.	.	PUNCT
ejpam-3478	176	1	this	this	DET
ejpam-3478	176	2	situation	situation	NOUN
ejpam-3478	176	3	is	be	AUX
ejpam-3478	176	4	likely	likely	ADJ
ejpam-3478	176	5	to	to	PART
ejpam-3478	176	6	be	be	AUX
ejpam-3478	176	7	found	find	VERB
ejpam-3478	176	8	in	in	ADP
ejpam-3478	176	9	developed	develop	VERB
ejpam-3478	176	10	markets	market	NOUN
ejpam-3478	176	11	where	where	SCONJ
ejpam-3478	176	12	policyholders	policyholder	NOUN
ejpam-3478	176	13	exhibit	exhibit	VERB
ejpam-3478	176	14	a	a	DET
ejpam-3478	176	15	high	high	ADJ
ejpam-3478	176	16	level	level	NOUN
ejpam-3478	176	17	of	of	ADP
ejpam-3478	176	18	financial	financial	ADJ
ejpam-3478	176	19	literacy	literacy	NOUN
ejpam-3478	176	20	and	and	CCONJ
ejpam-3478	176	21	hence	hence	ADV
ejpam-3478	176	22	will	will	AUX
ejpam-3478	176	23	demand	demand	VERB
ejpam-3478	176	24	that	that	SCONJ
ejpam-3478	176	25	the	the	DET
ejpam-3478	176	26	compensation	compensation	NOUN
ejpam-3478	176	27	for	for	ADP
ejpam-3478	176	28	opportunity	opportunity	NOUN
ejpam-3478	176	29	cost	cost	NOUN
ejpam-3478	176	30	be	be	VERB
ejpam-3478	176	31	on	on	ADP
ejpam-3478	176	32	par	par	NOUN
ejpam-3478	176	33	with	with	ADP
ejpam-3478	176	34	the	the	DET
ejpam-3478	176	35	observed	observe	VERB
ejpam-3478	176	36	riskfree	riskfree	NOUN
ejpam-3478	176	37	rate	rate	NOUN
ejpam-3478	176	38	.	.	PUNCT
ejpam-3478	177	1	hence	hence	ADV
ejpam-3478	177	2	,	,	PUNCT
ejpam-3478	177	3	for	for	ADP
ejpam-3478	177	4	this	this	DET
ejpam-3478	177	5	case	case	NOUN
ejpam-3478	177	6	,	,	PUNCT
ejpam-3478	177	7	we	we	PRON
ejpam-3478	177	8	can	can	AUX
ejpam-3478	177	9	solve	solve	VERB
ejpam-3478	177	10	for	for	ADP
ejpam-3478	177	11	a	a	DET
ejpam-3478	177	12	(	(	PUNCT
ejpam-3478	177	13	t	t	NOUN
ejpam-3478	177	14	)	)	PUNCT
ejpam-3478	177	15	.	.	PUNCT
ejpam-3478	178	1	to	to	PART
ejpam-3478	178	2	solve	solve	VERB
ejpam-3478	178	3	for	for	ADP
ejpam-3478	178	4	a	a	DET
ejpam-3478	178	5	(	(	PUNCT
ejpam-3478	178	6	t	t	NOUN
ejpam-3478	178	7	)	)	PUNCT
ejpam-3478	178	8	,	,	PUNCT
ejpam-3478	178	9	consider	consider	VERB
ejpam-3478	178	10	0	0	NUM
ejpam-3478	178	11	=	=	SYM
ejpam-3478	178	12	1	1	NUM
ejpam-3478	179	1	+	+	NOUN
ejpam-3478	179	2	a′	a′	NOUN
ejpam-3478	179	3	+	+	CCONJ
ejpam-3478	179	4	(	(	PUNCT
ejpam-3478	179	5	(	(	PUNCT
ejpam-3478	179	6	α−	α−	ADP
ejpam-3478	179	7	ra)q1	ra)q1	ADJ
ejpam-3478	179	8	+	+	CCONJ
ejpam-3478	179	9	1	1	NUM
ejpam-3478	179	10	2	2	NUM
ejpam-3478	179	11	σ2q2	σ2q2	NOUN
ejpam-3478	179	12	1	1	NUM
ejpam-3478	179	13	(	(	PUNCT
ejpam-3478	179	14	γ	γ	PROPN
ejpam-3478	179	15	−	−	PROPN
ejpam-3478	179	16	1)−	1)−	PROPN
ejpam-3478	179	17	{	{	PUNCT
ejpam-3478	179	18	c−m−	c−m−	PROPN
ejpam-3478	179	19	rl}q2	rl}q2	PROPN
ejpam-3478	179	20	−qσρq1q2	−qσρq1q2	PROPN
ejpam-3478	179	21	(	(	PUNCT
ejpam-3478	179	22	γ	γ	PROPN
ejpam-3478	179	23	−	−	PROPN
ejpam-3478	179	24	1	1	NUM
ejpam-3478	179	25	)	)	PUNCT
ejpam-3478	179	26	+	+	CCONJ
ejpam-3478	179	27	1	1	NUM
ejpam-3478	179	28	2	2	NUM
ejpam-3478	179	29	q2q2	q2q2	ADP
ejpam-3478	179	30	2	2	NUM
ejpam-3478	179	31	(	(	PUNCT
ejpam-3478	179	32	γ	γ	NOUN
ejpam-3478	179	33	−	−	PROPN
ejpam-3478	179	34	1	1	NUM
ejpam-3478	179	35	)	)	PUNCT
ejpam-3478	179	36	+	+	NUM
ejpam-3478	179	37	ra	ra	X
ejpam-3478	179	38	)	)	PUNCT
ejpam-3478	179	39	γa	γa	PROPN
ejpam-3478	179	40	.	.	PUNCT
ejpam-3478	180	1	(	(	PUNCT
ejpam-3478	180	2	36	36	NUM
ejpam-3478	180	3	)	)	PUNCT
ejpam-3478	180	4	we	we	PRON
ejpam-3478	180	5	can	can	AUX
ejpam-3478	180	6	rewrite	rewrite	VERB
ejpam-3478	180	7	(	(	PUNCT
ejpam-3478	180	8	34	34	NUM
ejpam-3478	180	9	)	)	PUNCT
ejpam-3478	180	10	by	by	ADP
ejpam-3478	180	11	letting	let	VERB
ejpam-3478	180	12	κ	κ	X
ejpam-3478	180	13	=	=	PUNCT
ejpam-3478	180	14	(	(	PUNCT
ejpam-3478	180	15	(	(	PUNCT
ejpam-3478	180	16	α−	α−	ADP
ejpam-3478	180	17	ra)q1	ra)q1	ADJ
ejpam-3478	181	1	+	+	CCONJ
ejpam-3478	181	2	1	1	NUM
ejpam-3478	181	3	2σ	2σ	NUM
ejpam-3478	181	4	2q2	2q2	NUM
ejpam-3478	181	5	1	1	NUM
ejpam-3478	181	6	(	(	PUNCT
ejpam-3478	181	7	γ	γ	PROPN
ejpam-3478	181	8	−	−	PROPN
ejpam-3478	181	9	1)−	1)−	PROPN
ejpam-3478	181	10	{	{	PUNCT
ejpam-3478	181	11	c−m−	c−m−	PROPN
ejpam-3478	181	12	rl}q2	rl}q2	PROPN
ejpam-3478	181	13	−qσρq1q2	−qσρq1q2	PROPN
ejpam-3478	181	14	(	(	PUNCT
ejpam-3478	181	15	γ	γ	PROPN
ejpam-3478	181	16	−	−	PROPN
ejpam-3478	181	17	1	1	NUM
ejpam-3478	181	18	)	)	PUNCT
ejpam-3478	181	19	+	+	CCONJ
ejpam-3478	181	20	1	1	NUM
ejpam-3478	181	21	2q	2q	NUM
ejpam-3478	181	22	2q2	2q2	NUM
ejpam-3478	181	23	2	2	NUM
ejpam-3478	181	24	(	(	PUNCT
ejpam-3478	181	25	γ	γ	NOUN
ejpam-3478	181	26	−	−	PROPN
ejpam-3478	181	27	1	1	NUM
ejpam-3478	181	28	)	)	PUNCT
ejpam-3478	181	29	+	+	NUM
ejpam-3478	181	30	ra	ra	NOUN
ejpam-3478	181	31	)	)	PUNCT
ejpam-3478	181	32	γ	γ	PROPN
ejpam-3478	181	33	then	then	ADV
ejpam-3478	181	34	0	0	X
ejpam-3478	181	35	=	=	SYM
ejpam-3478	181	36	da	da	ADJ
ejpam-3478	181	37	dt	dt	X
ejpam-3478	182	1	+	+	CCONJ
ejpam-3478	182	2	κa+	κa+	ADJ
ejpam-3478	182	3	1	1	NUM
ejpam-3478	182	4	and	and	CCONJ
ejpam-3478	182	5	a	a	DET
ejpam-3478	182	6	(	(	PUNCT
ejpam-3478	182	7	t	t	NOUN
ejpam-3478	182	8	)	)	PUNCT
ejpam-3478	182	9	=	=	PUNCT
ejpam-3478	183	1	−1	−1	NOUN
ejpam-3478	183	2	κ	κ	NOUN
ejpam-3478	183	3	+	+	NOUN
ejpam-3478	183	4	e−κtc1	e−κtc1	ADV
ejpam-3478	183	5	.	.	PUNCT
ejpam-3478	184	1	4.1.2	4.1.2	X
ejpam-3478	184	2	.	.	PUNCT
ejpam-3478	184	3	case	case	NOUN
ejpam-3478	184	4	:	:	PUNCT
ejpam-3478	184	5	ra	ra	PROPN
ejpam-3478	184	6	6=	6=	PROPN
ejpam-3478	184	7	rl	rl	ADP
ejpam-3478	184	8	it	it	PRON
ejpam-3478	184	9	is	be	AUX
ejpam-3478	184	10	clear	clear	ADJ
ejpam-3478	184	11	from	from	ADP
ejpam-3478	184	12	equation	equation	NOUN
ejpam-3478	184	13	(	(	PUNCT
ejpam-3478	184	14	35	35	NUM
ejpam-3478	184	15	)	)	PUNCT
ejpam-3478	184	16	that	that	SCONJ
ejpam-3478	184	17	the	the	DET
ejpam-3478	184	18	choice	choice	NOUN
ejpam-3478	184	19	of	of	ADP
ejpam-3478	184	20	j	j	PROPN
ejpam-3478	184	21	(	(	PUNCT
ejpam-3478	184	22	w	w	PROPN
ejpam-3478	184	23	,	,	PUNCT
ejpam-3478	184	24	l	l	NOUN
ejpam-3478	184	25	,	,	PUNCT
ejpam-3478	184	26	t	t	NOUN
ejpam-3478	184	27	)	)	PUNCT
ejpam-3478	184	28	=	=	PUNCT
ejpam-3478	185	1	a	a	PRON
ejpam-3478	185	2	(	(	PUNCT
ejpam-3478	185	3	t	t	NOUN
ejpam-3478	185	4	)	)	PUNCT
ejpam-3478	185	5	(	(	PUNCT
ejpam-3478	185	6	w−l)γ	w−l)γ	NOUN
ejpam-3478	185	7	γ	γ	PROPN
ejpam-3478	185	8	is	be	AUX
ejpam-3478	185	9	a	a	DET
ejpam-3478	185	10	solution	solution	NOUN
ejpam-3478	185	11	only	only	ADV
ejpam-3478	185	12	in	in	ADP
ejpam-3478	185	13	the	the	DET
ejpam-3478	185	14	case	case	NOUN
ejpam-3478	185	15	when	when	SCONJ
ejpam-3478	185	16	ra	ra	PROPN
ejpam-3478	185	17	=	=	VERB
ejpam-3478	185	18	rl	rl	VERB
ejpam-3478	185	19	because	because	SCONJ
ejpam-3478	185	20	only	only	ADV
ejpam-3478	185	21	then	then	ADV
ejpam-3478	185	22	do	do	AUX
ejpam-3478	185	23	w	w	NOUN
ejpam-3478	185	24	and	and	CCONJ
ejpam-3478	185	25	l	l	PROPN
ejpam-3478	185	26	disappear	disappear	VERB
ejpam-3478	185	27	in	in	ADP
ejpam-3478	185	28	equation	equation	NOUN
ejpam-3478	185	29	(	(	PUNCT
ejpam-3478	185	30	35	35	NUM
ejpam-3478	185	31	)	)	PUNCT
ejpam-3478	185	32	leaving	leave	VERB
ejpam-3478	185	33	an	an	DET
ejpam-3478	185	34	ordinary	ordinary	ADJ
ejpam-3478	185	35	differential	differential	ADJ
ejpam-3478	185	36	equation	equation	NOUN
ejpam-3478	185	37	for	for	ADP
ejpam-3478	185	38	a	a	DET
ejpam-3478	185	39	(	(	PUNCT
ejpam-3478	185	40	t	t	PROPN
ejpam-3478	185	41	)	)	PUNCT
ejpam-3478	185	42	.	.	PUNCT
ejpam-3478	186	1	however	however	ADV
ejpam-3478	186	2	,	,	PUNCT
ejpam-3478	186	3	if	if	SCONJ
ejpam-3478	186	4	the	the	DET
ejpam-3478	186	5	difference	difference	NOUN
ejpam-3478	186	6	between	between	ADP
ejpam-3478	186	7	ra	ra	PROPN
ejpam-3478	186	8	and	and	CCONJ
ejpam-3478	186	9	rl	rl	PROPN
ejpam-3478	186	10	is	be	AUX
ejpam-3478	186	11	assumed	assume	VERB
ejpam-3478	186	12	small	small	ADJ
ejpam-3478	186	13	it	it	PRON
ejpam-3478	186	14	is	be	AUX
ejpam-3478	186	15	possible	possible	ADJ
ejpam-3478	186	16	to	to	PART
ejpam-3478	186	17	solve	solve	VERB
ejpam-3478	186	18	equations	equation	NOUN
ejpam-3478	186	19	(	(	PUNCT
ejpam-3478	186	20	11	11	NUM
ejpam-3478	186	21	)	)	PUNCT
ejpam-3478	186	22	,	,	PUNCT
ejpam-3478	186	23	(	(	PUNCT
ejpam-3478	186	24	12	12	NUM
ejpam-3478	186	25	)	)	PUNCT
ejpam-3478	186	26	,	,	PUNCT
ejpam-3478	186	27	and	and	CCONJ
ejpam-3478	186	28	(	(	PUNCT
ejpam-3478	186	29	13	13	NUM
ejpam-3478	186	30	)	)	PUNCT
ejpam-3478	186	31	as	as	ADP
ejpam-3478	186	32	a	a	DET
ejpam-3478	186	33	power	power	NOUN
ejpam-3478	186	34	series	series	NOUN
ejpam-3478	186	35	in	in	ADP
ejpam-3478	186	36	ε	ε	PROPN
ejpam-3478	186	37	where	where	SCONJ
ejpam-3478	186	38	ε	ε	PROPN
ejpam-3478	186	39	is	be	AUX
ejpam-3478	186	40	the	the	DET
ejpam-3478	186	41	difference	difference	NOUN
ejpam-3478	186	42	between	between	ADP
ejpam-3478	186	43	ra	ra	PROPN
ejpam-3478	186	44	and	and	CCONJ
ejpam-3478	186	45	rl	rl	PROPN
ejpam-3478	186	46	.	.	PUNCT
ejpam-3478	187	1	in	in	ADP
ejpam-3478	187	2	less	less	ADJ
ejpam-3478	187	3	developed	develop	VERB
ejpam-3478	187	4	markets	market	NOUN
ejpam-3478	187	5	,	,	PUNCT
ejpam-3478	187	6	the	the	DET
ejpam-3478	187	7	policyholders	policyholder	NOUN
ejpam-3478	187	8	may	may	AUX
ejpam-3478	187	9	not	not	PART
ejpam-3478	187	10	demand	demand	VERB
ejpam-3478	187	11	that	that	SCONJ
ejpam-3478	187	12	the	the	DET
ejpam-3478	187	13	return	return	NOUN
ejpam-3478	187	14	on	on	ADP
ejpam-3478	187	15	their	their	PRON
ejpam-3478	187	16	policies	policy	NOUN
ejpam-3478	187	17	to	to	PART
ejpam-3478	187	18	match	match	VERB
ejpam-3478	187	19	the	the	DET
ejpam-3478	187	20	observed	observe	VERB
ejpam-3478	187	21	risk	risk	NOUN
ejpam-3478	187	22	free	free	ADJ
ejpam-3478	187	23	asset	asset	NOUN
ejpam-3478	187	24	unlike	unlike	ADP
ejpam-3478	187	25	the	the	DET
ejpam-3478	187	26	previous	previous	ADJ
ejpam-3478	187	27	case	case	NOUN
ejpam-3478	187	28	.	.	PUNCT
ejpam-3478	188	1	we	we	PRON
ejpam-3478	188	2	assume	assume	VERB
ejpam-3478	188	3	here	here	ADV
ejpam-3478	188	4	that	that	SCONJ
ejpam-3478	188	5	|ε|	|ε|	DET
ejpam-3478	188	6	�	�	PROPN
ejpam-3478	188	7	ra	ra	PROPN
ejpam-3478	188	8	and	and	CCONJ
ejpam-3478	188	9	describe	describe	VERB
ejpam-3478	188	10	the	the	DET
ejpam-3478	188	11	method	method	NOUN
ejpam-3478	188	12	for	for	ADP
ejpam-3478	188	13	determining	determine	VERB
ejpam-3478	188	14	the	the	DET
ejpam-3478	188	15	order	order	NOUN
ejpam-3478	188	16	ε	ε	PROPN
ejpam-3478	188	17	correction	correction	NOUN
ejpam-3478	188	18	we	we	PRON
ejpam-3478	188	19	generalise	generalise	VERB
ejpam-3478	188	20	the	the	DET
ejpam-3478	188	21	method	method	NOUN
ejpam-3478	188	22	to	to	PART
ejpam-3478	188	23	get	get	VERB
ejpam-3478	188	24	higher	high	ADJ
ejpam-3478	188	25	order	order	NOUN
ejpam-3478	188	26	terms	term	NOUN
ejpam-3478	188	27	in	in	ADP
ejpam-3478	188	28	the	the	DET
ejpam-3478	188	29	appendix	appendix	NOUN
ejpam-3478	188	30	.	.	PUNCT
ejpam-3478	189	1	we	we	PRON
ejpam-3478	189	2	write	write	VERB
ejpam-3478	189	3	j	j	PROPN
ejpam-3478	189	4	=	=	SYM
ejpam-3478	189	5	j0	j0	PROPN
ejpam-3478	189	6	+	+	CCONJ
ejpam-3478	189	7	εj1	εj1	NOUN
ejpam-3478	189	8	where	where	SCONJ
ejpam-3478	189	9	j0	j0	PROPN
ejpam-3478	189	10	is	be	AUX
ejpam-3478	189	11	the	the	DET
ejpam-3478	189	12	value	value	NOUN
ejpam-3478	189	13	function	function	NOUN
ejpam-3478	189	14	determined	determine	VERB
ejpam-3478	189	15	in	in	ADP
ejpam-3478	189	16	the	the	DET
ejpam-3478	189	17	last	last	ADJ
ejpam-3478	189	18	section	section	NOUN
ejpam-3478	189	19	.	.	PUNCT
ejpam-3478	190	1	note	note	VERB
ejpam-3478	190	2	that	that	SCONJ
ejpam-3478	190	3	when	when	SCONJ
ejpam-3478	190	4	ε	ε	PROPN
ejpam-3478	190	5	=	=	SYM
ejpam-3478	190	6	0	0	PROPN
ejpam-3478	190	7	,	,	PUNCT
ejpam-3478	190	8	we	we	PRON
ejpam-3478	190	9	have	have	VERB
ejpam-3478	190	10	the	the	DET
ejpam-3478	190	11	previous	previous	ADJ
ejpam-3478	190	12	case	case	NOUN
ejpam-3478	190	13	and	and	CCONJ
ejpam-3478	190	14	the	the	DET
ejpam-3478	190	15	value	value	NOUN
ejpam-3478	190	16	function	function	NOUN
ejpam-3478	190	17	j	j	PROPN
ejpam-3478	190	18	.	.	PUNCT
ejpam-3478	191	1	now	now	ADV
ejpam-3478	191	2	we	we	PRON
ejpam-3478	191	3	write	write	VERB
ejpam-3478	191	4	ww	ww	PROPN
ejpam-3478	191	5	=	=	SYM
ejpam-3478	191	6	w	w	PROPN
ejpam-3478	191	7	,	,	PUNCT
ejpam-3478	191	8	c.	c.	PROPN
ejpam-3478	191	9	atkinson	atkinson	PROPN
ejpam-3478	191	10	,	,	PUNCT
ejpam-3478	191	11	s.	s.	PROPN
ejpam-3478	191	12	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	191	13	,	,	PUNCT
ejpam-3478	191	14	p.	p.	PROPN
ejpam-3478	191	15	ingpochai	ingpochai	PROPN
ejpam-3478	191	16	/	/	SYM
ejpam-3478	191	17	eur	eur	PROPN
ejpam-3478	191	18	.	.	PUNCT
ejpam-3478	192	1	j.	j.	PROPN
ejpam-3478	192	2	pure	pure	PROPN
ejpam-3478	192	3	appl	appl	PROPN
ejpam-3478	192	4	.	.	PROPN
ejpam-3478	192	5	math	math	PROPN
ejpam-3478	192	6	,	,	PUNCT
ejpam-3478	192	7	12	12	NUM
ejpam-3478	192	8	(	(	PUNCT
ejpam-3478	192	9	3	3	NUM
ejpam-3478	192	10	)	)	PUNCT
ejpam-3478	192	11	(	(	PUNCT
ejpam-3478	192	12	2019	2019	NUM
ejpam-3478	192	13	)	)	PUNCT
ejpam-3478	192	14	,	,	PUNCT
ejpam-3478	192	15	1315	1315	NUM
ejpam-3478	192	16	-	-	SYM
ejpam-3478	192	17	1336	1336	NUM
ejpam-3478	192	18	1324	1324	NUM
ejpam-3478	192	19	ul	ul	NOUN
ejpam-3478	193	1	=	=	SYM
ejpam-3478	193	2	u	u	NOUN
ejpam-3478	193	3	and	and	CCONJ
ejpam-3478	193	4	expand	expand	VERB
ejpam-3478	193	5	as	as	ADP
ejpam-3478	193	6	w	w	PROPN
ejpam-3478	193	7	=	=	SYM
ejpam-3478	193	8	w0	w0	PROPN
ejpam-3478	193	9	+	+	CCONJ
ejpam-3478	193	10	εw1	εw1	PROPN
ejpam-3478	193	11	+	+	X
ejpam-3478	193	12	o	o	X
ejpam-3478	193	13	(	(	PUNCT
ejpam-3478	193	14	ε2	ε2	ADJ
ejpam-3478	193	15	)	)	PUNCT
ejpam-3478	193	16	u	u	NOUN
ejpam-3478	193	17	=	=	PUNCT
ejpam-3478	193	18	u0	u0	ADJ
ejpam-3478	193	19	+	+	CCONJ
ejpam-3478	193	20	εu1	εu1	X
ejpam-3478	194	1	+	+	X
ejpam-3478	194	2	o	o	X
ejpam-3478	194	3	(	(	PUNCT
ejpam-3478	194	4	ε2	ε2	PROPN
ejpam-3478	194	5	)	)	PUNCT
ejpam-3478	194	6	where	where	SCONJ
ejpam-3478	194	7	w0	w0	PROPN
ejpam-3478	194	8	and	and	CCONJ
ejpam-3478	194	9	u0	u0	PROPN
ejpam-3478	194	10	are	be	AUX
ejpam-3478	194	11	the	the	DET
ejpam-3478	194	12	solutions	solution	NOUN
ejpam-3478	194	13	of	of	ADP
ejpam-3478	194	14	equations	equation	NOUN
ejpam-3478	194	15	(	(	PUNCT
ejpam-3478	194	16	30	30	NUM
ejpam-3478	194	17	)	)	PUNCT
ejpam-3478	194	18	and	and	CCONJ
ejpam-3478	194	19	(	(	PUNCT
ejpam-3478	194	20	31	31	NUM
ejpam-3478	194	21	)	)	PUNCT
ejpam-3478	194	22	where	where	SCONJ
ejpam-3478	194	23	j	j	PROPN
ejpam-3478	194	24	=	=	PROPN
ejpam-3478	194	25	j0	j0	PROPN
ejpam-3478	194	26	.	.	PUNCT
ejpam-3478	195	1	with	with	ADP
ejpam-3478	195	2	the	the	DET
ejpam-3478	195	3	above	above	ADJ
ejpam-3478	195	4	notation	notation	NOUN
ejpam-3478	195	5	we	we	PRON
ejpam-3478	195	6	can	can	AUX
ejpam-3478	195	7	expand	expand	VERB
ejpam-3478	195	8	equations	equation	NOUN
ejpam-3478	195	9	(	(	PUNCT
ejpam-3478	195	10	11	11	NUM
ejpam-3478	195	11	)	)	PUNCT
ejpam-3478	195	12	and	and	CCONJ
ejpam-3478	195	13	(	(	PUNCT
ejpam-3478	195	14	12	12	NUM
ejpam-3478	195	15	)	)	PUNCT
ejpam-3478	195	16	to	to	PART
ejpam-3478	195	17	get	get	VERB
ejpam-3478	195	18	for	for	ADP
ejpam-3478	195	19	o	o	PROPN
ejpam-3478	195	20	(	(	PUNCT
ejpam-3478	195	21	1	1	NUM
ejpam-3478	195	22	)	)	PUNCT
ejpam-3478	195	23	a0	a0	NOUN
ejpam-3478	195	24	(	(	PUNCT
ejpam-3478	195	25	w1	w1	NOUN
ejpam-3478	195	26	u1	u1	PROPN
ejpam-3478	195	27	)	)	PUNCT
ejpam-3478	196	1	=	=	PUNCT
ejpam-3478	196	2	(	(	PUNCT
ejpam-3478	196	3	−	−	X
ejpam-3478	196	4	(	(	PUNCT
ejpam-3478	196	5	α−	α−	ADP
ejpam-3478	196	6	ra	ra	NOUN
ejpam-3478	196	7	)	)	PUNCT
ejpam-3478	196	8	j1w	j1w	PROPN
ejpam-3478	196	9	−	−	ADP
ejpam-3478	196	10	σ2w0j1ww	σ2w0j1ww	ADV
ejpam-3478	196	11	−	−	PROPN
ejpam-3478	196	12	qσρu0j1lw	qσρu0j1lw	NOUN
ejpam-3478	196	13	−cj1l	−cj1l	PROPN
ejpam-3478	197	1	−	−	PROPN
ejpam-3478	197	2	q2u0j1ll	q2u0j1ll	PROPN
ejpam-3478	197	3	−	−	PROPN
ejpam-3478	197	4	qσρw0j1lw	qσρw0j1lw	VERB
ejpam-3478	197	5	+	+	CCONJ
ejpam-3478	197	6	j0l	j0l	X
ejpam-3478	197	7	)	)	PUNCT
ejpam-3478	197	8	where	where	SCONJ
ejpam-3478	197	9	c	c	NOUN
ejpam-3478	197	10	=	=	SYM
ejpam-3478	197	11	c−m−	c−m−	PROPN
ejpam-3478	197	12	ra	ra	PROPN
ejpam-3478	197	13	and	and	CCONJ
ejpam-3478	197	14	a0	a0	PROPN
ejpam-3478	197	15	=	=	SYM
ejpam-3478	197	16	(	(	PUNCT
ejpam-3478	197	17	σ2	σ2	NOUN
ejpam-3478	197	18	∂	∂	NUM
ejpam-3478	197	19	2j0	2j0	NUM
ejpam-3478	197	20	∂w	∂w	PROPN
ejpam-3478	197	21	2	2	NUM
ejpam-3478	197	22	qσρ	qσρ	NOUN
ejpam-3478	197	23	∂2j0	∂2j0	PUNCT
ejpam-3478	197	24	∂l∂w	∂l∂w	NOUN
ejpam-3478	197	25	qσρ	qσρ	NOUN
ejpam-3478	197	26	∂2j0	∂2j0	PUNCT
ejpam-3478	197	27	∂l∂w	∂l∂w	PROPN
ejpam-3478	197	28	q2	q2	PROPN
ejpam-3478	197	29	∂	∂	NUM
ejpam-3478	197	30	2j0	2j0	NUM
ejpam-3478	197	31	∂l2	∂l2	PROPN
ejpam-3478	197	32	)	)	PUNCT
ejpam-3478	197	33	.	.	PUNCT
ejpam-3478	198	1	for	for	ADP
ejpam-3478	198	2	the	the	DET
ejpam-3478	198	3	hamilton	hamilton	PROPN
ejpam-3478	198	4	-	-	PUNCT
ejpam-3478	198	5	jacobi	jacobi	PROPN
ejpam-3478	198	6	equation	equation	NOUN
ejpam-3478	198	7	(	(	PUNCT
ejpam-3478	198	8	9	9	NUM
ejpam-3478	198	9	)	)	PUNCT
ejpam-3478	198	10	when	when	SCONJ
ejpam-3478	198	11	u	u	X
ejpam-3478	198	12	(	(	PUNCT
ejpam-3478	198	13	e	e	NOUN
ejpam-3478	198	14	)	)	PUNCT
ejpam-3478	198	15	=	=	PUNCT
ejpam-3478	198	16	eγ	eγ	ADP
ejpam-3478	198	17	γ	γ	PROPN
ejpam-3478	198	18	it	it	PRON
ejpam-3478	198	19	is	be	AUX
ejpam-3478	198	20	best	good	ADJ
ejpam-3478	198	21	to	to	PART
ejpam-3478	198	22	use	use	VERB
ejpam-3478	198	23	equation	equation	NOUN
ejpam-3478	198	24	(	(	PUNCT
ejpam-3478	198	25	14	14	NUM
ejpam-3478	198	26	)	)	PUNCT
ejpam-3478	198	27	i.e.	i.e.	X
ejpam-3478	198	28	0	0	X
ejpam-3478	198	29	=	=	SYM
ejpam-3478	198	30	u	u	NOUN
ejpam-3478	198	31	(	(	PUNCT
ejpam-3478	198	32	e	e	NOUN
ejpam-3478	198	33	)	)	PUNCT
ejpam-3478	198	34	+	+	SYM
ejpam-3478	198	35	∂j	∂j	PROPN
ejpam-3478	198	36	∂t	∂t	NOUN
ejpam-3478	198	37	+	+	CCONJ
ejpam-3478	198	38	1	1	NUM
ejpam-3478	198	39	2	2	NUM
ejpam-3478	198	40	(	(	PUNCT
ejpam-3478	198	41	α−	α−	ADP
ejpam-3478	198	42	ra)w	ra)w	NOUN
ejpam-3478	198	43	∂j	∂j	NOUN
ejpam-3478	199	1	∂w	∂w	NOUN
ejpam-3478	199	2	+	+	CCONJ
ejpam-3478	199	3	1	1	NUM
ejpam-3478	199	4	2	2	NUM
ejpam-3478	199	5	cu	cu	NOUN
ejpam-3478	199	6	∂j	∂j	NOUN
ejpam-3478	199	7	∂l	∂l	PROPN
ejpam-3478	200	1	+	+	CCONJ
ejpam-3478	200	2	ra	ra	PROPN
ejpam-3478	200	3	(	(	PUNCT
ejpam-3478	200	4	w	w	PROPN
ejpam-3478	200	5	∂j	∂j	PROPN
ejpam-3478	201	1	∂w	∂w	PROPN
ejpam-3478	202	1	+	+	NUM
ejpam-3478	202	2	l	l	NOUN
ejpam-3478	202	3	∂j	∂j	NOUN
ejpam-3478	202	4	∂l	∂l	NOUN
ejpam-3478	202	5	)	)	PUNCT
ejpam-3478	203	1	+	+	CCONJ
ejpam-3478	203	2	εl	εl	ADP
ejpam-3478	203	3	∂j	∂j	NOUN
ejpam-3478	203	4	∂l	∂l	PROPN
ejpam-3478	203	5	(	(	PUNCT
ejpam-3478	203	6	37	37	NUM
ejpam-3478	203	7	)	)	PUNCT
ejpam-3478	203	8	when	when	SCONJ
ejpam-3478	203	9	rl	rl	AUX
ejpam-3478	203	10	=	=	SYM
ejpam-3478	203	11	ra	ra	PROPN
ejpam-3478	203	12	+	+	CCONJ
ejpam-3478	203	13	ε	ε	PROPN
ejpam-3478	203	14	.	.	PUNCT
ejpam-3478	204	1	then	then	ADV
ejpam-3478	204	2	for	for	ADP
ejpam-3478	204	3	zero	zero	NUM
ejpam-3478	204	4	order	order	NOUN
ejpam-3478	204	5	we	we	PRON
ejpam-3478	204	6	have	have	VERB
ejpam-3478	204	7	0	0	NUM
ejpam-3478	204	8	=	=	SYM
ejpam-3478	204	9	u	u	NOUN
ejpam-3478	204	10	(	(	PUNCT
ejpam-3478	204	11	e	e	NOUN
ejpam-3478	204	12	)	)	PUNCT
ejpam-3478	205	1	+	+	CCONJ
ejpam-3478	205	2	∂j0	∂j0	ADV
ejpam-3478	205	3	∂t	∂t	PROPN
ejpam-3478	205	4	+	+	CCONJ
ejpam-3478	205	5	1	1	NUM
ejpam-3478	205	6	2	2	NUM
ejpam-3478	205	7	(	(	PUNCT
ejpam-3478	205	8	α−	α−	ADP
ejpam-3478	205	9	ra)w0	ra)w0	PROPN
ejpam-3478	205	10	∂j0	∂j0	ADV
ejpam-3478	205	11	∂w	∂w	PROPN
ejpam-3478	206	1	+	+	CCONJ
ejpam-3478	206	2	1	1	NUM
ejpam-3478	206	3	2	2	NUM
ejpam-3478	206	4	cu0	cu0	NOUN
ejpam-3478	206	5	∂j0	∂j0	ADV
ejpam-3478	206	6	∂l	∂l	PROPN
ejpam-3478	207	1	+	+	CCONJ
ejpam-3478	207	2	ra	ra	PROPN
ejpam-3478	207	3	(	(	PUNCT
ejpam-3478	207	4	w	w	NOUN
ejpam-3478	207	5	∂j0	∂j0	ADV
ejpam-3478	207	6	∂w	∂w	PROPN
ejpam-3478	208	1	+	+	NUM
ejpam-3478	208	2	l	l	NOUN
ejpam-3478	208	3	∂j0	∂j0	ADV
ejpam-3478	208	4	∂l	∂l	PROPN
ejpam-3478	208	5	)	)	PUNCT
ejpam-3478	209	1	(	(	PUNCT
ejpam-3478	209	2	38	38	NUM
ejpam-3478	209	3	)	)	PUNCT
ejpam-3478	209	4	which	which	PRON
ejpam-3478	209	5	we	we	PRON
ejpam-3478	209	6	can	can	AUX
ejpam-3478	209	7	write	write	VERB
ejpam-3478	209	8	as	as	ADP
ejpam-3478	209	9	u	u	NOUN
ejpam-3478	209	10	(	(	PUNCT
ejpam-3478	209	11	e	e	NOUN
ejpam-3478	209	12	)	)	PUNCT
ejpam-3478	210	1	+	+	CCONJ
ejpam-3478	210	2	l0	l0	PROPN
ejpam-3478	210	3	(	(	PUNCT
ejpam-3478	210	4	j0	j0	PROPN
ejpam-3478	210	5	)	)	PUNCT
ejpam-3478	210	6	=	=	SYM
ejpam-3478	210	7	0	0	X
ejpam-3478	210	8	.	.	PUNCT
ejpam-3478	211	1	for	for	ADP
ejpam-3478	211	2	order	order	NOUN
ejpam-3478	211	3	ε	ε	NOUN
ejpam-3478	211	4	,	,	PUNCT
ejpam-3478	211	5	from	from	ADP
ejpam-3478	211	6	(	(	PUNCT
ejpam-3478	211	7	37	37	NUM
ejpam-3478	211	8	)	)	PUNCT
ejpam-3478	211	9	we	we	PRON
ejpam-3478	211	10	also	also	ADV
ejpam-3478	211	11	get	get	VERB
ejpam-3478	211	12	0	0	NUM
ejpam-3478	211	13	=	=	SYM
ejpam-3478	211	14	l0	l0	PROPN
ejpam-3478	211	15	(	(	PUNCT
ejpam-3478	211	16	j1	j1	PROPN
ejpam-3478	211	17	)	)	PUNCT
ejpam-3478	212	1	+	+	NUM
ejpam-3478	212	2	l	l	NOUN
ejpam-3478	212	3	∂j0	∂j0	ADV
ejpam-3478	212	4	∂l	∂l	VERB
ejpam-3478	213	1	+	+	CCONJ
ejpam-3478	214	1	1	1	NUM
ejpam-3478	214	2	2	2	NUM
ejpam-3478	214	3	(	(	PUNCT
ejpam-3478	214	4	α−	α−	ADP
ejpam-3478	214	5	ra)w1	ra)w1	VERB
ejpam-3478	215	1	∂j0	∂j0	INTJ
ejpam-3478	215	2	∂w	∂w	PROPN
ejpam-3478	215	3	+	+	CCONJ
ejpam-3478	215	4	1	1	NUM
ejpam-3478	215	5	2	2	NUM
ejpam-3478	215	6	cu1	cu1	NOUN
ejpam-3478	215	7	∂j0	∂j0	ADV
ejpam-3478	215	8	∂l	∂l	PROPN
ejpam-3478	215	9	(	(	PUNCT
ejpam-3478	215	10	39	39	NUM
ejpam-3478	215	11	)	)	PUNCT
ejpam-3478	215	12	we	we	PRON
ejpam-3478	215	13	have	have	AUX
ejpam-3478	215	14	solved	solve	VERB
ejpam-3478	215	15	the	the	DET
ejpam-3478	215	16	zero	zero	NUM
ejpam-3478	215	17	order	order	NOUN
ejpam-3478	215	18	problem	problem	NOUN
ejpam-3478	215	19	for	for	ADP
ejpam-3478	215	20	u	u	PROPN
ejpam-3478	215	21	(	(	PUNCT
ejpam-3478	215	22	e	e	NOUN
ejpam-3478	215	23	)	)	PUNCT
ejpam-3478	215	24	=	=	PUNCT
ejpam-3478	215	25	eγ	eγ	ADP
ejpam-3478	215	26	γ	γ	X
ejpam-3478	215	27	=	=	SYM
ejpam-3478	215	28	(	(	PUNCT
ejpam-3478	215	29	w−l)γ	w−l)γ	PROPN
ejpam-3478	215	30	γ	γ	X
ejpam-3478	215	31	by	by	ADP
ejpam-3478	215	32	choosing	choose	VERB
ejpam-3478	215	33	j0	j0	PROPN
ejpam-3478	215	34	=	=	SYM
ejpam-3478	215	35	a	a	DET
ejpam-3478	215	36	(	(	PUNCT
ejpam-3478	215	37	t	t	NOUN
ejpam-3478	215	38	)	)	PUNCT
ejpam-3478	215	39	(	(	PUNCT
ejpam-3478	215	40	w−l)γ	w−l)γ	NOUN
ejpam-3478	215	41	γ	γ	X
ejpam-3478	215	42	and	and	CCONJ
ejpam-3478	215	43	solving	solve	VERB
ejpam-3478	215	44	for	for	ADP
ejpam-3478	215	45	a	a	DET
ejpam-3478	215	46	(	(	PUNCT
ejpam-3478	215	47	t	t	PROPN
ejpam-3478	215	48	)	)	PUNCT
ejpam-3478	215	49	.	.	PUNCT
ejpam-3478	216	1	the	the	DET
ejpam-3478	216	2	extra	extra	ADJ
ejpam-3478	216	3	terms	term	NOUN
ejpam-3478	216	4	in	in	ADP
ejpam-3478	216	5	the	the	DET
ejpam-3478	216	6	o	o	PROPN
ejpam-3478	216	7	(	(	PUNCT
ejpam-3478	216	8	ε	ε	PROPN
ejpam-3478	216	9	)	)	PUNCT
ejpam-3478	216	10	equation	equation	NOUN
ejpam-3478	216	11	depending	depend	VERB
ejpam-3478	216	12	on	on	ADP
ejpam-3478	216	13	j0	j0	PROPN
ejpam-3478	216	14	gives	give	VERB
ejpam-3478	216	15	l0	l0	PROPN
ejpam-3478	216	16	(	(	PUNCT
ejpam-3478	216	17	j1	j1	PROPN
ejpam-3478	216	18	)	)	PUNCT
ejpam-3478	217	1	+	+	CCONJ
ejpam-3478	217	2	(	(	PUNCT
ejpam-3478	217	3	w	w	NOUN
ejpam-3478	217	4	−	−	PROPN
ejpam-3478	217	5	l)γ−1a	l)γ−1a	PROPN
ejpam-3478	217	6	(	(	PUNCT
ejpam-3478	217	7	t	t	NOUN
ejpam-3478	217	8	)	)	PUNCT
ejpam-3478	217	9	[	[	PUNCT
ejpam-3478	217	10	−l+	−l+	NOUN
ejpam-3478	217	11	1	1	NUM
ejpam-3478	217	12	2	2	NUM
ejpam-3478	217	13	(	(	PUNCT
ejpam-3478	217	14	α−	α−	ADP
ejpam-3478	217	15	ra)w1	ra)w1	NOUN
ejpam-3478	217	16	−	−	NUM
ejpam-3478	217	17	1	1	NUM
ejpam-3478	217	18	2	2	NUM
ejpam-3478	217	19	cu1	cu1	NOUN
ejpam-3478	217	20	]	]	PUNCT
ejpam-3478	217	21	=	=	PUNCT
ejpam-3478	218	1	0	0	X
ejpam-3478	218	2	.	.	PUNCT
ejpam-3478	219	1	(	(	PUNCT
ejpam-3478	219	2	40	40	NUM
ejpam-3478	219	3	)	)	PUNCT
ejpam-3478	219	4	we	we	PRON
ejpam-3478	219	5	now	now	ADV
ejpam-3478	219	6	look	look	VERB
ejpam-3478	219	7	for	for	ADP
ejpam-3478	219	8	j1	j1	PROPN
ejpam-3478	219	9	in	in	ADP
ejpam-3478	219	10	the	the	DET
ejpam-3478	219	11	form	form	NOUN
ejpam-3478	219	12	j1	j1	NOUN
ejpam-3478	219	13	=	=	PUNCT
ejpam-3478	220	1	[	[	X
ejpam-3478	220	2	b	b	X
ejpam-3478	220	3	(	(	PUNCT
ejpam-3478	220	4	t)l+b1	t)l+b1	NOUN
ejpam-3478	220	5	(	(	PUNCT
ejpam-3478	220	6	t)w	t)w	X
ejpam-3478	220	7	]	]	PUNCT
ejpam-3478	220	8	(	(	PUNCT
ejpam-3478	220	9	w	w	PROPN
ejpam-3478	220	10	−	−	PROPN
ejpam-3478	220	11	l)γ−1	l)γ−1	PROPN
ejpam-3478	220	12	(	(	PUNCT
ejpam-3478	220	13	41	41	NUM
ejpam-3478	220	14	)	)	PUNCT
ejpam-3478	220	15	c.	c.	PROPN
ejpam-3478	220	16	atkinson	atkinson	PROPN
ejpam-3478	220	17	,	,	PUNCT
ejpam-3478	220	18	s.	s.	PROPN
ejpam-3478	220	19	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	220	20	,	,	PUNCT
ejpam-3478	220	21	p.	p.	PROPN
ejpam-3478	220	22	ingpochai	ingpochai	PROPN
ejpam-3478	220	23	/	/	SYM
ejpam-3478	220	24	eur	eur	PROPN
ejpam-3478	220	25	.	.	PUNCT
ejpam-3478	221	1	j.	j.	PROPN
ejpam-3478	221	2	pure	pure	PROPN
ejpam-3478	221	3	appl	appl	PROPN
ejpam-3478	221	4	.	.	PROPN
ejpam-3478	221	5	math	math	PROPN
ejpam-3478	221	6	,	,	PUNCT
ejpam-3478	221	7	12	12	NUM
ejpam-3478	221	8	(	(	PUNCT
ejpam-3478	221	9	3	3	NUM
ejpam-3478	221	10	)	)	PUNCT
ejpam-3478	221	11	(	(	PUNCT
ejpam-3478	221	12	2019	2019	NUM
ejpam-3478	221	13	)	)	PUNCT
ejpam-3478	221	14	,	,	PUNCT
ejpam-3478	221	15	1315	1315	NUM
ejpam-3478	221	16	-	-	SYM
ejpam-3478	221	17	1336	1336	NUM
ejpam-3478	221	18	1325	1325	NUM
ejpam-3478	222	1	so	so	SCONJ
ejpam-3478	222	2	that	that	SCONJ
ejpam-3478	222	3	l0	l0	PROPN
ejpam-3478	222	4	(	(	PUNCT
ejpam-3478	222	5	j1	j1	PROPN
ejpam-3478	222	6	)	)	PUNCT
ejpam-3478	222	7	=	=	PUNCT
ejpam-3478	222	8	[	[	PUNCT
ejpam-3478	222	9	ḃ	ḃ	PROPN
ejpam-3478	222	10	(	(	PUNCT
ejpam-3478	222	11	t)l+	t)l+	PROPN
ejpam-3478	222	12	ḃ1w	ḃ1w	X
ejpam-3478	222	13	]	]	PUNCT
ejpam-3478	222	14	(	(	PUNCT
ejpam-3478	222	15	w	w	NOUN
ejpam-3478	222	16	−	−	PROPN
ejpam-3478	222	17	l)γ−1	l)γ−1	PROPN
ejpam-3478	222	18	+	+	CCONJ
ejpam-3478	222	19	(	(	PUNCT
ejpam-3478	222	20	w	w	PROPN
ejpam-3478	222	21	−	−	PROPN
ejpam-3478	222	22	l)γ−1	l)γ−1	PROPN
ejpam-3478	222	23	{	{	PUNCT
ejpam-3478	222	24	(	(	PUNCT
ejpam-3478	222	25	1	1	NUM
ejpam-3478	222	26	2	2	NUM
ejpam-3478	222	27	(	(	PUNCT
ejpam-3478	222	28	α−	α−	ADP
ejpam-3478	222	29	ra)w0b1	ra)w0b1	PROPN
ejpam-3478	222	30	(	(	PUNCT
ejpam-3478	222	31	t	t	PROPN
ejpam-3478	222	32	)	)	PUNCT
ejpam-3478	222	33	+	+	CCONJ
ejpam-3478	222	34	1	1	NUM
ejpam-3478	222	35	2	2	NUM
ejpam-3478	222	36	cu0b	cu0b	NOUN
ejpam-3478	222	37	(	(	PUNCT
ejpam-3478	222	38	t	t	PROPN
ejpam-3478	222	39	)	)	PUNCT
ejpam-3478	223	1	+	+	NUM
ejpam-3478	223	2	ra	ra	PROPN
ejpam-3478	223	3	(	(	PUNCT
ejpam-3478	223	4	b1w	b1w	X
ejpam-3478	223	5	+	+	PROPN
ejpam-3478	223	6	bl	bl	NOUN
ejpam-3478	223	7	)	)	PUNCT
ejpam-3478	223	8	)	)	PUNCT
ejpam-3478	223	9	}	}	PUNCT
ejpam-3478	224	1	+	+	CCONJ
ejpam-3478	225	1	[	[	X
ejpam-3478	225	2	bl+b1w	bl+b1w	X
ejpam-3478	225	3	]	]	PUNCT
ejpam-3478	225	4	{	{	PUNCT
ejpam-3478	225	5	(	(	PUNCT
ejpam-3478	225	6	1	1	NUM
ejpam-3478	225	7	2	2	NUM
ejpam-3478	225	8	(	(	PUNCT
ejpam-3478	225	9	α−	α−	ADP
ejpam-3478	225	10	ra)w0	ra)w0	PROPN
ejpam-3478	225	11	−	−	PROPN
ejpam-3478	225	12	1	1	NUM
ejpam-3478	225	13	2	2	NUM
ejpam-3478	225	14	cu0	cu0	NOUN
ejpam-3478	225	15	)	)	PUNCT
ejpam-3478	225	16	(	(	PUNCT
ejpam-3478	225	17	γ	γ	X
ejpam-3478	225	18	−	−	PROPN
ejpam-3478	225	19	1	1	NUM
ejpam-3478	225	20	)	)	PUNCT
ejpam-3478	225	21	}	}	PUNCT
ejpam-3478	225	22	eγ−2	eγ−2	PROPN
ejpam-3478	225	23	+	+	CCONJ
ejpam-3478	225	24	rae	rae	PROPN
ejpam-3478	225	25	γ−1	γ−1	PROPN
ejpam-3478	225	26	(	(	PUNCT
ejpam-3478	225	27	γ	γ	X
ejpam-3478	225	28	−	−	PROPN
ejpam-3478	225	29	1	1	NUM
ejpam-3478	225	30	)	)	PUNCT
ejpam-3478	226	1	[	[	X
ejpam-3478	226	2	bl+b1w	bl+b1w	X
ejpam-3478	226	3	]	]	PUNCT
ejpam-3478	226	4	but	but	CCONJ
ejpam-3478	226	5	note	note	VERB
ejpam-3478	226	6	that	that	SCONJ
ejpam-3478	226	7	from	from	ADP
ejpam-3478	226	8	the	the	DET
ejpam-3478	226	9	zero	zero	NUM
ejpam-3478	226	10	order	order	NOUN
ejpam-3478	226	11	equation	equation	NOUN
ejpam-3478	226	12	(	(	PUNCT
ejpam-3478	226	13	38	38	NUM
ejpam-3478	226	14	)	)	PUNCT
ejpam-3478	226	15	we	we	PRON
ejpam-3478	226	16	have	have	VERB
ejpam-3478	226	17	0	0	NUM
ejpam-3478	226	18	=	=	SYM
ejpam-3478	226	19	(	(	PUNCT
ejpam-3478	226	20	1	1	NUM
ejpam-3478	226	21	2	2	NUM
ejpam-3478	226	22	(	(	PUNCT
ejpam-3478	226	23	α−	α−	ADP
ejpam-3478	226	24	ra)w0	ra)w0	PROPN
ejpam-3478	226	25	−	−	PROPN
ejpam-3478	226	26	1	1	NUM
ejpam-3478	226	27	2	2	NUM
ejpam-3478	226	28	cu0	cu0	NOUN
ejpam-3478	226	29	)	)	PUNCT
ejpam-3478	226	30	a	a	DET
ejpam-3478	226	31	(	(	PUNCT
ejpam-3478	226	32	t)eγ−1	t)eγ−1	PROPN
ejpam-3478	226	33	+	+	CCONJ
ejpam-3478	226	34	raa	raa	NOUN
ejpam-3478	226	35	(	(	PUNCT
ejpam-3478	226	36	t)eγ	t)eγ	PROPN
ejpam-3478	226	37	+	+	CCONJ
ejpam-3478	226	38	ȧ	ȧ	PROPN
ejpam-3478	226	39	(	(	PUNCT
ejpam-3478	226	40	t)eγ	t)eγ	PROPN
ejpam-3478	226	41	γ	γ	X
ejpam-3478	226	42	+	+	X
ejpam-3478	226	43	eγ	eγ	PROPN
ejpam-3478	226	44	γ	γ	PROPN
ejpam-3478	226	45	(	(	PUNCT
ejpam-3478	226	46	42	42	NUM
ejpam-3478	226	47	)	)	PUNCT
ejpam-3478	226	48	and	and	CCONJ
ejpam-3478	226	49	since	since	SCONJ
ejpam-3478	226	50	from	from	ADP
ejpam-3478	226	51	equations	equation	NOUN
ejpam-3478	226	52	(	(	PUNCT
ejpam-3478	226	53	30	30	NUM
ejpam-3478	226	54	)	)	PUNCT
ejpam-3478	226	55	and	and	CCONJ
ejpam-3478	226	56	(	(	PUNCT
ejpam-3478	226	57	31	31	NUM
ejpam-3478	226	58	)	)	PUNCT
ejpam-3478	226	59	,	,	PUNCT
ejpam-3478	226	60	w0	w0	PROPN
ejpam-3478	226	61	and	and	CCONJ
ejpam-3478	226	62	u0	u0	PROPN
ejpam-3478	226	63	are	be	AUX
ejpam-3478	226	64	proportional	proportional	ADJ
ejpam-3478	226	65	to	to	ADP
ejpam-3478	226	66	e	e	X
ejpam-3478	226	67	=	=	PUNCT
ejpam-3478	226	68	w	w	PROPN
ejpam-3478	226	69	−	−	PROPN
ejpam-3478	226	70	l	l	NOUN
ejpam-3478	226	71	,	,	PUNCT
ejpam-3478	226	72	this	this	DET
ejpam-3478	226	73	equation	equation	NOUN
ejpam-3478	226	74	reduces	reduce	VERB
ejpam-3478	226	75	to	to	ADP
ejpam-3478	226	76	0	0	NUM
ejpam-3478	226	77	=	=	SYM
ejpam-3478	226	78	{	{	PUNCT
ejpam-3478	226	79	[	[	PUNCT
ejpam-3478	226	80	1	1	NUM
ejpam-3478	226	81	2	2	NUM
ejpam-3478	226	82	(	(	PUNCT
ejpam-3478	226	83	α−	α−	ADP
ejpam-3478	226	84	ra)q1	ra)q1	ADJ
ejpam-3478	226	85	−	−	NOUN
ejpam-3478	226	86	1	1	NUM
ejpam-3478	226	87	2	2	NUM
ejpam-3478	226	88	cq2	cq2	NOUN
ejpam-3478	226	89	]	]	PUNCT
ejpam-3478	227	1	+	+	CCONJ
ejpam-3478	227	2	ra	ra	X
ejpam-3478	227	3	}	}	PUNCT
ejpam-3478	227	4	a	a	PROPN
ejpam-3478	227	5	(	(	PUNCT
ejpam-3478	227	6	t	t	NOUN
ejpam-3478	227	7	)	)	PUNCT
ejpam-3478	227	8	+	+	CCONJ
ejpam-3478	227	9	ȧ	ȧ	PROPN
ejpam-3478	227	10	(	(	PUNCT
ejpam-3478	227	11	t	t	PROPN
ejpam-3478	227	12	)	)	PUNCT
ejpam-3478	227	13	γ	γ	NOUN
ejpam-3478	227	14	+	+	NOUN
ejpam-3478	227	15	1	1	NUM
ejpam-3478	227	16	γ	γ	X
ejpam-3478	227	17	(	(	PUNCT
ejpam-3478	227	18	43	43	NUM
ejpam-3478	227	19	)	)	PUNCT
ejpam-3478	227	20	from	from	ADP
ejpam-3478	227	21	which	which	PRON
ejpam-3478	227	22	we	we	PRON
ejpam-3478	227	23	can	can	AUX
ejpam-3478	227	24	determine	determine	VERB
ejpam-3478	227	25	a	a	DET
ejpam-3478	227	26	(	(	PUNCT
ejpam-3478	227	27	t	t	NOUN
ejpam-3478	227	28	)	)	PUNCT
ejpam-3478	227	29	.	.	PUNCT
ejpam-3478	228	1	this	this	DET
ejpam-3478	228	2	expression	expression	NOUN
ejpam-3478	228	3	agrees	agree	VERB
ejpam-3478	228	4	with	with	ADP
ejpam-3478	228	5	that	that	PRON
ejpam-3478	228	6	of	of	ADP
ejpam-3478	228	7	equation	equation	NOUN
ejpam-3478	228	8	(	(	PUNCT
ejpam-3478	228	9	36	36	NUM
ejpam-3478	228	10	)	)	PUNCT
ejpam-3478	228	11	when	when	SCONJ
ejpam-3478	228	12	ra	ra	PROPN
ejpam-3478	228	13	=	=	NOUN
ejpam-3478	228	14	rl	rl	VERB
ejpam-3478	228	15	though	though	SCONJ
ejpam-3478	228	16	they	they	PRON
ejpam-3478	228	17	look	look	VERB
ejpam-3478	228	18	superficially	superficially	ADV
ejpam-3478	228	19	different	different	ADJ
ejpam-3478	228	20	.	.	PUNCT
ejpam-3478	229	1	furthermore	furthermore	ADV
ejpam-3478	229	2	,	,	PUNCT
ejpam-3478	229	3	using	use	VERB
ejpam-3478	229	4	w0	w0	PROPN
ejpam-3478	229	5	=	=	PROPN
ejpam-3478	229	6	q1	q1	PROPN
ejpam-3478	229	7	(	(	PUNCT
ejpam-3478	229	8	w	w	PROPN
ejpam-3478	229	9	−	−	PROPN
ejpam-3478	229	10	l	l	NOUN
ejpam-3478	229	11	)	)	PUNCT
ejpam-3478	229	12	u0	u0	ADJ
ejpam-3478	229	13	=	=	PROPN
ejpam-3478	229	14	q2	q2	PROPN
ejpam-3478	229	15	(	(	PUNCT
ejpam-3478	229	16	w	w	PROPN
ejpam-3478	229	17	−	−	PROPN
ejpam-3478	229	18	l	l	NOUN
ejpam-3478	229	19	)	)	PUNCT
ejpam-3478	229	20	in	in	ADP
ejpam-3478	229	21	equation	equation	NOUN
ejpam-3478	229	22	(	(	PUNCT
ejpam-3478	229	23	40	40	NUM
ejpam-3478	229	24	)	)	PUNCT
ejpam-3478	229	25	gives	give	VERB
ejpam-3478	229	26	to	to	PART
ejpam-3478	229	27	order	order	VERB
ejpam-3478	229	28	ε	ε	PROPN
ejpam-3478	229	29	.	.	NOUN
ejpam-3478	229	30	0	0	PUNCT
ejpam-3478	230	1	=	=	SYM
ejpam-3478	230	2	(	(	PUNCT
ejpam-3478	230	3	ḃ	ḃ	PROPN
ejpam-3478	230	4	(	(	PUNCT
ejpam-3478	230	5	t)l+	t)l+	PROPN
ejpam-3478	230	6	ḃ1w	ḃ1w	X
ejpam-3478	230	7	)	)	PUNCT
ejpam-3478	231	1	+	+	CCONJ
ejpam-3478	231	2	1	1	NUM
ejpam-3478	231	3	2	2	NUM
ejpam-3478	231	4	(	(	PUNCT
ejpam-3478	231	5	α−	α−	ADP
ejpam-3478	231	6	ra)q1b1	ra)q1b1	PROPN
ejpam-3478	231	7	(	(	PUNCT
ejpam-3478	231	8	w	w	PROPN
ejpam-3478	231	9	−	−	PROPN
ejpam-3478	231	10	l	l	NOUN
ejpam-3478	231	11	)	)	PUNCT
ejpam-3478	231	12	+	+	CCONJ
ejpam-3478	231	13	1	1	NUM
ejpam-3478	231	14	2	2	NUM
ejpam-3478	231	15	cbq2	cbq2	NOUN
ejpam-3478	231	16	(	(	PUNCT
ejpam-3478	231	17	w	w	PROPN
ejpam-3478	231	18	−	−	PROPN
ejpam-3478	231	19	l	l	NOUN
ejpam-3478	231	20	)	)	PUNCT
ejpam-3478	232	1	+	+	CCONJ
ejpam-3478	232	2	ra	ra	PROPN
ejpam-3478	232	3	(	(	PUNCT
ejpam-3478	232	4	b1w	b1w	X
ejpam-3478	232	5	+	+	NOUN
ejpam-3478	232	6	bl	bl	PROPN
ejpam-3478	232	7	)	)	PUNCT
ejpam-3478	232	8	+	+	CCONJ
ejpam-3478	232	9	(	(	PUNCT
ejpam-3478	232	10	γ	γ	X
ejpam-3478	232	11	−	−	PROPN
ejpam-3478	232	12	1	1	NUM
ejpam-3478	232	13	)	)	PUNCT
ejpam-3478	232	14	(	(	PUNCT
ejpam-3478	232	15	bl+b1w	bl+b1w	PROPN
ejpam-3478	232	16	)	)	PUNCT
ejpam-3478	232	17	{	{	PUNCT
ejpam-3478	232	18	1	1	NUM
ejpam-3478	232	19	2	2	NUM
ejpam-3478	232	20	(	(	PUNCT
ejpam-3478	232	21	α−	α−	ADP
ejpam-3478	232	22	ra)q1	ra)q1	ADJ
ejpam-3478	232	23	−	−	NOUN
ejpam-3478	232	24	1	1	NUM
ejpam-3478	232	25	2	2	NUM
ejpam-3478	232	26	cq2	cq2	NOUN
ejpam-3478	232	27	}	}	PUNCT
ejpam-3478	233	1	+	+	CCONJ
ejpam-3478	233	2	ra	ra	PROPN
ejpam-3478	233	3	(	(	PUNCT
ejpam-3478	233	4	γ	γ	X
ejpam-3478	233	5	−	−	PROPN
ejpam-3478	233	6	1	1	NUM
ejpam-3478	233	7	)	)	PUNCT
ejpam-3478	233	8	(	(	PUNCT
ejpam-3478	233	9	bl+b1w	bl+b1w	PROPN
ejpam-3478	233	10	)	)	PUNCT
ejpam-3478	234	1	+	+	ADP
ejpam-3478	234	2	a	a	DET
ejpam-3478	234	3	(	(	PUNCT
ejpam-3478	234	4	t	t	NOUN
ejpam-3478	234	5	)	)	PUNCT
ejpam-3478	234	6	[	[	PUNCT
ejpam-3478	234	7	−l+	−l+	NOUN
ejpam-3478	234	8	1	1	NUM
ejpam-3478	234	9	2	2	NUM
ejpam-3478	234	10	(	(	PUNCT
ejpam-3478	234	11	α−	α−	ADP
ejpam-3478	234	12	ra)w1	ra)w1	NOUN
ejpam-3478	234	13	−	−	NUM
ejpam-3478	234	14	1	1	NUM
ejpam-3478	234	15	2	2	NUM
ejpam-3478	234	16	cu1	cu1	NOUN
ejpam-3478	234	17	]	]	PUNCT
ejpam-3478	234	18	(	(	PUNCT
ejpam-3478	234	19	44	44	NUM
ejpam-3478	234	20	)	)	PUNCT
ejpam-3478	234	21	where	where	SCONJ
ejpam-3478	234	22	c	c	NOUN
ejpam-3478	234	23	=	=	SYM
ejpam-3478	234	24	c	c	PROPN
ejpam-3478	234	25	−m	−m	NOUN
ejpam-3478	234	26	−	−	X
ejpam-3478	234	27	rl	rl	NOUN
ejpam-3478	234	28	.	.	PUNCT
ejpam-3478	235	1	if	if	SCONJ
ejpam-3478	235	2	we	we	PRON
ejpam-3478	235	3	now	now	ADV
ejpam-3478	235	4	equate	equate	VERB
ejpam-3478	235	5	to	to	ADP
ejpam-3478	235	6	zero	zero	NUM
ejpam-3478	235	7	coefficients	coefficient	NOUN
ejpam-3478	235	8	of	of	ADP
ejpam-3478	235	9	l	l	NOUN
ejpam-3478	235	10	and	and	CCONJ
ejpam-3478	235	11	w	w	PROPN
ejpam-3478	235	12	,	,	PUNCT
ejpam-3478	235	13	we	we	PRON
ejpam-3478	235	14	get	get	AUX
ejpam-3478	235	15	coupled	couple	VERB
ejpam-3478	235	16	differential	differential	ADJ
ejpam-3478	235	17	equations	equation	NOUN
ejpam-3478	235	18	for	for	ADP
ejpam-3478	235	19	b	b	PROPN
ejpam-3478	235	20	(	(	PUNCT
ejpam-3478	235	21	t	t	PROPN
ejpam-3478	235	22	)	)	PUNCT
ejpam-3478	235	23	and	and	CCONJ
ejpam-3478	235	24	b1	b1	NOUN
ejpam-3478	235	25	(	(	PUNCT
ejpam-3478	235	26	t	t	NOUN
ejpam-3478	235	27	)	)	PUNCT
ejpam-3478	235	28	in	in	ADP
ejpam-3478	235	29	terms	term	NOUN
ejpam-3478	235	30	of	of	ADP
ejpam-3478	235	31	a	a	DET
ejpam-3478	235	32	(	(	PUNCT
ejpam-3478	235	33	t	t	PROPN
ejpam-3478	235	34	)	)	PUNCT
ejpam-3478	235	35	.	.	PUNCT
ejpam-3478	236	1	to	to	PART
ejpam-3478	236	2	proceed	proceed	VERB
ejpam-3478	236	3	further	far	ADV
ejpam-3478	236	4	we	we	PRON
ejpam-3478	236	5	need	need	VERB
ejpam-3478	236	6	w1	w1	PROPN
ejpam-3478	236	7	c.	c.	PROPN
ejpam-3478	236	8	atkinson	atkinson	PROPN
ejpam-3478	236	9	,	,	PUNCT
ejpam-3478	236	10	s.	s.	PROPN
ejpam-3478	236	11	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	236	12	,	,	PUNCT
ejpam-3478	236	13	p.	p.	PROPN
ejpam-3478	236	14	ingpochai	ingpochai	PROPN
ejpam-3478	236	15	/	/	SYM
ejpam-3478	236	16	eur	eur	PROPN
ejpam-3478	236	17	.	.	PUNCT
ejpam-3478	237	1	j.	j.	PROPN
ejpam-3478	237	2	pure	pure	PROPN
ejpam-3478	237	3	appl	appl	PROPN
ejpam-3478	237	4	.	.	PROPN
ejpam-3478	237	5	math	math	PROPN
ejpam-3478	237	6	,	,	PUNCT
ejpam-3478	237	7	12	12	NUM
ejpam-3478	237	8	(	(	PUNCT
ejpam-3478	237	9	3	3	NUM
ejpam-3478	237	10	)	)	PUNCT
ejpam-3478	237	11	(	(	PUNCT
ejpam-3478	237	12	2019	2019	NUM
ejpam-3478	237	13	)	)	PUNCT
ejpam-3478	237	14	,	,	PUNCT
ejpam-3478	237	15	1315	1315	NUM
ejpam-3478	237	16	-	-	SYM
ejpam-3478	237	17	1336	1336	NUM
ejpam-3478	237	18	1326	1326	NUM
ejpam-3478	237	19	and	and	CCONJ
ejpam-3478	237	20	u1	u1	NOUN
ejpam-3478	237	21	which	which	PRON
ejpam-3478	237	22	we	we	PRON
ejpam-3478	237	23	have	have	VERB
ejpam-3478	237	24	from	from	ADP
ejpam-3478	237	25	the	the	DET
ejpam-3478	237	26	o	o	PROPN
ejpam-3478	237	27	(	(	PUNCT
ejpam-3478	237	28	ε	ε	PROPN
ejpam-3478	237	29	)	)	PUNCT
ejpam-3478	237	30	equations	equation	NOUN
ejpam-3478	237	31	of	of	ADP
ejpam-3478	237	32	(	(	PUNCT
ejpam-3478	237	33	11	11	NUM
ejpam-3478	237	34	)	)	PUNCT
ejpam-3478	237	35	and	and	CCONJ
ejpam-3478	237	36	(	(	PUNCT
ejpam-3478	237	37	12	12	NUM
ejpam-3478	237	38	)	)	PUNCT
ejpam-3478	237	39	.	.	PUNCT
ejpam-3478	238	1	with	with	ADP
ejpam-3478	238	2	the	the	DET
ejpam-3478	238	3	above	above	ADJ
ejpam-3478	238	4	choice	choice	NOUN
ejpam-3478	238	5	of	of	ADP
ejpam-3478	238	6	j0	j0	PROPN
ejpam-3478	238	7	and	and	CCONJ
ejpam-3478	238	8	j1	j1	PROPN
ejpam-3478	238	9	these	these	PRON
ejpam-3478	238	10	become	become	VERB
ejpam-3478	238	11	a	a	DET
ejpam-3478	238	12	(	(	PUNCT
ejpam-3478	238	13	t	t	NOUN
ejpam-3478	238	14	)	)	PUNCT
ejpam-3478	238	15	(	(	PUNCT
ejpam-3478	238	16	σ2	σ2	NOUN
ejpam-3478	238	17	−qσρ	−qσρ	PROPN
ejpam-3478	238	18	−qσρ	−qσρ	PROPN
ejpam-3478	238	19	q2	q2	PROPN
ejpam-3478	238	20	)	)	PUNCT
ejpam-3478	238	21	(	(	PUNCT
ejpam-3478	238	22	w1	w1	NOUN
ejpam-3478	238	23	u1	u1	NOUN
ejpam-3478	238	24	)	)	PUNCT
ejpam-3478	239	1	=	=	PUNCT
ejpam-3478	240	1	(	(	PUNCT
ejpam-3478	240	2	ξ1	ξ1	NOUN
ejpam-3478	240	3	ξ2	ξ2	PROPN
ejpam-3478	240	4	)	)	PUNCT
ejpam-3478	240	5	(	(	PUNCT
ejpam-3478	240	6	45	45	NUM
ejpam-3478	240	7	)	)	PUNCT
ejpam-3478	240	8	where	where	SCONJ
ejpam-3478	240	9	ξ1	ξ1	NOUN
ejpam-3478	240	10	=	=	SYM
ejpam-3478	240	11	−	−	PROPN
ejpam-3478	240	12	(	(	PUNCT
ejpam-3478	240	13	α−	α−	ADP
ejpam-3478	240	14	ra	ra	NOUN
ejpam-3478	240	15	)	)	PUNCT
ejpam-3478	240	16	[	[	PUNCT
ejpam-3478	240	17	bl+	bl+	PROPN
ejpam-3478	240	18	b1γw	b1γw	X
ejpam-3478	240	19	(	(	PUNCT
ejpam-3478	240	20	γ	γ	X
ejpam-3478	240	21	−	−	PROPN
ejpam-3478	240	22	1	1	NUM
ejpam-3478	240	23	)	)	PUNCT
ejpam-3478	240	24	−	−	PROPN
ejpam-3478	240	25	b1l	b1l	PROPN
ejpam-3478	240	26	(	(	PUNCT
ejpam-3478	240	27	γ	γ	NOUN
ejpam-3478	240	28	−	−	PROPN
ejpam-3478	240	29	1	1	NUM
ejpam-3478	240	30	)	)	PUNCT
ejpam-3478	240	31	]	]	PUNCT
ejpam-3478	241	1	−	−	PUNCT
ejpam-3478	241	2	σ2q1	σ2q1	X
ejpam-3478	242	1	[	[	X
ejpam-3478	242	2	b1	b1	NOUN
ejpam-3478	242	3	{	{	PUNCT
ejpam-3478	242	4	γw	γw	NOUN
ejpam-3478	242	5	−	−	PROPN
ejpam-3478	242	6	2l}+	2l}+	NUM
ejpam-3478	242	7	(	(	PUNCT
ejpam-3478	242	8	γ	γ	X
ejpam-3478	242	9	−	−	PROPN
ejpam-3478	242	10	2)bl	2)bl	NUM
ejpam-3478	242	11	]	]	PUNCT
ejpam-3478	242	12	−	−	NOUN
ejpam-3478	242	13	qσρq2	qσρq2	NOUN
ejpam-3478	243	1	[	[	X
ejpam-3478	243	2	b	b	X
ejpam-3478	243	3	{	{	PUNCT
ejpam-3478	243	4	w	w	NOUN
ejpam-3478	243	5	−	−	PROPN
ejpam-3478	243	6	(	(	PUNCT
ejpam-3478	243	7	γ	γ	PROPN
ejpam-3478	243	8	−	−	PROPN
ejpam-3478	243	9	1)l	1)l	NUM
ejpam-3478	243	10	}	}	PUNCT
ejpam-3478	243	11	−	−	PROPN
ejpam-3478	243	12	(	(	PUNCT
ejpam-3478	243	13	γ	γ	X
ejpam-3478	243	14	−	−	PROPN
ejpam-3478	243	15	1)b1w	1)b1w	NUM
ejpam-3478	243	16	+	+	NOUN
ejpam-3478	243	17	b1l	b1l	NOUN
ejpam-3478	243	18	]	]	X
ejpam-3478	243	19	(	(	PUNCT
ejpam-3478	243	20	46	46	NUM
ejpam-3478	243	21	)	)	PUNCT
ejpam-3478	243	22	and	and	CCONJ
ejpam-3478	243	23	ξ2	ξ2	NOUN
ejpam-3478	243	24	=	=	NOUN
ejpam-3478	243	25	−c	−c	NOUN
ejpam-3478	243	26	[	[	PUNCT
ejpam-3478	243	27	bw	bw	X
ejpam-3478	243	28	(	(	PUNCT
ejpam-3478	243	29	γ	γ	PROPN
ejpam-3478	243	30	−	−	PROPN
ejpam-3478	243	31	1	1	NUM
ejpam-3478	243	32	)	)	PUNCT
ejpam-3478	243	33	−	−	PROPN
ejpam-3478	243	34	blγ	blγ	PROPN
ejpam-3478	243	35	(	(	PUNCT
ejpam-3478	243	36	γ	γ	NOUN
ejpam-3478	243	37	−	−	PROPN
ejpam-3478	243	38	1	1	NUM
ejpam-3478	243	39	)	)	PUNCT
ejpam-3478	243	40	−b1w	−b1w	NUM
ejpam-3478	243	41	]	]	PUNCT
ejpam-3478	244	1	−	−	PUNCT
ejpam-3478	245	1	q2q2	q2q2	X
ejpam-3478	246	1	[	[	X
ejpam-3478	246	2	−2bw	−2bw	X
ejpam-3478	246	3	+	+	PUNCT
ejpam-3478	246	4	γbl+	γbl+	NOUN
ejpam-3478	246	5	(	(	PUNCT
ejpam-3478	246	6	γ	γ	X
ejpam-3478	246	7	−	−	PROPN
ejpam-3478	246	8	2)b1w	2)b1w	NUM
ejpam-3478	246	9	]	]	PUNCT
ejpam-3478	246	10	−	−	PROPN
ejpam-3478	246	11	qσρq1	qσρq1	PROPN
ejpam-3478	247	1	[	[	X
ejpam-3478	247	2	bw	bw	X
ejpam-3478	247	3	−	−	PROPN
ejpam-3478	247	4	(	(	PUNCT
ejpam-3478	247	5	γ	γ	PROPN
ejpam-3478	247	6	−	−	PROPN
ejpam-3478	247	7	1)bl+b1l−	1)bl+b1l−	NUM
ejpam-3478	247	8	(	(	PUNCT
ejpam-3478	247	9	γ	γ	X
ejpam-3478	247	10	−	−	PROPN
ejpam-3478	247	11	1)b1w	1)b1w	NUM
ejpam-3478	247	12	]	]	X
ejpam-3478	247	13	−a	−a	NOUN
ejpam-3478	247	14	(	(	PUNCT
ejpam-3478	247	15	t	t	PROPN
ejpam-3478	247	16	)	)	PUNCT
ejpam-3478	247	17	w	w	NOUN
ejpam-3478	247	18	−	−	PROPN
ejpam-3478	247	19	l	l	NOUN
ejpam-3478	247	20	γ	γ	X
ejpam-3478	247	21	−	−	PROPN
ejpam-3478	247	22	1	1	NUM
ejpam-3478	247	23	.	.	PUNCT
ejpam-3478	248	1	(	(	PUNCT
ejpam-3478	248	2	47	47	NUM
ejpam-3478	248	3	)	)	PUNCT
ejpam-3478	248	4	from	from	ADP
ejpam-3478	248	5	this	this	DET
ejpam-3478	248	6	equation	equation	NOUN
ejpam-3478	248	7	we	we	PRON
ejpam-3478	248	8	can	can	AUX
ejpam-3478	248	9	see	see	VERB
ejpam-3478	248	10	that	that	SCONJ
ejpam-3478	248	11	a	a	DET
ejpam-3478	248	12	(	(	PUNCT
ejpam-3478	248	13	t)w1	t)w1	PROPN
ejpam-3478	248	14	and	and	CCONJ
ejpam-3478	248	15	a	a	PRON
ejpam-3478	248	16	(	(	PUNCT
ejpam-3478	248	17	t)u1	t)u1	NOUN
ejpam-3478	248	18	are	be	AUX
ejpam-3478	248	19	expressions	expression	NOUN
ejpam-3478	248	20	linear	linear	ADJ
ejpam-3478	248	21	in	in	ADP
ejpam-3478	248	22	w	w	PROPN
ejpam-3478	248	23	and	and	CCONJ
ejpam-3478	248	24	l	l	NOUN
ejpam-3478	248	25	so	so	ADV
ejpam-3478	248	26	when	when	SCONJ
ejpam-3478	248	27	substituted	substitute	VERB
ejpam-3478	248	28	in	in	ADP
ejpam-3478	248	29	(	(	PUNCT
ejpam-3478	248	30	44	44	NUM
ejpam-3478	248	31	)	)	PUNCT
ejpam-3478	248	32	,	,	PUNCT
ejpam-3478	248	33	we	we	PRON
ejpam-3478	248	34	get	get	VERB
ejpam-3478	248	35	two	two	NUM
ejpam-3478	248	36	linear	linear	ADJ
ejpam-3478	248	37	coupled	couple	VERB
ejpam-3478	248	38	differential	differential	ADJ
ejpam-3478	248	39	equations	equation	NOUN
ejpam-3478	248	40	in	in	ADP
ejpam-3478	248	41	b	b	PROPN
ejpam-3478	248	42	(	(	PUNCT
ejpam-3478	248	43	t	t	PROPN
ejpam-3478	248	44	)	)	PUNCT
ejpam-3478	248	45	and	and	CCONJ
ejpam-3478	248	46	b1	b1	NOUN
ejpam-3478	248	47	(	(	PUNCT
ejpam-3478	248	48	t	t	PROPN
ejpam-3478	248	49	)	)	PUNCT
ejpam-3478	248	50	.	.	PUNCT
ejpam-3478	249	1	further	far	ADV
ejpam-3478	249	2	as	as	SCONJ
ejpam-3478	249	3	can	can	AUX
ejpam-3478	249	4	be	be	AUX
ejpam-3478	249	5	seen	see	VERB
ejpam-3478	249	6	in	in	ADP
ejpam-3478	249	7	(	(	PUNCT
ejpam-3478	249	8	44	44	NUM
ejpam-3478	249	9	)	)	PUNCT
ejpam-3478	249	10	there	there	PRON
ejpam-3478	249	11	is	be	VERB
ejpam-3478	249	12	one	one	NUM
ejpam-3478	249	13	term	term	NOUN
ejpam-3478	249	14	which	which	PRON
ejpam-3478	249	15	is	be	AUX
ejpam-3478	249	16	−a	−a	ADJ
ejpam-3478	249	17	(	(	PUNCT
ejpam-3478	249	18	t)l	t)l	X
ejpam-3478	249	19	which	which	PRON
ejpam-3478	249	20	stands	stand	VERB
ejpam-3478	249	21	alone	alone	ADJ
ejpam-3478	249	22	hence	hence	ADV
ejpam-3478	249	23	both	both	PRON
ejpam-3478	249	24	b	b	PROPN
ejpam-3478	249	25	(	(	PUNCT
ejpam-3478	249	26	t	t	PROPN
ejpam-3478	249	27	)	)	PUNCT
ejpam-3478	249	28	and	and	CCONJ
ejpam-3478	249	29	b1	b1	PROPN
ejpam-3478	249	30	(	(	PUNCT
ejpam-3478	249	31	t	t	NOUN
ejpam-3478	249	32	)	)	PUNCT
ejpam-3478	249	33	will	will	AUX
ejpam-3478	249	34	depend	depend	VERB
ejpam-3478	249	35	on	on	ADP
ejpam-3478	249	36	a	a	DET
ejpam-3478	249	37	(	(	PUNCT
ejpam-3478	249	38	t	t	PROPN
ejpam-3478	249	39	)	)	PUNCT
ejpam-3478	249	40	.	.	PUNCT
ejpam-3478	250	1	finally	finally	ADV
ejpam-3478	250	2	since	since	SCONJ
ejpam-3478	250	3	the	the	DET
ejpam-3478	250	4	condition	condition	NOUN
ejpam-3478	250	5	at	at	ADP
ejpam-3478	250	6	t	t	PROPN
ejpam-3478	250	7	=	=	SYM
ejpam-3478	250	8	t	t	PROPN
ejpam-3478	250	9	has	have	AUX
ejpam-3478	250	10	been	be	AUX
ejpam-3478	250	11	satisfied	satisfy	VERB
ejpam-3478	250	12	by	by	ADP
ejpam-3478	250	13	a	a	DET
ejpam-3478	250	14	(	(	PUNCT
ejpam-3478	250	15	t	t	NOUN
ejpam-3478	250	16	)	)	PUNCT
ejpam-3478	250	17	we	we	PRON
ejpam-3478	250	18	will	will	AUX
ejpam-3478	250	19	have	have	VERB
ejpam-3478	250	20	b	b	NUM
ejpam-3478	250	21	(	(	PUNCT
ejpam-3478	250	22	t	t	PROPN
ejpam-3478	250	23	)	)	PUNCT
ejpam-3478	250	24	=	=	SYM
ejpam-3478	250	25	0	0	NUM
ejpam-3478	250	26	and	and	CCONJ
ejpam-3478	250	27	b1	b1	PROPN
ejpam-3478	250	28	(	(	PUNCT
ejpam-3478	250	29	t	t	PROPN
ejpam-3478	250	30	)	)	PUNCT
ejpam-3478	251	1	=	=	PUNCT
ejpam-3478	251	2	0	0	X
ejpam-3478	251	3	.	.	PUNCT
ejpam-3478	252	1	the	the	DET
ejpam-3478	252	2	functional	functional	ADJ
ejpam-3478	252	3	form	form	NOUN
ejpam-3478	252	4	of	of	ADP
ejpam-3478	252	5	a	a	DET
ejpam-3478	252	6	(	(	PUNCT
ejpam-3478	252	7	t	t	NOUN
ejpam-3478	252	8	)	)	PUNCT
ejpam-3478	252	9	is	be	AUX
ejpam-3478	252	10	derived	derive	VERB
ejpam-3478	252	11	in	in	ADP
ejpam-3478	252	12	the	the	DET
ejpam-3478	252	13	appendix	appendix	NOUN
ejpam-3478	252	14	.	.	PUNCT
ejpam-3478	253	1	5	5	X
ejpam-3478	253	2	.	.	X
ejpam-3478	253	3	conclusion	conclusion	NOUN
ejpam-3478	253	4	&	&	CCONJ
ejpam-3478	253	5	final	final	ADJ
ejpam-3478	253	6	remarks	remark	NOUN
ejpam-3478	253	7	this	this	DET
ejpam-3478	253	8	paper	paper	NOUN
ejpam-3478	253	9	investigates	investigate	VERB
ejpam-3478	253	10	the	the	DET
ejpam-3478	253	11	optimal	optimal	ADJ
ejpam-3478	253	12	portfolio	portfolio	NOUN
ejpam-3478	253	13	selection	selection	NOUN
ejpam-3478	253	14	for	for	ADP
ejpam-3478	253	15	insurers	insurer	NOUN
ejpam-3478	253	16	with	with	ADP
ejpam-3478	253	17	stochastic	stochastic	ADJ
ejpam-3478	253	18	liabilities	liability	NOUN
ejpam-3478	253	19	.	.	PUNCT
ejpam-3478	254	1	the	the	DET
ejpam-3478	254	2	model	model	NOUN
ejpam-3478	254	3	considers	consider	VERB
ejpam-3478	254	4	characteristics	characteristic	NOUN
ejpam-3478	254	5	of	of	ADP
ejpam-3478	254	6	the	the	DET
ejpam-3478	254	7	insurers	insurer	NOUN
ejpam-3478	254	8	balance	balance	NOUN
ejpam-3478	254	9	sheet	sheet	NOUN
ejpam-3478	254	10	and	and	CCONJ
ejpam-3478	254	11	the	the	DET
ejpam-3478	254	12	dependence	dependence	NOUN
ejpam-3478	254	13	on	on	ADP
ejpam-3478	254	14	control	control	NOUN
ejpam-3478	254	15	variables	variable	NOUN
ejpam-3478	254	16	w	w	ADP
ejpam-3478	254	17	of	of	ADP
ejpam-3478	254	18	the	the	DET
ejpam-3478	254	19	wealth	wealth	NOUN
ejpam-3478	254	20	investment	investment	NOUN
ejpam-3478	254	21	(	(	PUNCT
ejpam-3478	254	22	for	for	ADP
ejpam-3478	254	23	which	which	PRON
ejpam-3478	254	24	ww	ww	PROPN
ejpam-3478	254	25	is	be	AUX
ejpam-3478	254	26	the	the	DET
ejpam-3478	254	27	risky	risky	ADJ
ejpam-3478	254	28	part	part	NOUN
ejpam-3478	254	29	see	see	VERB
ejpam-3478	254	30	figure	figure	NOUN
ejpam-3478	254	31	1	1	NUM
ejpam-3478	254	32	)	)	PUNCT
ejpam-3478	254	33	and	and	CCONJ
ejpam-3478	254	34	u	u	NOUN
ejpam-3478	254	35	of	of	ADP
ejpam-3478	254	36	the	the	DET
ejpam-3478	254	37	liability	liability	NOUN
ejpam-3478	254	38	of	of	ADP
ejpam-3478	254	39	which	which	PRON
ejpam-3478	254	40	ul	ul	INTJ
ejpam-3478	254	41	is	be	AUX
ejpam-3478	254	42	the	the	DET
ejpam-3478	254	43	amount	amount	NOUN
ejpam-3478	254	44	of	of	ADP
ejpam-3478	254	45	risky	risky	ADJ
ejpam-3478	254	46	liability	liability	NOUN
ejpam-3478	254	47	.	.	PUNCT
ejpam-3478	255	1	these	these	DET
ejpam-3478	255	2	controls	control	NOUN
ejpam-3478	255	3	are	be	AUX
ejpam-3478	255	4	found	find	VERB
ejpam-3478	255	5	for	for	ADP
ejpam-3478	255	6	a	a	DET
ejpam-3478	255	7	variety	variety	NOUN
ejpam-3478	255	8	of	of	ADP
ejpam-3478	255	9	utility	utility	NOUN
ejpam-3478	255	10	functions	function	NOUN
ejpam-3478	255	11	where	where	SCONJ
ejpam-3478	255	12	portfolio	portfolio	NOUN
ejpam-3478	255	13	selection	selection	NOUN
ejpam-3478	255	14	is	be	AUX
ejpam-3478	255	15	found	find	VERB
ejpam-3478	255	16	via	via	ADP
ejpam-3478	255	17	a	a	DET
ejpam-3478	255	18	maximum	maximum	ADJ
ejpam-3478	255	19	expected	expect	VERB
ejpam-3478	255	20	utility	utility	NOUN
ejpam-3478	255	21	over	over	ADP
ejpam-3478	255	22	a	a	DET
ejpam-3478	255	23	life	life	NOUN
ejpam-3478	255	24	time	time	NOUN
ejpam-3478	255	25	.	.	PUNCT
ejpam-3478	256	1	for	for	ADP
ejpam-3478	256	2	the	the	DET
ejpam-3478	256	3	simplest	simple	ADJ
ejpam-3478	256	4	case	case	NOUN
ejpam-3478	256	5	(	(	PUNCT
ejpam-3478	256	6	section	section	NOUN
ejpam-3478	256	7	3	3	NUM
ejpam-3478	256	8	)	)	PUNCT
ejpam-3478	256	9	where	where	SCONJ
ejpam-3478	256	10	the	the	DET
ejpam-3478	256	11	utility	utility	NOUN
ejpam-3478	256	12	(	(	PUNCT
ejpam-3478	256	13	u	u	NOUN
ejpam-3478	256	14	=	=	PROPN
ejpam-3478	256	15	w	w	PROPN
ejpam-3478	256	16	γ	γ	X
ejpam-3478	256	17	γ	γ	X
ejpam-3478	256	18	)	)	PUNCT
ejpam-3478	256	19	depends	depend	VERB
ejpam-3478	256	20	only	only	ADV
ejpam-3478	256	21	on	on	ADP
ejpam-3478	256	22	wealth	wealth	NOUN
ejpam-3478	256	23	we	we	PRON
ejpam-3478	256	24	find	find	VERB
ejpam-3478	256	25	(	(	PUNCT
ejpam-3478	256	26	equation	equation	NOUN
ejpam-3478	256	27	18	18	NUM
ejpam-3478	256	28	)	)	PUNCT
ejpam-3478	256	29	that	that	SCONJ
ejpam-3478	256	30	the	the	DET
ejpam-3478	256	31	optimal	optimal	ADJ
ejpam-3478	256	32	allocation	allocation	NOUN
ejpam-3478	256	33	to	to	ADP
ejpam-3478	256	34	the	the	DET
ejpam-3478	256	35	risky	risky	ADJ
ejpam-3478	256	36	asset	asset	NOUN
ejpam-3478	256	37	is	be	AUX
ejpam-3478	256	38	w∗	w∗	NOUN
ejpam-3478	256	39	=	=	PUNCT
ejpam-3478	256	40	(	(	PUNCT
ejpam-3478	256	41	α−	α−	ADP
ejpam-3478	256	42	ra	ra	NOUN
ejpam-3478	256	43	)	)	PUNCT
ejpam-3478	256	44	σ2(1−	σ2(1−	PROPN
ejpam-3478	256	45	γ	γ	PROPN
ejpam-3478	256	46	)	)	PUNCT
ejpam-3478	256	47	and	and	CCONJ
ejpam-3478	256	48	u	u	PRON
ejpam-3478	256	49	can	can	AUX
ejpam-3478	256	50	take	take	VERB
ejpam-3478	256	51	any	any	DET
ejpam-3478	256	52	value	value	NOUN
ejpam-3478	256	53	.	.	PUNCT
ejpam-3478	257	1	c.	c.	PROPN
ejpam-3478	257	2	atkinson	atkinson	PROPN
ejpam-3478	257	3	,	,	PUNCT
ejpam-3478	257	4	s.	s.	PROPN
ejpam-3478	257	5	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	257	6	,	,	PUNCT
ejpam-3478	257	7	p.	p.	PROPN
ejpam-3478	257	8	ingpochai	ingpochai	PROPN
ejpam-3478	257	9	/	/	SYM
ejpam-3478	257	10	eur	eur	PROPN
ejpam-3478	257	11	.	.	PUNCT
ejpam-3478	258	1	j.	j.	PROPN
ejpam-3478	258	2	pure	pure	PROPN
ejpam-3478	258	3	appl	appl	PROPN
ejpam-3478	258	4	.	.	PROPN
ejpam-3478	258	5	math	math	PROPN
ejpam-3478	258	6	,	,	PUNCT
ejpam-3478	258	7	12	12	NUM
ejpam-3478	258	8	(	(	PUNCT
ejpam-3478	258	9	3	3	NUM
ejpam-3478	258	10	)	)	PUNCT
ejpam-3478	258	11	(	(	PUNCT
ejpam-3478	258	12	2019	2019	NUM
ejpam-3478	258	13	)	)	PUNCT
ejpam-3478	258	14	,	,	PUNCT
ejpam-3478	258	15	1315	1315	NUM
ejpam-3478	258	16	-	-	SYM
ejpam-3478	258	17	1336	1336	NUM
ejpam-3478	258	18	1327	1327	NUM
ejpam-3478	258	19	in	in	ADP
ejpam-3478	258	20	section	section	NOUN
ejpam-3478	258	21	4	4	NUM
ejpam-3478	258	22	,	,	PUNCT
ejpam-3478	258	23	we	we	PRON
ejpam-3478	258	24	consider	consider	VERB
ejpam-3478	258	25	a	a	DET
ejpam-3478	258	26	utility	utility	NOUN
ejpam-3478	258	27	function	function	NOUN
ejpam-3478	258	28	of	of	ADP
ejpam-3478	258	29	the	the	DET
ejpam-3478	258	30	form	form	NOUN
ejpam-3478	258	31	u	u	NOUN
ejpam-3478	258	32	(	(	PUNCT
ejpam-3478	258	33	w	w	PROPN
ejpam-3478	258	34	,	,	PUNCT
ejpam-3478	258	35	l	l	NOUN
ejpam-3478	258	36	)	)	PUNCT
ejpam-3478	258	37	=	=	SYM
ejpam-3478	259	1	(	(	PUNCT
ejpam-3478	259	2	w	w	NOUN
ejpam-3478	259	3	−	−	PROPN
ejpam-3478	259	4	l)γ	l)γ	NOUN
ejpam-3478	259	5	γ	γ	X
ejpam-3478	259	6	.	.	PUNCT
ejpam-3478	260	1	for	for	ADP
ejpam-3478	260	2	this	this	DET
ejpam-3478	260	3	case	case	NOUN
ejpam-3478	260	4	if	if	SCONJ
ejpam-3478	260	5	ra	ra	PROPN
ejpam-3478	260	6	=	=	SYM
ejpam-3478	260	7	rl	rl	X
ejpam-3478	260	8	(	(	PUNCT
ejpam-3478	260	9	i.e.	i.e.	X
ejpam-3478	260	10	asset	asset	NOUN
ejpam-3478	260	11	interest	interest	NOUN
ejpam-3478	260	12	rate	rate	NOUN
ejpam-3478	260	13	is	be	AUX
ejpam-3478	260	14	equal	equal	ADJ
ejpam-3478	260	15	to	to	ADP
ejpam-3478	260	16	liability	liability	NOUN
ejpam-3478	260	17	interest	interest	NOUN
ejpam-3478	260	18	rate	rate	NOUN
ejpam-3478	260	19	)	)	PUNCT
ejpam-3478	260	20	and	and	CCONJ
ejpam-3478	260	21	for	for	ADP
ejpam-3478	260	22	any	any	DET
ejpam-3478	260	23	correlation	correlation	NOUN
ejpam-3478	260	24	ρ	ρ	NOUN
ejpam-3478	260	25	,	,	PUNCT
ejpam-3478	260	26	we	we	PRON
ejpam-3478	260	27	have	have	VERB
ejpam-3478	260	28	the	the	DET
ejpam-3478	260	29	optimal	optimal	ADJ
ejpam-3478	260	30	weights	weight	NOUN
ejpam-3478	260	31	w	w	NOUN
ejpam-3478	260	32	and	and	CCONJ
ejpam-3478	260	33	u	u	PRON
ejpam-3478	260	34	given	give	VERB
ejpam-3478	260	35	as	as	ADP
ejpam-3478	260	36	w0	w0	PROPN
ejpam-3478	260	37	and	and	CCONJ
ejpam-3478	260	38	u0	u0	ADJ
ejpam-3478	260	39	below	below	ADP
ejpam-3478	260	40	which	which	PRON
ejpam-3478	260	41	are	be	AUX
ejpam-3478	260	42	exact	exact	ADJ
ejpam-3478	260	43	in	in	ADP
ejpam-3478	260	44	this	this	DET
ejpam-3478	260	45	case	case	NOUN
ejpam-3478	260	46	since	since	SCONJ
ejpam-3478	260	47	ε	ε	PROPN
ejpam-3478	260	48	=	=	SYM
ejpam-3478	260	49	rl	rl	PROPN
ejpam-3478	260	50	−	−	PROPN
ejpam-3478	260	51	ra	ra	NOUN
ejpam-3478	261	1	=	=	NOUN
ejpam-3478	261	2	0	0	PROPN
ejpam-3478	261	3	.	.	PUNCT
ejpam-3478	262	1	for	for	ADP
ejpam-3478	262	2	the	the	DET
ejpam-3478	262	3	situation	situation	NOUN
ejpam-3478	262	4	when	when	SCONJ
ejpam-3478	262	5	ra	ra	PROPN
ejpam-3478	262	6	6=	6=	PROPN
ejpam-3478	262	7	rl	rl	PROPN
ejpam-3478	262	8	but	but	CCONJ
ejpam-3478	262	9	|ε|	|ε|	PRON
ejpam-3478	262	10	�	�	PROPN
ejpam-3478	262	11	ra	ra	PROPN
ejpam-3478	262	12	,	,	PUNCT
ejpam-3478	262	13	we	we	PRON
ejpam-3478	262	14	use	use	VERB
ejpam-3478	262	15	an	an	DET
ejpam-3478	262	16	expansion	expansion	NOUN
ejpam-3478	262	17	such	such	ADJ
ejpam-3478	262	18	as	as	ADP
ejpam-3478	262	19	that	that	PRON
ejpam-3478	262	20	described	describe	VERB
ejpam-3478	262	21	below	below	ADV
ejpam-3478	262	22	(	(	PUNCT
ejpam-3478	262	23	see	see	VERB
ejpam-3478	262	24	also	also	ADV
ejpam-3478	262	25	the	the	DET
ejpam-3478	262	26	appendix	appendix	NOUN
ejpam-3478	262	27	)	)	PUNCT
ejpam-3478	262	28	.	.	PUNCT
ejpam-3478	263	1	we	we	PRON
ejpam-3478	263	2	have	have	AUX
ejpam-3478	263	3	solved	solve	VERB
ejpam-3478	263	4	for	for	ADP
ejpam-3478	263	5	the	the	DET
ejpam-3478	263	6	optimal	optimal	ADJ
ejpam-3478	263	7	weight	weight	NOUN
ejpam-3478	263	8	w	w	NOUN
ejpam-3478	263	9	and	and	CCONJ
ejpam-3478	263	10	u	u	PROPN
ejpam-3478	263	11	w	w	PROPN
ejpam-3478	263	12	=	=	PUNCT
ejpam-3478	263	13	ww	ww	PROPN
ejpam-3478	263	14	=	=	PROPN
ejpam-3478	263	15	w0	w0	PROPN
ejpam-3478	263	16	+	+	CCONJ
ejpam-3478	263	17	εw1	εw1	ADV
ejpam-3478	263	18	+	+	CCONJ
ejpam-3478	263	19	ε2w2	ε2w2	X
ejpam-3478	263	20	+	+	ADJ
ejpam-3478	263	21	o	o	X
ejpam-3478	263	22	(	(	PUNCT
ejpam-3478	263	23	ε3	ε3	PROPN
ejpam-3478	263	24	)	)	PUNCT
ejpam-3478	263	25	(	(	PUNCT
ejpam-3478	263	26	48	48	NUM
ejpam-3478	263	27	)	)	PUNCT
ejpam-3478	263	28	u	u	NOUN
ejpam-3478	263	29	=	=	PROPN
ejpam-3478	263	30	ul	ul	NOUN
ejpam-3478	263	31	=	=	PUNCT
ejpam-3478	263	32	u0	u0	PROPN
ejpam-3478	263	33	+	+	CCONJ
ejpam-3478	263	34	εu1	εu1	X
ejpam-3478	264	1	+	+	CCONJ
ejpam-3478	264	2	ε2u2	ε2u2	PROPN
ejpam-3478	264	3	+	+	ADJ
ejpam-3478	264	4	o	o	X
ejpam-3478	264	5	(	(	PUNCT
ejpam-3478	264	6	ε3	ε3	PROPN
ejpam-3478	264	7	)	)	PUNCT
ejpam-3478	264	8	(	(	PUNCT
ejpam-3478	264	9	49	49	NUM
ejpam-3478	264	10	)	)	PUNCT
ejpam-3478	264	11	this	this	PRON
ejpam-3478	264	12	can	can	AUX
ejpam-3478	264	13	be	be	AUX
ejpam-3478	264	14	solved	solve	VERB
ejpam-3478	264	15	to	to	PART
ejpam-3478	264	16	give	give	VERB
ejpam-3478	264	17	to	to	ADP
ejpam-3478	264	18	o	o	PROPN
ejpam-3478	264	19	(	(	PUNCT
ejpam-3478	264	20	1	1	NUM
ejpam-3478	264	21	)	)	PUNCT
ejpam-3478	264	22	as	as	ADP
ejpam-3478	264	23	w0	w0	PROPN
ejpam-3478	264	24	=	=	PROPN
ejpam-3478	264	25	w0w	w0w	PROPN
ejpam-3478	264	26	=	=	PROPN
ejpam-3478	264	27	q1	q1	PROPN
ejpam-3478	264	28	(	(	PUNCT
ejpam-3478	264	29	w	w	PROPN
ejpam-3478	264	30	−	−	PROPN
ejpam-3478	264	31	l	l	NOUN
ejpam-3478	264	32	)	)	PUNCT
ejpam-3478	264	33	(	(	PUNCT
ejpam-3478	264	34	50	50	NUM
ejpam-3478	264	35	)	)	PUNCT
ejpam-3478	264	36	u0	u0	ADJ
ejpam-3478	264	37	=	=	PUNCT
ejpam-3478	264	38	u0l	u0l	PROPN
ejpam-3478	264	39	=	=	SYM
ejpam-3478	264	40	q2	q2	NOUN
ejpam-3478	264	41	(	(	PUNCT
ejpam-3478	264	42	w	w	PROPN
ejpam-3478	264	43	−	−	PROPN
ejpam-3478	264	44	l	l	NOUN
ejpam-3478	264	45	)	)	PUNCT
ejpam-3478	264	46	(	(	PUNCT
ejpam-3478	264	47	51	51	NUM
ejpam-3478	264	48	)	)	PUNCT
ejpam-3478	264	49	where	where	SCONJ
ejpam-3478	264	50	q1	q1	NOUN
ejpam-3478	265	1	=	=	PUNCT
ejpam-3478	265	2	[	[	PUNCT
ejpam-3478	265	3	−	−	X
ejpam-3478	265	4	(	(	PUNCT
ejpam-3478	265	5	α−	α−	ADP
ejpam-3478	265	6	ra	ra	NOUN
ejpam-3478	265	7	)	)	PUNCT
ejpam-3478	265	8	q2	q2	NOUN
ejpam-3478	266	1	+	+	CCONJ
ejpam-3478	266	2	qσρ	qσρ	NOUN
ejpam-3478	266	3	{	{	PUNCT
ejpam-3478	266	4	c−m−	c−m−	PROPN
ejpam-3478	266	5	rl	rl	PROPN
ejpam-3478	266	6	}	}	PUNCT
ejpam-3478	266	7	]	]	PUNCT
ejpam-3478	266	8	σ2q2	σ2q2	X
ejpam-3478	266	9	(	(	PUNCT
ejpam-3478	266	10	γ	γ	PROPN
ejpam-3478	266	11	−	−	PROPN
ejpam-3478	266	12	1	1	NUM
ejpam-3478	266	13	)	)	PUNCT
ejpam-3478	266	14	(	(	PUNCT
ejpam-3478	266	15	1−	1−	NUM
ejpam-3478	266	16	ρ2	ρ2	NOUN
ejpam-3478	266	17	)	)	PUNCT
ejpam-3478	266	18	(	(	PUNCT
ejpam-3478	266	19	52	52	NUM
ejpam-3478	266	20	)	)	PUNCT
ejpam-3478	266	21	and	and	CCONJ
ejpam-3478	266	22	q2	q2	NOUN
ejpam-3478	266	23	=	=	PUNCT
ejpam-3478	266	24	[	[	PUNCT
ejpam-3478	266	25	−qσρ	−qσρ	NUM
ejpam-3478	266	26	(	(	PUNCT
ejpam-3478	266	27	α−	α−	ADP
ejpam-3478	266	28	ra	ra	PROPN
ejpam-3478	266	29	)	)	PUNCT
ejpam-3478	267	1	+	+	CCONJ
ejpam-3478	267	2	σ2	σ2	PROPN
ejpam-3478	267	3	{	{	PUNCT
ejpam-3478	267	4	c−m−	c−m−	PROPN
ejpam-3478	267	5	rl	rl	PROPN
ejpam-3478	267	6	}	}	PUNCT
ejpam-3478	267	7	]	]	PUNCT
ejpam-3478	267	8	σ2q2	σ2q2	X
ejpam-3478	267	9	(	(	PUNCT
ejpam-3478	267	10	γ	γ	PROPN
ejpam-3478	267	11	−	−	PROPN
ejpam-3478	267	12	1	1	NUM
ejpam-3478	267	13	)	)	PUNCT
ejpam-3478	267	14	(	(	PUNCT
ejpam-3478	267	15	1−	1−	NUM
ejpam-3478	267	16	ρ2	ρ2	NOUN
ejpam-3478	267	17	)	)	PUNCT
ejpam-3478	267	18	(	(	PUNCT
ejpam-3478	267	19	53	53	NUM
ejpam-3478	267	20	)	)	PUNCT
ejpam-3478	267	21	w0	w0	PROPN
ejpam-3478	267	22	and	and	CCONJ
ejpam-3478	267	23	u0	u0	PROPN
ejpam-3478	267	24	have	have	VERB
ejpam-3478	267	25	no	no	DET
ejpam-3478	267	26	explicit	explicit	ADJ
ejpam-3478	267	27	dependence	dependence	NOUN
ejpam-3478	267	28	of	of	ADP
ejpam-3478	267	29	time	time	NOUN
ejpam-3478	267	30	.	.	PUNCT
ejpam-3478	268	1	the	the	DET
ejpam-3478	268	2	o	o	PROPN
ejpam-3478	268	3	(	(	PUNCT
ejpam-3478	268	4	ε	ε	PROPN
ejpam-3478	268	5	)	)	PUNCT
ejpam-3478	268	6	approximation	approximation	NOUN
ejpam-3478	268	7	can	can	AUX
ejpam-3478	268	8	be	be	AUX
ejpam-3478	268	9	deduced	deduce	VERB
ejpam-3478	268	10	from	from	ADP
ejpam-3478	268	11	the	the	DET
ejpam-3478	268	12	equation	equation	NOUN
ejpam-3478	268	13	a	a	DET
ejpam-3478	268	14	(	(	PUNCT
ejpam-3478	268	15	t	t	NOUN
ejpam-3478	268	16	)	)	PUNCT
ejpam-3478	268	17	(	(	PUNCT
ejpam-3478	268	18	σ2	σ2	NOUN
ejpam-3478	268	19	−qσρ	−qσρ	PROPN
ejpam-3478	268	20	−qσρ	−qσρ	PROPN
ejpam-3478	268	21	q2	q2	PROPN
ejpam-3478	268	22	)	)	PUNCT
ejpam-3478	268	23	(	(	PUNCT
ejpam-3478	268	24	w1	w1	NOUN
ejpam-3478	268	25	u1	u1	NOUN
ejpam-3478	268	26	)	)	PUNCT
ejpam-3478	268	27	=	=	PUNCT
ejpam-3478	269	1	(	(	PUNCT
ejpam-3478	269	2	ξ1	ξ1	NOUN
ejpam-3478	269	3	ξ2	ξ2	PROPN
ejpam-3478	269	4	)	)	PUNCT
ejpam-3478	269	5	(	(	PUNCT
ejpam-3478	269	6	54	54	NUM
ejpam-3478	269	7	)	)	PUNCT
ejpam-3478	269	8	with	with	ADP
ejpam-3478	269	9	ξ1	ξ1	NOUN
ejpam-3478	269	10	=	=	SYM
ejpam-3478	269	11	−	−	PROPN
ejpam-3478	270	1	(	(	PUNCT
ejpam-3478	270	2	α−	α−	ADP
ejpam-3478	270	3	ra	ra	NOUN
ejpam-3478	270	4	)	)	PUNCT
ejpam-3478	270	5	[	[	PUNCT
ejpam-3478	270	6	bl+	bl+	PROPN
ejpam-3478	270	7	b1γw	b1γw	X
ejpam-3478	270	8	(	(	PUNCT
ejpam-3478	270	9	γ	γ	X
ejpam-3478	270	10	−	−	PROPN
ejpam-3478	270	11	1	1	NUM
ejpam-3478	270	12	)	)	PUNCT
ejpam-3478	270	13	−	−	PROPN
ejpam-3478	270	14	b1l	b1l	PROPN
ejpam-3478	270	15	(	(	PUNCT
ejpam-3478	270	16	γ	γ	NOUN
ejpam-3478	270	17	−	−	PROPN
ejpam-3478	270	18	1	1	NUM
ejpam-3478	270	19	)	)	PUNCT
ejpam-3478	270	20	]	]	PUNCT
ejpam-3478	271	1	−	−	PUNCT
ejpam-3478	271	2	σ2q1	σ2q1	X
ejpam-3478	272	1	[	[	X
ejpam-3478	272	2	b1	b1	NOUN
ejpam-3478	272	3	{	{	PUNCT
ejpam-3478	272	4	γw	γw	NOUN
ejpam-3478	272	5	−	−	PROPN
ejpam-3478	272	6	2l}+	2l}+	NUM
ejpam-3478	272	7	(	(	PUNCT
ejpam-3478	272	8	γ	γ	X
ejpam-3478	272	9	−	−	PROPN
ejpam-3478	272	10	2)bl	2)bl	NUM
ejpam-3478	272	11	]	]	PUNCT
ejpam-3478	272	12	−	−	NOUN
ejpam-3478	272	13	qσρq2	qσρq2	NOUN
ejpam-3478	273	1	[	[	X
ejpam-3478	273	2	b	b	X
ejpam-3478	273	3	{	{	PUNCT
ejpam-3478	273	4	w	w	NOUN
ejpam-3478	273	5	−	−	PROPN
ejpam-3478	273	6	(	(	PUNCT
ejpam-3478	273	7	γ	γ	PROPN
ejpam-3478	273	8	−	−	PROPN
ejpam-3478	273	9	1)l	1)l	NUM
ejpam-3478	273	10	}	}	PUNCT
ejpam-3478	273	11	−	−	PROPN
ejpam-3478	273	12	(	(	PUNCT
ejpam-3478	273	13	γ	γ	X
ejpam-3478	273	14	−	−	PROPN
ejpam-3478	273	15	1)b1w	1)b1w	NUM
ejpam-3478	273	16	+	+	NOUN
ejpam-3478	273	17	b1l	b1l	NOUN
ejpam-3478	273	18	]	]	X
ejpam-3478	273	19	(	(	PUNCT
ejpam-3478	273	20	55	55	NUM
ejpam-3478	273	21	)	)	PUNCT
ejpam-3478	273	22	and	and	CCONJ
ejpam-3478	273	23	ξ2	ξ2	NOUN
ejpam-3478	273	24	=	=	NOUN
ejpam-3478	273	25	−c	−c	NOUN
ejpam-3478	273	26	[	[	PUNCT
ejpam-3478	273	27	bw	bw	X
ejpam-3478	273	28	(	(	PUNCT
ejpam-3478	273	29	γ	γ	PROPN
ejpam-3478	273	30	−	−	PROPN
ejpam-3478	273	31	1	1	NUM
ejpam-3478	273	32	)	)	PUNCT
ejpam-3478	273	33	−	−	PROPN
ejpam-3478	273	34	blγ	blγ	PROPN
ejpam-3478	273	35	(	(	PUNCT
ejpam-3478	273	36	γ	γ	NOUN
ejpam-3478	273	37	−	−	PROPN
ejpam-3478	273	38	1	1	NUM
ejpam-3478	273	39	)	)	PUNCT
ejpam-3478	273	40	−b1w	−b1w	NUM
ejpam-3478	273	41	]	]	PUNCT
ejpam-3478	274	1	−	−	PUNCT
ejpam-3478	275	1	q2q2	q2q2	X
ejpam-3478	276	1	[	[	X
ejpam-3478	276	2	−2bw	−2bw	X
ejpam-3478	276	3	+	+	PUNCT
ejpam-3478	276	4	γbl+	γbl+	NOUN
ejpam-3478	276	5	(	(	PUNCT
ejpam-3478	276	6	γ	γ	X
ejpam-3478	276	7	−	−	PROPN
ejpam-3478	276	8	2)b1w	2)b1w	NUM
ejpam-3478	276	9	]	]	PUNCT
ejpam-3478	276	10	−	−	PROPN
ejpam-3478	276	11	qσρq1	qσρq1	PROPN
ejpam-3478	277	1	[	[	X
ejpam-3478	277	2	bw	bw	X
ejpam-3478	277	3	−	−	PROPN
ejpam-3478	277	4	(	(	PUNCT
ejpam-3478	277	5	γ	γ	PROPN
ejpam-3478	277	6	−	−	PROPN
ejpam-3478	277	7	1)bl+b1l−	1)bl+b1l−	NUM
ejpam-3478	277	8	(	(	PUNCT
ejpam-3478	277	9	γ	γ	X
ejpam-3478	277	10	−	−	PROPN
ejpam-3478	277	11	1)b1w	1)b1w	NUM
ejpam-3478	277	12	]	]	PUNCT
ejpam-3478	277	13	c.	c.	PROPN
ejpam-3478	277	14	atkinson	atkinson	PROPN
ejpam-3478	277	15	,	,	PUNCT
ejpam-3478	277	16	s.	s.	PROPN
ejpam-3478	277	17	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	277	18	,	,	PUNCT
ejpam-3478	277	19	p.	p.	PROPN
ejpam-3478	277	20	ingpochai	ingpochai	PROPN
ejpam-3478	277	21	/	/	SYM
ejpam-3478	277	22	eur	eur	PROPN
ejpam-3478	277	23	.	.	PUNCT
ejpam-3478	278	1	j.	j.	PROPN
ejpam-3478	278	2	pure	pure	PROPN
ejpam-3478	278	3	appl	appl	PROPN
ejpam-3478	278	4	.	.	PROPN
ejpam-3478	278	5	math	math	PROPN
ejpam-3478	278	6	,	,	PUNCT
ejpam-3478	278	7	12	12	NUM
ejpam-3478	278	8	(	(	PUNCT
ejpam-3478	278	9	3	3	NUM
ejpam-3478	278	10	)	)	PUNCT
ejpam-3478	278	11	(	(	PUNCT
ejpam-3478	278	12	2019	2019	NUM
ejpam-3478	278	13	)	)	PUNCT
ejpam-3478	278	14	,	,	PUNCT
ejpam-3478	278	15	1315	1315	NUM
ejpam-3478	278	16	-	-	SYM
ejpam-3478	278	17	1336	1336	NUM
ejpam-3478	278	18	1328	1328	NUM
ejpam-3478	278	19	−a	−a	NOUN
ejpam-3478	278	20	(	(	PUNCT
ejpam-3478	278	21	t	t	PROPN
ejpam-3478	278	22	)	)	PUNCT
ejpam-3478	278	23	w	w	NOUN
ejpam-3478	278	24	−	−	PROPN
ejpam-3478	278	25	l	l	NOUN
ejpam-3478	278	26	γ	γ	X
ejpam-3478	278	27	−	−	PROPN
ejpam-3478	278	28	1	1	NUM
ejpam-3478	278	29	,	,	PUNCT
ejpam-3478	278	30	(	(	PUNCT
ejpam-3478	278	31	56	56	NUM
ejpam-3478	278	32	)	)	PUNCT
ejpam-3478	278	33	where	where	SCONJ
ejpam-3478	278	34	a	a	DET
ejpam-3478	278	35	(	(	PUNCT
ejpam-3478	278	36	t	t	NOUN
ejpam-3478	278	37	)	)	PUNCT
ejpam-3478	278	38	follows	follow	VERB
ejpam-3478	278	39	from	from	ADP
ejpam-3478	278	40	equation	equation	NOUN
ejpam-3478	278	41	(	(	PUNCT
ejpam-3478	278	42	43	43	NUM
ejpam-3478	278	43	)	)	PUNCT
ejpam-3478	278	44	and	and	CCONJ
ejpam-3478	278	45	b	b	NOUN
ejpam-3478	278	46	and	and	CCONJ
ejpam-3478	278	47	b1	b1	NOUN
ejpam-3478	278	48	can	can	AUX
ejpam-3478	278	49	be	be	AUX
ejpam-3478	278	50	deduced	deduce	VERB
ejpam-3478	278	51	from	from	ADP
ejpam-3478	278	52	a	a	DET
ejpam-3478	278	53	pair	pair	NOUN
ejpam-3478	278	54	of	of	ADP
ejpam-3478	278	55	first	first	ADJ
ejpam-3478	278	56	order	order	NOUN
ejpam-3478	278	57	coupled	couple	VERB
ejpam-3478	278	58	differential	differential	ADJ
ejpam-3478	278	59	equation	equation	NOUN
ejpam-3478	278	60	in	in	ADP
ejpam-3478	278	61	time	time	NOUN
ejpam-3478	278	62	.	.	PUNCT
ejpam-3478	279	1	from	from	ADP
ejpam-3478	279	2	(	(	PUNCT
ejpam-3478	279	3	54	54	NUM
ejpam-3478	279	4	)	)	PUNCT
ejpam-3478	279	5	we	we	PRON
ejpam-3478	279	6	can	can	AUX
ejpam-3478	279	7	write	write	VERB
ejpam-3478	279	8	a	a	DET
ejpam-3478	279	9	(	(	PUNCT
ejpam-3478	279	10	t)w1	t)w1	PROPN
ejpam-3478	279	11	=	=	SYM
ejpam-3478	279	12	q2ξ1	q2ξ1	ADJ
ejpam-3478	279	13	σ2q2	σ2q2	NOUN
ejpam-3478	279	14	(	(	PUNCT
ejpam-3478	279	15	1−	1−	NUM
ejpam-3478	279	16	ρ2	ρ2	NOUN
ejpam-3478	279	17	)	)	PUNCT
ejpam-3478	280	1	+	+	NUM
ejpam-3478	280	2	qσρξ2	qσρξ2	NOUN
ejpam-3478	280	3	σ2q2	σ2q2	PROPN
ejpam-3478	280	4	(	(	PUNCT
ejpam-3478	280	5	1−	1−	NUM
ejpam-3478	280	6	ρ2	ρ2	NOUN
ejpam-3478	280	7	)	)	PUNCT
ejpam-3478	280	8	≡	≡	PROPN
ejpam-3478	280	9	t1l+	t1l+	NOUN
ejpam-3478	280	10	t2w	t2w	PROPN
ejpam-3478	280	11	(	(	PUNCT
ejpam-3478	280	12	57	57	NUM
ejpam-3478	280	13	)	)	PUNCT
ejpam-3478	280	14	a	a	PRON
ejpam-3478	280	15	(	(	PUNCT
ejpam-3478	280	16	t)u1	t)u1	NOUN
ejpam-3478	280	17	=	=	PUNCT
ejpam-3478	280	18	qσρξ1	qσρξ1	NOUN
ejpam-3478	280	19	σ2q2	σ2q2	X
ejpam-3478	280	20	(	(	PUNCT
ejpam-3478	280	21	1−	1−	NUM
ejpam-3478	280	22	ρ2	ρ2	NOUN
ejpam-3478	280	23	)	)	PUNCT
ejpam-3478	281	1	+	+	NUM
ejpam-3478	281	2	σ2ξ2	σ2ξ2	X
ejpam-3478	281	3	σ2q2	σ2q2	X
ejpam-3478	281	4	(	(	PUNCT
ejpam-3478	281	5	1−	1−	NUM
ejpam-3478	281	6	ρ2	ρ2	NOUN
ejpam-3478	281	7	)	)	PUNCT
ejpam-3478	281	8	≡	≡	PROPN
ejpam-3478	281	9	t3l+	t3l+	NOUN
ejpam-3478	281	10	t4w	t4w	PROPN
ejpam-3478	281	11	(	(	PUNCT
ejpam-3478	281	12	58	58	X
ejpam-3478	281	13	)	)	PUNCT
ejpam-3478	281	14	equating	equate	VERB
ejpam-3478	281	15	coefficients	coefficient	NOUN
ejpam-3478	281	16	of	of	ADP
ejpam-3478	281	17	l	l	NOUN
ejpam-3478	281	18	and	and	CCONJ
ejpam-3478	281	19	w	w	NOUN
ejpam-3478	281	20	in	in	ADP
ejpam-3478	281	21	equation	equation	NOUN
ejpam-3478	281	22	(	(	PUNCT
ejpam-3478	281	23	44	44	NUM
ejpam-3478	281	24	)	)	PUNCT
ejpam-3478	281	25	gives	give	VERB
ejpam-3478	281	26	0	0	NUM
ejpam-3478	282	1	=	=	SYM
ejpam-3478	282	2	·	·	PUNCT
ejpam-3478	282	3	b	b	X
ejpam-3478	283	1	−	−	NOUN
ejpam-3478	283	2	1	1	NUM
ejpam-3478	283	3	2	2	NUM
ejpam-3478	283	4	(	(	PUNCT
ejpam-3478	283	5	α−	α−	ADP
ejpam-3478	283	6	ra)q1b1	ra)q1b1	ADV
ejpam-3478	284	1	+	+	NOUN
ejpam-3478	284	2	b	b	X
ejpam-3478	284	3	{	{	PUNCT
ejpam-3478	284	4	raγ	raγ	NOUN
ejpam-3478	284	5	−	−	NOUN
ejpam-3478	284	6	1	1	NUM
ejpam-3478	284	7	2	2	NUM
ejpam-3478	284	8	cq2γ	cq2γ	VERB
ejpam-3478	284	9	+	+	CCONJ
ejpam-3478	284	10	1	1	NUM
ejpam-3478	284	11	2	2	NUM
ejpam-3478	284	12	(	(	PUNCT
ejpam-3478	284	13	γ	γ	NOUN
ejpam-3478	284	14	−	−	PROPN
ejpam-3478	284	15	1	1	NUM
ejpam-3478	284	16	)	)	PUNCT
ejpam-3478	284	17	(	(	PUNCT
ejpam-3478	284	18	α−	α−	ADP
ejpam-3478	284	19	ra)q1	ra)q1	PROPN
ejpam-3478	284	20	}	}	PUNCT
ejpam-3478	284	21	+	+	CCONJ
ejpam-3478	284	22	(	(	PUNCT
ejpam-3478	284	23	α−	α−	ADP
ejpam-3478	284	24	ra	ra	NOUN
ejpam-3478	284	25	)	)	PUNCT
ejpam-3478	284	26	2	2	NUM
ejpam-3478	284	27	t1	t1	NOUN
ejpam-3478	284	28	−	−	NOUN
ejpam-3478	284	29	1	1	NUM
ejpam-3478	284	30	2	2	NUM
ejpam-3478	284	31	ct3	ct3	NOUN
ejpam-3478	284	32	−a	−a	NOUN
ejpam-3478	284	33	(	(	PUNCT
ejpam-3478	284	34	t	t	NOUN
ejpam-3478	284	35	)	)	PUNCT
ejpam-3478	284	36	(	(	PUNCT
ejpam-3478	284	37	59	59	NUM
ejpam-3478	284	38	)	)	PUNCT
ejpam-3478	284	39	and	and	CCONJ
ejpam-3478	284	40	0	0	NUM
ejpam-3478	284	41	=	=	SYM
ejpam-3478	284	42	·	·	PUNCT
ejpam-3478	284	43	b1	b1	NOUN
ejpam-3478	284	44	−	−	NOUN
ejpam-3478	284	45	1	1	NUM
ejpam-3478	284	46	2	2	NUM
ejpam-3478	284	47	cq2b	cq2b	PROPN
ejpam-3478	284	48	+	+	NOUN
ejpam-3478	284	49	b1	b1	NOUN
ejpam-3478	284	50	{	{	PUNCT
ejpam-3478	284	51	raγ	raγ	NOUN
ejpam-3478	285	1	+	+	CCONJ
ejpam-3478	285	2	1	1	NUM
ejpam-3478	285	3	2	2	NUM
ejpam-3478	285	4	(	(	PUNCT
ejpam-3478	285	5	α−	α−	ADP
ejpam-3478	285	6	ra	ra	NOUN
ejpam-3478	285	7	)	)	PUNCT
ejpam-3478	285	8	γq1	γq1	NOUN
ejpam-3478	286	1	−	−	NOUN
ejpam-3478	286	2	1	1	NUM
ejpam-3478	286	3	2	2	NUM
ejpam-3478	286	4	cq2	cq2	NOUN
ejpam-3478	286	5	(	(	PUNCT
ejpam-3478	286	6	γ	γ	NOUN
ejpam-3478	286	7	−	−	PROPN
ejpam-3478	286	8	1	1	NUM
ejpam-3478	286	9	)	)	PUNCT
ejpam-3478	286	10	}	}	PUNCT
ejpam-3478	287	1	+	+	CCONJ
ejpam-3478	287	2	(	(	PUNCT
ejpam-3478	287	3	α−	α−	ADP
ejpam-3478	287	4	ra	ra	NOUN
ejpam-3478	287	5	)	)	PUNCT
ejpam-3478	287	6	2	2	NUM
ejpam-3478	287	7	t2	t2	NOUN
ejpam-3478	287	8	−	−	NOUN
ejpam-3478	287	9	1	1	NUM
ejpam-3478	287	10	2	2	NUM
ejpam-3478	287	11	ct4	ct4	NOUN
ejpam-3478	287	12	(	(	PUNCT
ejpam-3478	287	13	60	60	NUM
ejpam-3478	287	14	)	)	PUNCT
ejpam-3478	287	15	5.1	5.1	NUM
ejpam-3478	287	16	.	.	PUNCT
ejpam-3478	288	1	example	example	NOUN
ejpam-3478	288	2	:	:	PUNCT
ejpam-3478	288	3	results	result	VERB
ejpam-3478	288	4	for	for	ADP
ejpam-3478	288	5	ra	ra	PROPN
ejpam-3478	288	6	=	=	SYM
ejpam-3478	288	7	rl	rl	PROPN
ejpam-3478	288	8	,	,	PUNCT
ejpam-3478	288	9	ρ	ρ	PROPN
ejpam-3478	288	10	6=	6=	ADP
ejpam-3478	288	11	0	0	NUM
ejpam-3478	288	12	for	for	ADP
ejpam-3478	288	13	this	this	DET
ejpam-3478	288	14	case	case	NOUN
ejpam-3478	288	15	,	,	PUNCT
ejpam-3478	288	16	the	the	DET
ejpam-3478	288	17	ratios	ratio	NOUN
ejpam-3478	288	18	ww	ww	PROPN
ejpam-3478	288	19	e	e	PROPN
ejpam-3478	288	20	,	,	PUNCT
ejpam-3478	288	21	ule	ule	INTJ
ejpam-3478	288	22	,	,	PUNCT
ejpam-3478	288	23	(	(	PUNCT
ejpam-3478	288	24	e	e	NOUN
ejpam-3478	288	25	=	=	PUNCT
ejpam-3478	288	26	w	w	PROPN
ejpam-3478	288	27	−	−	PROPN
ejpam-3478	288	28	l	l	NOUN
ejpam-3478	288	29	)	)	PUNCT
ejpam-3478	288	30	are	be	AUX
ejpam-3478	288	31	time	time	NOUN
ejpam-3478	288	32	independent	independent	ADJ
ejpam-3478	288	33	for	for	ADP
ejpam-3478	288	34	the	the	DET
ejpam-3478	288	35	example	example	NOUN
ejpam-3478	288	36	we	we	PRON
ejpam-3478	288	37	consider	consider	VERB
ejpam-3478	288	38	ra	ra	NOUN
ejpam-3478	288	39	=	=	VERB
ejpam-3478	288	40	rl	rl	PROPN
ejpam-3478	288	41	,	,	PUNCT
ejpam-3478	288	42	we	we	PRON
ejpam-3478	288	43	plot	plot	VERB
ejpam-3478	288	44	q1	q1	PROPN
ejpam-3478	288	45	and	and	CCONJ
ejpam-3478	288	46	q2	q2	NOUN
ejpam-3478	288	47	for	for	ADP
ejpam-3478	288	48	the	the	DET
ejpam-3478	288	49	parameters	parameter	NOUN
ejpam-3478	288	50	α	α	X
ejpam-3478	288	51	=	=	SYM
ejpam-3478	288	52	0.1	0.1	NUM
ejpam-3478	288	53	,	,	PUNCT
ejpam-3478	288	54	ra	ra	PROPN
ejpam-3478	289	1	=	=	NOUN
ejpam-3478	289	2	0.03	0.03	NUM
ejpam-3478	289	3	,	,	PUNCT
ejpam-3478	289	4	q	q	NOUN
ejpam-3478	289	5	=	=	NOUN
ejpam-3478	289	6	0.25	0.25	NUM
ejpam-3478	289	7	,	,	PUNCT
ejpam-3478	289	8	σ	σ	NOUN
ejpam-3478	289	9	=	=	PUNCT
ejpam-3478	289	10	0.3	0.3	NUM
ejpam-3478	289	11	,	,	PUNCT
ejpam-3478	289	12	c	c	NOUN
ejpam-3478	289	13	=	=	SYM
ejpam-3478	289	14	1.5	1.5	NUM
ejpam-3478	289	15	,	,	PUNCT
ejpam-3478	289	16	m	m	VERB
ejpam-3478	289	17	=	=	NOUN
ejpam-3478	289	18	1.3	1.3	NUM
ejpam-3478	289	19	,	,	PUNCT
ejpam-3478	289	20	rl	rl	X
ejpam-3478	289	21	=	=	PUNCT
ejpam-3478	289	22	0.025	0.025	NUM
ejpam-3478	289	23	,	,	PUNCT
ejpam-3478	289	24	γ	γ	NOUN
ejpam-3478	289	25	=	=	SYM
ejpam-3478	289	26	0.5	0.5	NUM
ejpam-3478	289	27	but	but	CCONJ
ejpam-3478	289	28	with	with	ADP
ejpam-3478	289	29	ρ	ρ	PROPN
ejpam-3478	289	30	and	and	CCONJ
ejpam-3478	289	31	c	c	NOUN
ejpam-3478	289	32	varying	varying	NOUN
ejpam-3478	289	33	,	,	PUNCT
ejpam-3478	289	34	see	see	VERB
ejpam-3478	289	35	figure	figure	NOUN
ejpam-3478	289	36	2	2	NUM
ejpam-3478	289	37	and	and	CCONJ
ejpam-3478	289	38	figure	figure	VERB
ejpam-3478	289	39	3	3	NUM
ejpam-3478	289	40	.	.	PUNCT
ejpam-3478	289	41	c.	c.	PROPN
ejpam-3478	289	42	atkinson	atkinson	PROPN
ejpam-3478	289	43	,	,	PUNCT
ejpam-3478	289	44	s.	s.	PROPN
ejpam-3478	289	45	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	289	46	,	,	PUNCT
ejpam-3478	289	47	p.	p.	PROPN
ejpam-3478	289	48	ingpochai	ingpochai	PROPN
ejpam-3478	289	49	/	/	SYM
ejpam-3478	289	50	eur	eur	PROPN
ejpam-3478	289	51	.	.	PUNCT
ejpam-3478	290	1	j.	j.	PROPN
ejpam-3478	290	2	pure	pure	PROPN
ejpam-3478	290	3	appl	appl	PROPN
ejpam-3478	290	4	.	.	PROPN
ejpam-3478	290	5	math	math	PROPN
ejpam-3478	290	6	,	,	PUNCT
ejpam-3478	290	7	12	12	NUM
ejpam-3478	290	8	(	(	PUNCT
ejpam-3478	290	9	3	3	NUM
ejpam-3478	290	10	)	)	PUNCT
ejpam-3478	290	11	(	(	PUNCT
ejpam-3478	290	12	2019	2019	NUM
ejpam-3478	290	13	)	)	PUNCT
ejpam-3478	290	14	,	,	PUNCT
ejpam-3478	290	15	1315	1315	NUM
ejpam-3478	290	16	-	-	SYM
ejpam-3478	290	17	1336	1336	NUM
ejpam-3478	290	18	1329	1329	NUM
ejpam-3478	290	19	figure	figure	NOUN
ejpam-3478	290	20	2	2	NUM
ejpam-3478	290	21	:	:	PUNCT
ejpam-3478	290	22	plot	plot	NOUN
ejpam-3478	290	23	of	of	ADP
ejpam-3478	290	24	q1	q1	PROPN
ejpam-3478	290	25	when	when	SCONJ
ejpam-3478	290	26	ra	ra	PROPN
ejpam-3478	290	27	=	=	SYM
ejpam-3478	290	28	rl	rl	PROPN
ejpam-3478	290	29	.	.	NOUN
ejpam-3478	290	30	figure	figure	NOUN
ejpam-3478	290	31	3	3	NUM
ejpam-3478	290	32	:	:	PUNCT
ejpam-3478	290	33	plot	plot	NOUN
ejpam-3478	290	34	of	of	ADP
ejpam-3478	290	35	q2	q2	NOUN
ejpam-3478	290	36	when	when	SCONJ
ejpam-3478	290	37	ra	ra	PROPN
ejpam-3478	290	38	=	=	SYM
ejpam-3478	290	39	rl	rl	PROPN
ejpam-3478	290	40	.	.	PUNCT
ejpam-3478	291	1	as	as	SCONJ
ejpam-3478	291	2	is	be	AUX
ejpam-3478	291	3	evident	evident	ADJ
ejpam-3478	291	4	from	from	ADP
ejpam-3478	291	5	the	the	DET
ejpam-3478	291	6	plot	plot	NOUN
ejpam-3478	291	7	of	of	ADP
ejpam-3478	291	8	q1	q1	PROPN
ejpam-3478	291	9	,	,	PUNCT
ejpam-3478	291	10	we	we	PRON
ejpam-3478	291	11	must	must	AUX
ejpam-3478	291	12	exclude	exclude	VERB
ejpam-3478	291	13	regions	region	NOUN
ejpam-3478	291	14	where	where	SCONJ
ejpam-3478	291	15	q1	q1	VERB
ejpam-3478	291	16	<	<	X
ejpam-3478	291	17	0	0	PUNCT
ejpam-3478	292	1	since	since	SCONJ
ejpam-3478	292	2	it	it	PRON
ejpam-3478	292	3	is	be	AUX
ejpam-3478	292	4	inadmissible	inadmissible	ADJ
ejpam-3478	292	5	given	give	VERB
ejpam-3478	292	6	our	our	PRON
ejpam-3478	292	7	short	short	ADJ
ejpam-3478	292	8	selling	selling	NOUN
ejpam-3478	292	9	constraint	constraint	NOUN
ejpam-3478	292	10	of	of	ADP
ejpam-3478	292	11	the	the	DET
ejpam-3478	292	12	risky	risky	ADJ
ejpam-3478	292	13	asset	asset	NOUN
ejpam-3478	292	14	.	.	PUNCT
ejpam-3478	293	1	if	if	SCONJ
ejpam-3478	293	2	we	we	PRON
ejpam-3478	293	3	examine	examine	VERB
ejpam-3478	293	4	q1	q1	NOUN
ejpam-3478	293	5	when	when	SCONJ
ejpam-3478	293	6	c	c	NOUN
ejpam-3478	293	7	=	=	SYM
ejpam-3478	293	8	0	0	NUM
ejpam-3478	293	9	,	,	PUNCT
ejpam-3478	293	10	we	we	PRON
ejpam-3478	293	11	see	see	VERB
ejpam-3478	293	12	the	the	DET
ejpam-3478	293	13	convexity	convexity	NOUN
ejpam-3478	293	14	structure	structure	NOUN
ejpam-3478	293	15	and	and	CCONJ
ejpam-3478	293	16	if	if	SCONJ
ejpam-3478	293	17	ρ	ρ	PROPN
ejpam-3478	293	18	=	=	SYM
ejpam-3478	293	19	0	0	NUM
ejpam-3478	293	20	,	,	PUNCT
ejpam-3478	293	21	then	then	ADV
ejpam-3478	293	22	q1	q1	VERB
ejpam-3478	293	23	=	=	NOUN
ejpam-3478	293	24	1.56	1.56	NUM
ejpam-3478	293	25	,	,	PUNCT
ejpam-3478	293	26	which	which	PRON
ejpam-3478	293	27	implies	imply	VERB
ejpam-3478	293	28	the	the	DET
ejpam-3478	293	29	amount	amount	NOUN
ejpam-3478	293	30	of	of	ADP
ejpam-3478	293	31	risky	risky	ADJ
ejpam-3478	293	32	asset	asset	NOUN
ejpam-3478	293	33	is	be	AUX
ejpam-3478	293	34	1.56	1.56	NUM
ejpam-3478	293	35	times	time	NOUN
ejpam-3478	293	36	that	that	PRON
ejpam-3478	293	37	of	of	ADP
ejpam-3478	293	38	the	the	DET
ejpam-3478	293	39	shareholders	shareholders	PROPN
ejpam-3478	293	40	equity	equity	PROPN
ejpam-3478	293	41	w	w	PROPN
ejpam-3478	293	42	−l	−l	PROPN
ejpam-3478	293	43	,	,	PUNCT
ejpam-3478	293	44	refer	refer	VERB
ejpam-3478	293	45	to	to	PART
ejpam-3478	293	46	figure	figure	VERB
ejpam-3478	293	47	4	4	NUM
ejpam-3478	293	48	.	.	PUNCT
ejpam-3478	294	1	for	for	ADP
ejpam-3478	294	2	ease	ease	NOUN
ejpam-3478	294	3	of	of	ADP
ejpam-3478	294	4	explanation	explanation	NOUN
ejpam-3478	294	5	,	,	PUNCT
ejpam-3478	294	6	we	we	PRON
ejpam-3478	294	7	plot	plot	VERB
ejpam-3478	294	8	q2	q2	NOUN
ejpam-3478	294	9	(	(	PUNCT
ejpam-3478	294	10	optimal	optimal	ADJ
ejpam-3478	294	11	allocation	allocation	NOUN
ejpam-3478	294	12	into	into	ADP
ejpam-3478	294	13	risky	risky	ADJ
ejpam-3478	294	14	liability	liability	NOUN
ejpam-3478	294	15	)	)	PUNCT
ejpam-3478	294	16	for	for	ADP
ejpam-3478	294	17	the	the	DET
ejpam-3478	294	18	case	case	NOUN
ejpam-3478	294	19	where	where	SCONJ
ejpam-3478	294	20	c	c	NOUN
ejpam-3478	294	21	=	=	SYM
ejpam-3478	294	22	0	0	NUM
ejpam-3478	294	23	,	,	PUNCT
ejpam-3478	294	24	we	we	PRON
ejpam-3478	294	25	see	see	VERB
ejpam-3478	294	26	that	that	SCONJ
ejpam-3478	294	27	the	the	DET
ejpam-3478	294	28	q2	q2	NOUN
ejpam-3478	294	29	=	=	SYM
ejpam-3478	294	30	0	0	PUNCT
ejpam-3478	294	31	when	when	SCONJ
ejpam-3478	294	32	ρ	ρ	PROPN
ejpam-3478	294	33	=	=	SYM
ejpam-3478	294	34	0	0	NUM
ejpam-3478	294	35	,	,	PUNCT
ejpam-3478	294	36	refer	refer	VERB
ejpam-3478	294	37	to	to	PART
ejpam-3478	294	38	figure	figure	VERB
ejpam-3478	294	39	5	5	NUM
ejpam-3478	294	40	.	.	PUNCT
ejpam-3478	295	1	this	this	PRON
ejpam-3478	295	2	is	be	AUX
ejpam-3478	295	3	sensible	sensible	ADJ
ejpam-3478	295	4	because	because	SCONJ
ejpam-3478	295	5	the	the	DET
ejpam-3478	295	6	movements	movement	NOUN
ejpam-3478	295	7	of	of	ADP
ejpam-3478	295	8	the	the	DET
ejpam-3478	295	9	risky	risky	ADJ
ejpam-3478	295	10	assets	asset	NOUN
ejpam-3478	295	11	are	be	AUX
ejpam-3478	295	12	not	not	PART
ejpam-3478	295	13	correlated	correlate	VERB
ejpam-3478	295	14	to	to	ADP
ejpam-3478	295	15	that	that	PRON
ejpam-3478	295	16	of	of	ADP
ejpam-3478	295	17	the	the	DET
ejpam-3478	295	18	risky	risky	ADJ
ejpam-3478	295	19	liabilities	liability	NOUN
ejpam-3478	295	20	hence	hence	ADV
ejpam-3478	295	21	the	the	DET
ejpam-3478	295	22	policy	policy	NOUN
ejpam-3478	295	23	should	should	AUX
ejpam-3478	295	24	suggest	suggest	VERB
ejpam-3478	295	25	we	we	PRON
ejpam-3478	295	26	minimise	minimise	VERB
ejpam-3478	295	27	the	the	DET
ejpam-3478	295	28	unnecessary	unnecessary	ADJ
ejpam-3478	295	29	volatility	volatility	NOUN
ejpam-3478	295	30	this	this	DET
ejpam-3478	295	31	stochastic	stochastic	ADJ
ejpam-3478	295	32	liability	liability	NOUN
ejpam-3478	295	33	may	may	AUX
ejpam-3478	295	34	cause	cause	VERB
ejpam-3478	295	35	.	.	PUNCT
ejpam-3478	296	1	as	as	ADP
ejpam-3478	296	2	the	the	DET
ejpam-3478	296	3	correlation	correlation	NOUN
ejpam-3478	296	4	increases	increase	NOUN
ejpam-3478	296	5	,	,	PUNCT
ejpam-3478	296	6	q2	q2	NOUN
ejpam-3478	296	7	increases	increase	VERB
ejpam-3478	296	8	monotonically	monotonically	ADV
ejpam-3478	296	9	to	to	PART
ejpam-3478	296	10	help	help	AUX
ejpam-3478	296	11	match	match	VERB
ejpam-3478	296	12	the	the	DET
ejpam-3478	296	13	movements	movement	NOUN
ejpam-3478	296	14	of	of	ADP
ejpam-3478	296	15	the	the	DET
ejpam-3478	296	16	assets	asset	NOUN
ejpam-3478	296	17	.	.	PUNCT
ejpam-3478	297	1	c.	c.	PROPN
ejpam-3478	297	2	atkinson	atkinson	PROPN
ejpam-3478	297	3	,	,	PUNCT
ejpam-3478	297	4	s.	s.	PROPN
ejpam-3478	297	5	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	297	6	,	,	PUNCT
ejpam-3478	297	7	p.	p.	PROPN
ejpam-3478	297	8	ingpochai	ingpochai	PROPN
ejpam-3478	297	9	/	/	SYM
ejpam-3478	297	10	eur	eur	PROPN
ejpam-3478	297	11	.	.	PUNCT
ejpam-3478	298	1	j.	j.	PROPN
ejpam-3478	298	2	pure	pure	PROPN
ejpam-3478	298	3	appl	appl	PROPN
ejpam-3478	298	4	.	.	PROPN
ejpam-3478	298	5	math	math	PROPN
ejpam-3478	298	6	,	,	PUNCT
ejpam-3478	298	7	12	12	NUM
ejpam-3478	298	8	(	(	PUNCT
ejpam-3478	298	9	3	3	NUM
ejpam-3478	298	10	)	)	PUNCT
ejpam-3478	298	11	(	(	PUNCT
ejpam-3478	298	12	2019	2019	NUM
ejpam-3478	298	13	)	)	PUNCT
ejpam-3478	298	14	,	,	PUNCT
ejpam-3478	298	15	1315	1315	NUM
ejpam-3478	298	16	-	-	SYM
ejpam-3478	298	17	1336	1336	NUM
ejpam-3478	298	18	1330	1330	NUM
ejpam-3478	298	19	-0.6	-0.6	X
ejpam-3478	298	20	-0.4	-0.4	X
ejpam-3478	298	21	-0.2	-0.2	PROPN
ejpam-3478	298	22	0.2	0.2	NUM
ejpam-3478	298	23	0.4	0.4	NUM
ejpam-3478	298	24	0.6	0.6	NUM
ejpam-3478	298	25	ρ	ρ	PROPN
ejpam-3478	298	26	2.0	2.0	NUM
ejpam-3478	298	27	2.5	2.5	NUM
ejpam-3478	298	28	3.0	3.0	NUM
ejpam-3478	298	29	q1	q1	NOUN
ejpam-3478	298	30	figure	figure	NOUN
ejpam-3478	298	31	4	4	NUM
ejpam-3478	298	32	:	:	PUNCT
ejpam-3478	298	33	plot	plot	NOUN
ejpam-3478	298	34	of	of	ADP
ejpam-3478	298	35	q1	q1	PROPN
ejpam-3478	298	36	when	when	SCONJ
ejpam-3478	298	37	ra	ra	PROPN
ejpam-3478	298	38	=	=	VERB
ejpam-3478	298	39	rl	rl	PROPN
ejpam-3478	298	40	and	and	CCONJ
ejpam-3478	298	41	c	c	NOUN
ejpam-3478	298	42	=	=	SYM
ejpam-3478	298	43	0	0	PROPN
ejpam-3478	298	44	.	.	PUNCT
ejpam-3478	299	1	-0.6	-0.6	NOUN
ejpam-3478	299	2	-0.4	-0.4	NUM
ejpam-3478	299	3	-0.2	-0.2	PROPN
ejpam-3478	299	4	0.2	0.2	NUM
ejpam-3478	299	5	0.4	0.4	NUM
ejpam-3478	299	6	0.6	0.6	NUM
ejpam-3478	299	7	ρ	ρ	NUM
ejpam-3478	299	8	-2	-2	INTJ
ejpam-3478	299	9	-1	-1	NOUN
ejpam-3478	299	10	1	1	NUM
ejpam-3478	299	11	2	2	NUM
ejpam-3478	299	12	q2	q2	NOUN
ejpam-3478	299	13	figure	figure	NOUN
ejpam-3478	299	14	5	5	NUM
ejpam-3478	299	15	:	:	PUNCT
ejpam-3478	299	16	plot	plot	NOUN
ejpam-3478	299	17	of	of	ADP
ejpam-3478	299	18	q2	q2	NOUN
ejpam-3478	299	19	when	when	SCONJ
ejpam-3478	299	20	ra	ra	PROPN
ejpam-3478	299	21	=	=	AUX
ejpam-3478	299	22	rl	rl	PROPN
ejpam-3478	299	23	and	and	CCONJ
ejpam-3478	299	24	c	c	NOUN
ejpam-3478	299	25	=	=	SYM
ejpam-3478	299	26	0	0	NUM
ejpam-3478	299	27	.	.	X
ejpam-3478	300	1	5.2	5.2	NUM
ejpam-3478	300	2	.	.	PUNCT
ejpam-3478	301	1	example	example	NOUN
ejpam-3478	301	2	:	:	PUNCT
ejpam-3478	301	3	results	result	VERB
ejpam-3478	301	4	for	for	ADP
ejpam-3478	301	5	ra	ra	PROPN
ejpam-3478	301	6	6=	6=	PROPN
ejpam-3478	301	7	rl	rl	PROPN
ejpam-3478	301	8	but	but	CCONJ
ejpam-3478	301	9	|ε|	|ε|	DET
ejpam-3478	301	10	�	�	PROPN
ejpam-3478	301	11	ra	ra	PROPN
ejpam-3478	301	12	o	o	NOUN
ejpam-3478	301	13	(	(	PUNCT
ejpam-3478	301	14	1	1	NUM
ejpam-3478	301	15	)	)	PUNCT
ejpam-3478	301	16	solution	solution	NOUN
ejpam-3478	301	17	as	as	ADP
ejpam-3478	301	18	above	above	ADV
ejpam-3478	301	19	but	but	CCONJ
ejpam-3478	301	20	now	now	ADV
ejpam-3478	301	21	ra	ra	PROPN
ejpam-3478	301	22	6=	6=	PROPN
ejpam-3478	302	1	rl	rl	PROPN
ejpam-3478	302	2	w0w	w0w	PROPN
ejpam-3478	302	3	(	(	PUNCT
ejpam-3478	302	4	w	w	PROPN
ejpam-3478	302	5	−	−	PROPN
ejpam-3478	302	6	l	l	NOUN
ejpam-3478	302	7	)	)	PUNCT
ejpam-3478	303	1	=	=	SYM
ejpam-3478	303	2	q1	q1	NOUN
ejpam-3478	303	3	u0l	u0l	PROPN
ejpam-3478	303	4	(	(	PUNCT
ejpam-3478	303	5	w	w	PROPN
ejpam-3478	303	6	−	−	PROPN
ejpam-3478	303	7	l	l	NOUN
ejpam-3478	303	8	)	)	PUNCT
ejpam-3478	303	9	=	=	SYM
ejpam-3478	303	10	q2	q2	NOUN
ejpam-3478	303	11	to	to	PART
ejpam-3478	303	12	correct	correct	VERB
ejpam-3478	303	13	for	for	ADP
ejpam-3478	303	14	order	order	NOUN
ejpam-3478	303	15	ε	ε	PROPN
ejpam-3478	303	16	the	the	DET
ejpam-3478	303	17	behavior	behavior	NOUN
ejpam-3478	303	18	will	will	AUX
ejpam-3478	303	19	depend	depend	VERB
ejpam-3478	303	20	on	on	ADP
ejpam-3478	303	21	b	b	PROPN
ejpam-3478	303	22	(	(	PUNCT
ejpam-3478	303	23	t	t	PROPN
ejpam-3478	303	24	)	)	PUNCT
ejpam-3478	303	25	and	and	CCONJ
ejpam-3478	303	26	b1	b1	NOUN
ejpam-3478	303	27	(	(	PUNCT
ejpam-3478	303	28	t	t	PROPN
ejpam-3478	303	29	)	)	PUNCT
ejpam-3478	303	30	and	and	CCONJ
ejpam-3478	303	31	will	will	AUX
ejpam-3478	303	32	potentially	potentially	ADV
ejpam-3478	303	33	require	require	VERB
ejpam-3478	303	34	us	we	PRON
ejpam-3478	303	35	to	to	PART
ejpam-3478	303	36	correct	correct	VERB
ejpam-3478	303	37	for	for	ADP
ejpam-3478	303	38	the	the	DET
ejpam-3478	303	39	optimal	optimal	ADJ
ejpam-3478	303	40	ratios	ratio	NOUN
ejpam-3478	303	41	as	as	SCONJ
ejpam-3478	303	42	t	t	PROPN
ejpam-3478	303	43	evolves	evolve	NOUN
ejpam-3478	303	44	.	.	PUNCT
ejpam-3478	304	1	the	the	DET
ejpam-3478	304	2	general	general	ADJ
ejpam-3478	304	3	result	result	NOUN
ejpam-3478	304	4	for	for	SCONJ
ejpam-3478	304	5	w1	w1	NOUN
ejpam-3478	304	6	and	and	CCONJ
ejpam-3478	304	7	u1	u1	NOUN
ejpam-3478	304	8	can	can	AUX
ejpam-3478	304	9	be	be	AUX
ejpam-3478	304	10	deduced	deduce	VERB
ejpam-3478	304	11	from	from	ADP
ejpam-3478	304	12	equations	equation	NOUN
ejpam-3478	304	13	(	(	PUNCT
ejpam-3478	304	14	54	54	NUM
ejpam-3478	304	15	)	)	PUNCT
ejpam-3478	304	16	,	,	PUNCT
ejpam-3478	304	17	(	(	PUNCT
ejpam-3478	304	18	55	55	NUM
ejpam-3478	304	19	)	)	PUNCT
ejpam-3478	304	20	and	and	CCONJ
ejpam-3478	304	21	(	(	PUNCT
ejpam-3478	304	22	56	56	NUM
ejpam-3478	304	23	)	)	PUNCT
ejpam-3478	304	24	.	.	PUNCT
ejpam-3478	305	1	to	to	ADP
ejpam-3478	305	2	this	this	DET
ejpam-3478	305	3	order	order	NOUN
ejpam-3478	305	4	we	we	PRON
ejpam-3478	305	5	deduce	deduce	VERB
ejpam-3478	305	6	ww	ww	PROPN
ejpam-3478	305	7	=	=	PROPN
ejpam-3478	305	8	q1	q1	PROPN
ejpam-3478	305	9	(	(	PUNCT
ejpam-3478	305	10	w	w	PROPN
ejpam-3478	305	11	−	−	PROPN
ejpam-3478	305	12	l	l	NOUN
ejpam-3478	305	13	)	)	PUNCT
ejpam-3478	306	1	+	+	CCONJ
ejpam-3478	306	2	ε	ε	PROPN
ejpam-3478	307	1	[	[	X
ejpam-3478	307	2	p1	p1	PROPN
ejpam-3478	307	3	(	(	PUNCT
ejpam-3478	307	4	w	w	PROPN
ejpam-3478	307	5	−	−	PROPN
ejpam-3478	307	6	l	l	NOUN
ejpam-3478	307	7	)	)	PUNCT
ejpam-3478	308	1	+	+	CCONJ
ejpam-3478	308	2	p2l	p2l	X
ejpam-3478	308	3	]	]	X
ejpam-3478	308	4	+	+	NOUN
ejpam-3478	308	5	o	o	X
ejpam-3478	308	6	(	(	PUNCT
ejpam-3478	308	7	ε2	ε2	ADJ
ejpam-3478	308	8	)	)	PUNCT
ejpam-3478	308	9	references	reference	NOUN
ejpam-3478	308	10	1331	1331	NUM
ejpam-3478	308	11	and	and	CCONJ
ejpam-3478	308	12	ul	ul	NOUN
ejpam-3478	308	13	=	=	PROPN
ejpam-3478	308	14	q2	q2	PROPN
ejpam-3478	308	15	(	(	PUNCT
ejpam-3478	308	16	w	w	PROPN
ejpam-3478	308	17	−	−	PROPN
ejpam-3478	308	18	l	l	NOUN
ejpam-3478	308	19	)	)	PUNCT
ejpam-3478	309	1	+	+	CCONJ
ejpam-3478	309	2	ε	ε	PROPN
ejpam-3478	310	1	[	[	X
ejpam-3478	310	2	p3	p3	PROPN
ejpam-3478	310	3	(	(	PUNCT
ejpam-3478	310	4	w	w	PROPN
ejpam-3478	310	5	−	−	PROPN
ejpam-3478	310	6	l	l	NOUN
ejpam-3478	310	7	)	)	PUNCT
ejpam-3478	310	8	+	+	CCONJ
ejpam-3478	310	9	p4w	p4w	NOUN
ejpam-3478	310	10	]	]	PUNCT
ejpam-3478	311	1	+	+	PUNCT
ejpam-3478	311	2	o	o	X
ejpam-3478	311	3	(	(	PUNCT
ejpam-3478	311	4	ε2	ε2	PROPN
ejpam-3478	311	5	)	)	PUNCT
ejpam-3478	311	6	where	where	SCONJ
ejpam-3478	311	7	p1	p1	NOUN
ejpam-3478	311	8	and	and	CCONJ
ejpam-3478	311	9	p3	p3	PROPN
ejpam-3478	311	10	are	be	AUX
ejpam-3478	311	11	constants	constant	NOUN
ejpam-3478	311	12	depending	depend	VERB
ejpam-3478	311	13	on	on	ADP
ejpam-3478	311	14	the	the	DET
ejpam-3478	311	15	various	various	ADJ
ejpam-3478	311	16	parameters	parameter	NOUN
ejpam-3478	311	17	of	of	ADP
ejpam-3478	311	18	the	the	DET
ejpam-3478	311	19	problem	problem	NOUN
ejpam-3478	311	20	.	.	PUNCT
ejpam-3478	312	1	note	note	VERB
ejpam-3478	312	2	that	that	SCONJ
ejpam-3478	312	3	higher	high	ADJ
ejpam-3478	312	4	order	order	NOUN
ejpam-3478	312	5	terms	term	NOUN
ejpam-3478	312	6	could	could	AUX
ejpam-3478	312	7	be	be	AUX
ejpam-3478	312	8	attained	attain	VERB
ejpam-3478	312	9	if	if	SCONJ
ejpam-3478	312	10	necessary	necessary	ADJ
ejpam-3478	312	11	,	,	PUNCT
ejpam-3478	312	12	see	see	VERB
ejpam-3478	312	13	the	the	DET
ejpam-3478	312	14	appendix	appendix	NOUN
ejpam-3478	312	15	.	.	PUNCT
ejpam-3478	313	1	also	also	ADV
ejpam-3478	313	2	a	a	DET
ejpam-3478	313	3	full	full	ADJ
ejpam-3478	313	4	numerical	numerical	ADJ
ejpam-3478	313	5	solution	solution	NOUN
ejpam-3478	313	6	could	could	AUX
ejpam-3478	313	7	be	be	AUX
ejpam-3478	313	8	obtained	obtain	VERB
ejpam-3478	313	9	by	by	ADP
ejpam-3478	313	10	solving	solve	VERB
ejpam-3478	313	11	equation	equation	NOUN
ejpam-3478	313	12	(	(	PUNCT
ejpam-3478	313	13	9	9	NUM
ejpam-3478	313	14	)	)	PUNCT
ejpam-3478	313	15	or	or	CCONJ
ejpam-3478	313	16	equation	equation	NOUN
ejpam-3478	313	17	(	(	PUNCT
ejpam-3478	313	18	14	14	NUM
ejpam-3478	313	19	)	)	PUNCT
ejpam-3478	313	20	as	as	ADP
ejpam-3478	313	21	a	a	DET
ejpam-3478	313	22	backward	backward	ADJ
ejpam-3478	313	23	diffusion	diffusion	NOUN
ejpam-3478	313	24	equation	equation	NOUN
ejpam-3478	313	25	together	together	ADV
ejpam-3478	313	26	with	with	ADP
ejpam-3478	313	27	the	the	DET
ejpam-3478	313	28	constraints	constraint	NOUN
ejpam-3478	313	29	equations	equation	NOUN
ejpam-3478	313	30	(	(	PUNCT
ejpam-3478	313	31	11	11	NUM
ejpam-3478	313	32	)	)	PUNCT
ejpam-3478	313	33	and	and	CCONJ
ejpam-3478	313	34	(	(	PUNCT
ejpam-3478	313	35	12	12	NUM
ejpam-3478	313	36	)	)	PUNCT
ejpam-3478	313	37	.	.	PUNCT
ejpam-3478	314	1	references	reference	NOUN
ejpam-3478	314	2	[	[	X
ejpam-3478	314	3	1	1	NUM
ejpam-3478	314	4	]	]	X
ejpam-3478	314	5	atkinson	atkinson	PROPN
ejpam-3478	314	6	,	,	PUNCT
ejpam-3478	314	7	c.	c.	PROPN
ejpam-3478	314	8	and	and	CCONJ
ejpam-3478	314	9	al	al	PROPN
ejpam-3478	314	10	-	-	PUNCT
ejpam-3478	314	11	ali	ali	PROPN
ejpam-3478	314	12	,	,	PUNCT
ejpam-3478	314	13	b.	b.	PROPN
ejpam-3478	314	14	(	(	PUNCT
ejpam-3478	314	15	1997	1997	NUM
ejpam-3478	314	16	)	)	PUNCT
ejpam-3478	314	17	on	on	ADP
ejpam-3478	314	18	investment	investment	NOUN
ejpam-3478	314	19	consumption	consumption	NOUN
ejpam-3478	314	20	model	model	NOUN
ejpam-3478	314	21	with	with	ADP
ejpam-3478	314	22	transaction	transaction	NOUN
ejpam-3478	314	23	costs	cost	NOUN
ejpam-3478	314	24	:	:	PUNCT
ejpam-3478	314	25	an	an	DET
ejpam-3478	314	26	asymptotic	asymptotic	ADJ
ejpam-3478	314	27	analysis	analysis	NOUN
ejpam-3478	314	28	.	.	PUNCT
ejpam-3478	315	1	applied	apply	VERB
ejpam-3478	315	2	mathematical	mathematical	ADJ
ejpam-3478	315	3	finance	finance	NOUN
ejpam-3478	315	4	4	4	NUM
ejpam-3478	315	5	,	,	PUNCT
ejpam-3478	315	6	109	109	NUM
ejpam-3478	315	7	-	-	SYM
ejpam-3478	315	8	133	133	NUM
ejpam-3478	315	9	.	.	PUNCT
ejpam-3478	316	1	[	[	X
ejpam-3478	316	2	2	2	NUM
ejpam-3478	316	3	]	]	SYM
ejpam-3478	316	4	atkinson	atkinson	PROPN
ejpam-3478	316	5	,	,	PUNCT
ejpam-3478	316	6	c.	c.	PROPN
ejpam-3478	316	7	and	and	CCONJ
ejpam-3478	316	8	ingpochai	ingpochai	PROPN
ejpam-3478	316	9	,	,	PUNCT
ejpam-3478	316	10	p.	p.	NOUN
ejpam-3478	316	11	(	(	PUNCT
ejpam-3478	316	12	2012	2012	NUM
ejpam-3478	316	13	)	)	PUNCT
ejpam-3478	316	14	the	the	DET
ejpam-3478	316	15	effect	effect	NOUN
ejpam-3478	316	16	of	of	ADP
ejpam-3478	316	17	correlation	correlation	NOUN
ejpam-3478	316	18	and	and	CCONJ
ejpam-3478	316	19	transaction	transaction	NOUN
ejpam-3478	316	20	costs	cost	NOUN
ejpam-3478	316	21	on	on	ADP
ejpam-3478	316	22	the	the	DET
ejpam-3478	316	23	pricing	pricing	NOUN
ejpam-3478	316	24	of	of	ADP
ejpam-3478	316	25	basket	basket	NOUN
ejpam-3478	316	26	options	option	NOUN
ejpam-3478	316	27	.	.	PUNCT
ejpam-3478	317	1	applied	apply	VERB
ejpam-3478	317	2	mathematical	mathematical	ADJ
ejpam-3478	317	3	finance	finance	NOUN
ejpam-3478	317	4	19	19	NUM
ejpam-3478	317	5	,	,	PUNCT
ejpam-3478	317	6	131	131	NUM
ejpam-3478	317	7	-	-	SYM
ejpam-3478	317	8	179	179	NUM
ejpam-3478	317	9	.	.	PUNCT
ejpam-3478	318	1	[	[	X
ejpam-3478	318	2	3	3	NUM
ejpam-3478	318	3	]	]	X
ejpam-3478	318	4	atkinson	atkinson	PROPN
ejpam-3478	318	5	,	,	PUNCT
ejpam-3478	318	6	c.	c.	PROPN
ejpam-3478	318	7	and	and	CCONJ
ejpam-3478	318	8	ingpochai	ingpochai	PROPN
ejpam-3478	318	9	,	,	PUNCT
ejpam-3478	318	10	p.	p.	NOUN
ejpam-3478	318	11	(	(	PUNCT
ejpam-3478	318	12	2010	2010	NUM
ejpam-3478	318	13	)	)	PUNCT
ejpam-3478	318	14	optimisation	optimisation	NOUN
ejpam-3478	318	15	of	of	ADP
ejpam-3478	318	16	n	n	CCONJ
ejpam-3478	318	17	-	-	PUNCT
ejpam-3478	318	18	risky	risky	ADJ
ejpam-3478	318	19	asset	asset	NOUN
ejpam-3478	318	20	portfolios	portfolio	NOUN
ejpam-3478	318	21	with	with	ADP
ejpam-3478	318	22	stochastic	stochastic	ADJ
ejpam-3478	318	23	variance	variance	NOUN
ejpam-3478	318	24	and	and	CCONJ
ejpam-3478	318	25	transaction	transaction	NOUN
ejpam-3478	318	26	costs	cost	NOUN
ejpam-3478	318	27	.	.	PUNCT
ejpam-3478	319	1	journal	journal	NOUN
ejpam-3478	319	2	of	of	ADP
ejpam-3478	319	3	quantitative	quantitative	ADJ
ejpam-3478	319	4	finance	finance	NOUN
ejpam-3478	319	5	10(5	10(5	NOUN
ejpam-3478	319	6	)	)	PUNCT
ejpam-3478	319	7	,	,	PUNCT
ejpam-3478	319	8	503	503	NUM
ejpam-3478	319	9	-	-	SYM
ejpam-3478	319	10	514	514	NUM
ejpam-3478	319	11	.	.	PUNCT
ejpam-3478	320	1	[	[	X
ejpam-3478	320	2	4	4	NUM
ejpam-3478	320	3	]	]	X
ejpam-3478	320	4	atkinson	atkinson	PROPN
ejpam-3478	320	5	,	,	PUNCT
ejpam-3478	320	6	c.	c.	PROPN
ejpam-3478	320	7	and	and	CCONJ
ejpam-3478	320	8	ingpochai	ingpochai	PROPN
ejpam-3478	320	9	,	,	PUNCT
ejpam-3478	320	10	p.	p.	NOUN
ejpam-3478	320	11	(	(	PUNCT
ejpam-3478	320	12	2006	2006	NUM
ejpam-3478	320	13	)	)	PUNCT
ejpam-3478	320	14	the	the	DET
ejpam-3478	320	15	influence	influence	NOUN
ejpam-3478	320	16	of	of	ADP
ejpam-3478	320	17	correlation	correlation	NOUN
ejpam-3478	320	18	on	on	ADP
ejpam-3478	320	19	multi	multi	ADJ
ejpam-3478	320	20	-	-	ADJ
ejpam-3478	320	21	asset	asset	ADJ
ejpam-3478	320	22	portfolio	portfolio	NOUN
ejpam-3478	320	23	optimization	optimization	NOUN
ejpam-3478	320	24	with	with	ADP
ejpam-3478	320	25	transaction	transaction	NOUN
ejpam-3478	320	26	costs	cost	NOUN
ejpam-3478	320	27	journal	journal	NOUN
ejpam-3478	320	28	of	of	ADP
ejpam-3478	320	29	computational	computational	ADJ
ejpam-3478	320	30	finance	finance	NOUN
ejpam-3478	320	31	10(2	10(2	NUM
ejpam-3478	320	32	)	)	PUNCT
ejpam-3478	320	33	,	,	PUNCT
ejpam-3478	320	34	53	53	NUM
ejpam-3478	320	35	-	-	SYM
ejpam-3478	320	36	96	96	NUM
ejpam-3478	320	37	.	.	PUNCT
ejpam-3478	321	1	[	[	X
ejpam-3478	321	2	5	5	NUM
ejpam-3478	321	3	]	]	SYM
ejpam-3478	321	4	atkinson	atkinson	PROPN
ejpam-3478	321	5	,	,	PUNCT
ejpam-3478	321	6	c.	c.	PROPN
ejpam-3478	321	7	and	and	CCONJ
ejpam-3478	321	8	mokkhavesa	mokkhavesa	PROPN
ejpam-3478	321	9	,	,	PUNCT
ejpam-3478	321	10	s.	s.	PROPN
ejpam-3478	321	11	(	(	PUNCT
ejpam-3478	321	12	2001	2001	NUM
ejpam-3478	321	13	)	)	PUNCT
ejpam-3478	321	14	towards	towards	ADP
ejpam-3478	321	15	the	the	DET
ejpam-3478	321	16	determination	determination	NOUN
ejpam-3478	321	17	of	of	ADP
ejpam-3478	321	18	utility	utility	NOUN
ejpam-3478	321	19	preference	preference	NOUN
ejpam-3478	321	20	from	from	ADP
ejpam-3478	321	21	optimal	optimal	ADJ
ejpam-3478	321	22	portfolio	portfolio	NOUN
ejpam-3478	321	23	selections	selection	NOUN
ejpam-3478	321	24	.	.	PUNCT
ejpam-3478	322	1	applied	apply	VERB
ejpam-3478	322	2	mathematical	mathematical	ADJ
ejpam-3478	322	3	finance	finance	NOUN
ejpam-3478	322	4	8	8	NUM
ejpam-3478	322	5	,	,	PUNCT
ejpam-3478	322	6	1	1	NUM
ejpam-3478	322	7	-	-	SYM
ejpam-3478	322	8	26	26	NUM
ejpam-3478	322	9	.	.	PUNCT
ejpam-3478	323	1	[	[	X
ejpam-3478	323	2	6	6	NUM
ejpam-3478	323	3	]	]	SYM
ejpam-3478	323	4	atkinson	atkinson	PROPN
ejpam-3478	323	5	,	,	PUNCT
ejpam-3478	323	6	c.	c.	PROPN
ejpam-3478	323	7	,	,	PUNCT
ejpam-3478	323	8	pliska	pliska	PROPN
ejpam-3478	323	9	,	,	PUNCT
ejpam-3478	323	10	s.r	s.r	PROPN
ejpam-3478	323	11	.	.	PROPN
ejpam-3478	323	12	and	and	CCONJ
ejpam-3478	323	13	wilmott	wilmott	PROPN
ejpam-3478	323	14	,	,	PUNCT
ejpam-3478	323	15	p.	p.	NOUN
ejpam-3478	323	16	(	(	PUNCT
ejpam-3478	323	17	1997	1997	NUM
ejpam-3478	323	18	)	)	PUNCT
ejpam-3478	323	19	portfolio	portfolio	NOUN
ejpam-3478	323	20	management	management	NOUN
ejpam-3478	323	21	with	with	ADP
ejpam-3478	323	22	transaction	transaction	NOUN
ejpam-3478	323	23	costs	cost	NOUN
ejpam-3478	323	24	.	.	PUNCT
ejpam-3478	324	1	proceedings	proceeding	NOUN
ejpam-3478	324	2	of	of	ADP
ejpam-3478	324	3	the	the	DET
ejpam-3478	324	4	royal	royal	ADJ
ejpam-3478	324	5	society	society	NOUN
ejpam-3478	324	6	,	,	PUNCT
ejpam-3478	324	7	london	london	PROPN
ejpam-3478	324	8	a	a	DET
ejpam-3478	324	9	453	453	NUM
ejpam-3478	324	10	,	,	PUNCT
ejpam-3478	324	11	551	551	NUM
ejpam-3478	324	12	-	-	SYM
ejpam-3478	324	13	562	562	NUM
ejpam-3478	324	14	.	.	PUNCT
ejpam-3478	325	1	[	[	X
ejpam-3478	325	2	7	7	NUM
ejpam-3478	325	3	]	]	SYM
ejpam-3478	325	4	atkinson	atkinson	PROPN
ejpam-3478	325	5	,	,	PUNCT
ejpam-3478	325	6	c.	c.	PROPN
ejpam-3478	325	7	and	and	CCONJ
ejpam-3478	325	8	wilmott	wilmott	PROPN
ejpam-3478	325	9	,	,	PUNCT
ejpam-3478	325	10	p.	p.	NOUN
ejpam-3478	325	11	(	(	PUNCT
ejpam-3478	325	12	1995	1995	NUM
ejpam-3478	325	13	)	)	PUNCT
ejpam-3478	325	14	portfolio	portfolio	NOUN
ejpam-3478	325	15	management	management	NOUN
ejpam-3478	325	16	with	with	ADP
ejpam-3478	325	17	transaction	transaction	NOUN
ejpam-3478	325	18	costs	cost	NOUN
ejpam-3478	325	19	:	:	PUNCT
ejpam-3478	325	20	an	an	DET
ejpam-3478	325	21	asymptotic	asymptotic	ADJ
ejpam-3478	325	22	analysis	analysis	NOUN
ejpam-3478	325	23	.	.	PUNCT
ejpam-3478	325	24	mathematical	mathematical	ADJ
ejpam-3478	325	25	finance	finance	NOUN
ejpam-3478	325	26	5	5	NUM
ejpam-3478	325	27	,	,	PUNCT
ejpam-3478	325	28	357	357	NUM
ejpam-3478	325	29	-	-	SYM
ejpam-3478	325	30	367	367	NUM
ejpam-3478	325	31	.	.	PUNCT
ejpam-3478	326	1	[	[	X
ejpam-3478	326	2	8	8	NUM
ejpam-3478	326	3	]	]	X
ejpam-3478	326	4	gerstner	gerstner	NOUN
ejpam-3478	326	5	,	,	PUNCT
ejpam-3478	326	6	t.	t.	PROPN
ejpam-3478	326	7	,	,	PUNCT
ejpam-3478	326	8	griebel	griebel	NOUN
ejpam-3478	326	9	,	,	PUNCT
ejpam-3478	326	10	m.	m.	NOUN
ejpam-3478	326	11	and	and	CCONJ
ejpam-3478	326	12	holtz	holtz	NOUN
ejpam-3478	326	13	,	,	PUNCT
ejpam-3478	326	14	m.	m.	NOUN
ejpam-3478	326	15	(	(	PUNCT
ejpam-3478	326	16	2009	2009	NUM
ejpam-3478	326	17	)	)	PUNCT
ejpam-3478	326	18	efficient	efficient	ADJ
ejpam-3478	326	19	deterministic	deterministic	ADJ
ejpam-3478	326	20	numerical	numerical	ADJ
ejpam-3478	326	21	simulation	simulation	NOUN
ejpam-3478	326	22	of	of	ADP
ejpam-3478	326	23	stochastic	stochastic	ADJ
ejpam-3478	326	24	asset	asset	NOUN
ejpam-3478	326	25	-	-	PUNCT
ejpam-3478	326	26	liability	liability	NOUN
ejpam-3478	326	27	management	management	NOUN
ejpam-3478	326	28	models	model	NOUN
ejpam-3478	326	29	in	in	ADP
ejpam-3478	326	30	life	life	NOUN
ejpam-3478	326	31	insurance	insurance	NOUN
ejpam-3478	326	32	,	,	PUNCT
ejpam-3478	326	33	insurance	insurance	NOUN
ejpam-3478	326	34	:	:	PUNCT
ejpam-3478	326	35	mathematics	mathematic	NOUN
ejpam-3478	326	36	and	and	CCONJ
ejpam-3478	326	37	economics	economic	NOUN
ejpam-3478	326	38	44(3	44(3	NUM
ejpam-3478	326	39	)	)	PUNCT
ejpam-3478	326	40	,	,	PUNCT
ejpam-3478	326	41	434	434	NUM
ejpam-3478	326	42	-	-	SYM
ejpam-3478	326	43	446	446	NUM
ejpam-3478	326	44	.	.	PUNCT
ejpam-3478	327	1	[	[	X
ejpam-3478	327	2	9	9	NUM
ejpam-3478	327	3	]	]	SYM
ejpam-3478	327	4	merton	merton	PROPN
ejpam-3478	327	5	,	,	PUNCT
ejpam-3478	327	6	r.c	r.c	PROPN
ejpam-3478	327	7	.	.	PROPN
ejpam-3478	327	8	(	(	PUNCT
ejpam-3478	327	9	1969	1969	NUM
ejpam-3478	327	10	)	)	PUNCT
ejpam-3478	327	11	lifetime	lifetime	NOUN
ejpam-3478	327	12	portfolio	portfolio	NOUN
ejpam-3478	327	13	selection	selection	NOUN
ejpam-3478	327	14	under	under	ADP
ejpam-3478	327	15	uncertainty	uncertainty	NOUN
ejpam-3478	327	16	:	:	PUNCT
ejpam-3478	327	17	the	the	DET
ejpam-3478	327	18	continuoustime	continuoustime	ADJ
ejpam-3478	327	19	case	case	NOUN
ejpam-3478	327	20	,	,	PUNCT
ejpam-3478	327	21	the	the	DET
ejpam-3478	327	22	review	review	NOUN
ejpam-3478	327	23	of	of	ADP
ejpam-3478	327	24	economics	economic	NOUN
ejpam-3478	327	25	and	and	CCONJ
ejpam-3478	327	26	statistics	statistic	NOUN
ejpam-3478	327	27	51	51	NUM
ejpam-3478	327	28	,	,	PUNCT
ejpam-3478	327	29	247	247	NUM
ejpam-3478	327	30	-	-	SYM
ejpam-3478	327	31	257	257	NUM
ejpam-3478	327	32	.	.	PUNCT
ejpam-3478	328	1	[	[	X
ejpam-3478	328	2	10	10	NUM
ejpam-3478	328	3	]	]	SYM
ejpam-3478	328	4	merton	merton	PROPN
ejpam-3478	328	5	,	,	PUNCT
ejpam-3478	328	6	r.c	r.c	PROPN
ejpam-3478	328	7	.	.	PROPN
ejpam-3478	328	8	(	(	PUNCT
ejpam-3478	328	9	1971	1971	NUM
ejpam-3478	328	10	)	)	PUNCT
ejpam-3478	328	11	optimal	optimal	ADJ
ejpam-3478	328	12	consumption	consumption	NOUN
ejpam-3478	328	13	and	and	CCONJ
ejpam-3478	328	14	portfolio	portfolio	NOUN
ejpam-3478	328	15	rules	rule	NOUN
ejpam-3478	328	16	in	in	ADP
ejpam-3478	328	17	a	a	DET
ejpam-3478	328	18	continuous	continuous	ADJ
ejpam-3478	328	19	time	time	NOUN
ejpam-3478	328	20	model	model	NOUN
ejpam-3478	328	21	.	.	PUNCT
ejpam-3478	329	1	j.	j.	PROPN
ejpam-3478	329	2	economic	economic	PROPN
ejpam-3478	329	3	theory	theory	NOUN
ejpam-3478	329	4	3	3	NUM
ejpam-3478	329	5	,	,	PUNCT
ejpam-3478	329	6	373	373	NUM
ejpam-3478	329	7	-	-	SYM
ejpam-3478	329	8	413	413	NUM
ejpam-3478	329	9	.	.	PUNCT
ejpam-3478	330	1	[	[	X
ejpam-3478	330	2	11	11	NUM
ejpam-3478	330	3	]	]	SYM
ejpam-3478	330	4	merton	merton	PROPN
ejpam-3478	330	5	,	,	PUNCT
ejpam-3478	330	6	r.c	r.c	PROPN
ejpam-3478	330	7	.	.	PROPN
ejpam-3478	330	8	(	(	PUNCT
ejpam-3478	330	9	1992	1992	NUM
ejpam-3478	330	10	)	)	PUNCT
ejpam-3478	330	11	continuous	continuous	ADJ
ejpam-3478	330	12	time	time	NOUN
ejpam-3478	330	13	finance	finance	NOUN
ejpam-3478	330	14	.	.	PUNCT
ejpam-3478	331	1	blackwell	blackwell	PROPN
ejpam-3478	331	2	,	,	PUNCT
ejpam-3478	331	3	cambridge	cambridge	PROPN
ejpam-3478	331	4	,	,	PUNCT
ejpam-3478	331	5	ma	ma	PROPN
ejpam-3478	331	6	.	.	PUNCT
ejpam-3478	332	1	[	[	X
ejpam-3478	332	2	12	12	NUM
ejpam-3478	332	3	]	]	PUNCT
ejpam-3478	332	4	mokkhavesa	mokkhavesa	NOUN
ejpam-3478	332	5	,	,	PUNCT
ejpam-3478	332	6	s.	s.	PROPN
ejpam-3478	332	7	and	and	CCONJ
ejpam-3478	332	8	atkinson	atkinson	PROPN
ejpam-3478	332	9	,	,	PUNCT
ejpam-3478	332	10	c.	c.	PROPN
ejpam-3478	332	11	(	(	PUNCT
ejpam-3478	332	12	2002	2002	NUM
ejpam-3478	332	13	)	)	PUNCT
ejpam-3478	332	14	perturbation	perturbation	NOUN
ejpam-3478	332	15	solution	solution	NOUN
ejpam-3478	332	16	of	of	ADP
ejpam-3478	332	17	optimal	optimal	ADJ
ejpam-3478	332	18	portfolio	portfolio	NOUN
ejpam-3478	332	19	theory	theory	NOUN
ejpam-3478	332	20	with	with	ADP
ejpam-3478	332	21	transaction	transaction	NOUN
ejpam-3478	332	22	costs	cost	NOUN
ejpam-3478	332	23	for	for	ADP
ejpam-3478	332	24	any	any	DET
ejpam-3478	332	25	utility	utility	NOUN
ejpam-3478	332	26	function	function	NOUN
ejpam-3478	332	27	.	.	PUNCT
ejpam-3478	333	1	i	i	PRON
ejpam-3478	333	2	m	m	VERB
ejpam-3478	333	3	a	a	DET
ejpam-3478	333	4	journal	journal	NOUN
ejpam-3478	333	5	of	of	ADP
ejpam-3478	333	6	management	management	NOUN
ejpam-3478	333	7	mathematics	mathematic	NOUN
ejpam-3478	333	8	13	13	NUM
ejpam-3478	333	9	,	,	PUNCT
ejpam-3478	333	10	131	131	NUM
ejpam-3478	333	11	-	-	SYM
ejpam-3478	333	12	151	151	NUM
ejpam-3478	333	13	.	.	PUNCT
ejpam-3478	334	1	references	reference	NOUN
ejpam-3478	334	2	1332	1332	NUM
ejpam-3478	334	3	[	[	SYM
ejpam-3478	334	4	13	13	NUM
ejpam-3478	334	5	]	]	SYM
ejpam-3478	334	6	morton	morton	PROPN
ejpam-3478	334	7	,	,	PUNCT
ejpam-3478	334	8	a.	a.	NOUN
ejpam-3478	334	9	and	and	CCONJ
ejpam-3478	334	10	pliska	pliska	PROPN
ejpam-3478	334	11	,	,	PUNCT
ejpam-3478	334	12	s.	s.	PROPN
ejpam-3478	334	13	(	(	PUNCT
ejpam-3478	334	14	1995	1995	NUM
ejpam-3478	334	15	)	)	PUNCT
ejpam-3478	334	16	optimal	optimal	ADJ
ejpam-3478	334	17	portfolio	portfolio	NOUN
ejpam-3478	334	18	management	management	NOUN
ejpam-3478	334	19	with	with	ADP
ejpam-3478	334	20	fixed	fix	VERB
ejpam-3478	334	21	transaction	transaction	NOUN
ejpam-3478	334	22	costs	cost	NOUN
ejpam-3478	334	23	.	.	PUNCT
ejpam-3478	335	1	mathematical	mathematical	ADJ
ejpam-3478	335	2	finance	finance	NOUN
ejpam-3478	335	3	5	5	NUM
ejpam-3478	335	4	,	,	PUNCT
ejpam-3478	335	5	337	337	NUM
ejpam-3478	335	6	-	-	SYM
ejpam-3478	335	7	356	356	NUM
ejpam-3478	335	8	.	.	PUNCT
ejpam-3478	336	1	appendix	appendix	VERB
ejpam-3478	336	2	1333	1333	NUM
ejpam-3478	336	3	appendix	appendix	NOUN
ejpam-3478	336	4	we	we	PRON
ejpam-3478	336	5	assume	assume	VERB
ejpam-3478	336	6	here	here	ADV
ejpam-3478	336	7	that	that	SCONJ
ejpam-3478	336	8	|ε|	|ε|	DET
ejpam-3478	336	9	�	�	PROPN
ejpam-3478	336	10	ra	ra	PROPN
ejpam-3478	336	11	and	and	CCONJ
ejpam-3478	336	12	show	show	VERB
ejpam-3478	336	13	how	how	SCONJ
ejpam-3478	336	14	the	the	DET
ejpam-3478	336	15	method	method	NOUN
ejpam-3478	336	16	for	for	ADP
ejpam-3478	336	17	determining	determine	VERB
ejpam-3478	336	18	the	the	DET
ejpam-3478	336	19	order	order	NOUN
ejpam-3478	336	20	ε	ε	PROPN
ejpam-3478	336	21	correction	correction	NOUN
ejpam-3478	336	22	can	can	AUX
ejpam-3478	336	23	be	be	AUX
ejpam-3478	336	24	extended	extend	VERB
ejpam-3478	336	25	to	to	PART
ejpam-3478	336	26	obtain	obtain	VERB
ejpam-3478	336	27	higher	high	ADJ
ejpam-3478	336	28	order	order	NOUN
ejpam-3478	336	29	terms	term	NOUN
ejpam-3478	336	30	.	.	PUNCT
ejpam-3478	337	1	j	j	PROPN
ejpam-3478	337	2	(	(	PUNCT
ejpam-3478	337	3	w	w	PROPN
ejpam-3478	337	4	,	,	PUNCT
ejpam-3478	337	5	l	l	PROPN
ejpam-3478	337	6	,	,	PUNCT
ejpam-3478	337	7	t	t	PROPN
ejpam-3478	337	8	)	)	PUNCT
ejpam-3478	337	9	=	=	SYM
ejpam-3478	337	10	j0	j0	PROPN
ejpam-3478	338	1	+	+	CCONJ
ejpam-3478	338	2	εj1	εj1	NOUN
ejpam-3478	338	3	+	+	CCONJ
ejpam-3478	338	4	ε2j2	ε2j2	X
ejpam-3478	339	1	+	+	NOUN
ejpam-3478	339	2	o	o	X
ejpam-3478	339	3	(	(	PUNCT
ejpam-3478	339	4	ε3	ε3	PROPN
ejpam-3478	339	5	)	)	PUNCT
ejpam-3478	339	6	ww	ww	PROPN
ejpam-3478	339	7	=	=	PROPN
ejpam-3478	339	8	w0	w0	PROPN
ejpam-3478	339	9	+	+	CCONJ
ejpam-3478	339	10	εw1	εw1	ADV
ejpam-3478	339	11	+	+	CCONJ
ejpam-3478	339	12	ε2w2	ε2w2	X
ejpam-3478	339	13	+	+	ADJ
ejpam-3478	339	14	o	o	X
ejpam-3478	339	15	(	(	PUNCT
ejpam-3478	339	16	ε3	ε3	PROPN
ejpam-3478	339	17	)	)	PUNCT
ejpam-3478	339	18	ul	ul	NOUN
ejpam-3478	339	19	=	=	PUNCT
ejpam-3478	339	20	u0	u0	PROPN
ejpam-3478	339	21	+	+	CCONJ
ejpam-3478	339	22	εu1	εu1	X
ejpam-3478	339	23	+	+	CCONJ
ejpam-3478	339	24	ε2u2	ε2u2	PROPN
ejpam-3478	339	25	+	+	ADJ
ejpam-3478	339	26	o	o	X
ejpam-3478	339	27	(	(	PUNCT
ejpam-3478	339	28	ε3	ε3	PROPN
ejpam-3478	339	29	)	)	PUNCT
ejpam-3478	339	30	j	j	PROPN
ejpam-3478	339	31	(	(	PUNCT
ejpam-3478	339	32	w	w	PROPN
ejpam-3478	339	33	,	,	PUNCT
ejpam-3478	339	34	l	l	PROPN
ejpam-3478	339	35	,	,	PUNCT
ejpam-3478	339	36	t	t	PROPN
ejpam-3478	339	37	)	)	PUNCT
ejpam-3478	339	38	=	=	SYM
ejpam-3478	340	1	a	a	PRON
ejpam-3478	340	2	(	(	PUNCT
ejpam-3478	340	3	t	t	NOUN
ejpam-3478	340	4	)	)	PUNCT
ejpam-3478	340	5	(	(	PUNCT
ejpam-3478	340	6	w	w	NOUN
ejpam-3478	340	7	−	−	PROPN
ejpam-3478	340	8	l)γ	l)γ	NOUN
ejpam-3478	340	9	γ	γ	X
ejpam-3478	340	10	+	+	CCONJ
ejpam-3478	340	11	ε	ε	PROPN
ejpam-3478	340	12	(	(	PUNCT
ejpam-3478	340	13	bl+b1w	bl+b1w	PROPN
ejpam-3478	340	14	)	)	PUNCT
ejpam-3478	341	1	(	(	PUNCT
ejpam-3478	341	2	w	w	NOUN
ejpam-3478	341	3	−	−	PROPN
ejpam-3478	341	4	l)γ−1	l)γ−1	PROPN
ejpam-3478	341	5	+	+	CCONJ
ejpam-3478	341	6	ε2	ε2	ADJ
ejpam-3478	341	7	(	(	PUNCT
ejpam-3478	341	8	c1w	c1w	NOUN
ejpam-3478	341	9	2	2	NUM
ejpam-3478	341	10	+	+	CCONJ
ejpam-3478	341	11	c2lw	c2lw	X
ejpam-3478	341	12	+	+	CCONJ
ejpam-3478	341	13	c3l	c3l	X
ejpam-3478	341	14	2	2	NUM
ejpam-3478	341	15	)	)	PUNCT
ejpam-3478	341	16	(	(	PUNCT
ejpam-3478	341	17	w	w	NOUN
ejpam-3478	341	18	−	−	PROPN
ejpam-3478	341	19	l)γ−2	l)γ−2	NOUN
ejpam-3478	341	20	where	where	SCONJ
ejpam-3478	341	21	b	b	X
ejpam-3478	341	22	(	(	PUNCT
ejpam-3478	341	23	t	t	PROPN
ejpam-3478	341	24	)	)	PUNCT
ejpam-3478	341	25	,	,	PUNCT
ejpam-3478	341	26	b1	b1	NOUN
ejpam-3478	341	27	(	(	PUNCT
ejpam-3478	341	28	t	t	PROPN
ejpam-3478	341	29	)	)	PUNCT
ejpam-3478	341	30	are	be	AUX
ejpam-3478	341	31	to	to	PART
ejpam-3478	341	32	be	be	AUX
ejpam-3478	341	33	determined	determine	VERB
ejpam-3478	341	34	in	in	ADP
ejpam-3478	341	35	terms	term	NOUN
ejpam-3478	341	36	of	of	ADP
ejpam-3478	341	37	a	a	DET
ejpam-3478	341	38	(	(	PUNCT
ejpam-3478	341	39	t	t	PROPN
ejpam-3478	341	40	)	)	PUNCT
ejpam-3478	341	41	.	.	PUNCT
ejpam-3478	342	1	to	to	ADP
ejpam-3478	342	2	this	this	DET
ejpam-3478	342	3	order	order	NOUN
ejpam-3478	342	4	,	,	PUNCT
ejpam-3478	342	5	equations	equation	NOUN
ejpam-3478	342	6	(	(	PUNCT
ejpam-3478	342	7	11	11	NUM
ejpam-3478	342	8	)	)	PUNCT
ejpam-3478	342	9	and	and	CCONJ
ejpam-3478	342	10	(	(	PUNCT
ejpam-3478	342	11	12	12	NUM
ejpam-3478	342	12	)	)	PUNCT
ejpam-3478	342	13	(	(	PUNCT
ejpam-3478	342	14	the	the	DET
ejpam-3478	342	15	conditions	condition	NOUN
ejpam-3478	342	16	for	for	ADP
ejpam-3478	342	17	the	the	DET
ejpam-3478	342	18	maximum	maximum	ADJ
ejpam-3478	342	19	)	)	PUNCT
ejpam-3478	342	20	give	give	VERB
ejpam-3478	342	21	0	0	NUM
ejpam-3478	343	1	=	=	SYM
ejpam-3478	343	2	(	(	PUNCT
ejpam-3478	343	3	α−	α−	ADP
ejpam-3478	343	4	r	r	NOUN
ejpam-3478	343	5	)	)	PUNCT
ejpam-3478	343	6	[	[	PUNCT
ejpam-3478	343	7	j0w	j0w	X
ejpam-3478	343	8	+	+	CCONJ
ejpam-3478	343	9	εj1w	εj1w	ADJ
ejpam-3478	343	10	+	+	CCONJ
ejpam-3478	343	11	ε2j2w	ε2j2w	PUNCT
ejpam-3478	343	12	]	]	X
ejpam-3478	344	1	+	+	CCONJ
ejpam-3478	344	2	σ2	σ2	PROPN
ejpam-3478	344	3	[	[	PUNCT
ejpam-3478	344	4	j0ww	j0ww	PUNCT
ejpam-3478	344	5	+	+	NUM
ejpam-3478	344	6	εj1ww	εj1ww	NUM
ejpam-3478	344	7	+	+	CCONJ
ejpam-3478	344	8	ε2j2ww	ε2j2ww	X
ejpam-3478	344	9	]	]	PUNCT
ejpam-3478	345	1	[	[	PUNCT
ejpam-3478	345	2	w0	w0	PROPN
ejpam-3478	345	3	+	+	CCONJ
ejpam-3478	345	4	εw1	εw1	NOUN
ejpam-3478	345	5	+	+	CCONJ
ejpam-3478	345	6	ε2w2	ε2w2	X
ejpam-3478	345	7	]	]	X
ejpam-3478	346	1	+	+	CCONJ
ejpam-3478	346	2	qσρ	qσρ	X
ejpam-3478	346	3	[	[	PUNCT
ejpam-3478	346	4	j0lw	j0lw	X
ejpam-3478	346	5	+	+	X
ejpam-3478	346	6	εj1lw	εj1lw	NOUN
ejpam-3478	346	7	+	+	CCONJ
ejpam-3478	346	8	ε2j2lw	ε2j2lw	NOUN
ejpam-3478	346	9	]	]	PUNCT
ejpam-3478	346	10	[	[	PUNCT
ejpam-3478	346	11	u0	u0	X
ejpam-3478	346	12	+	+	CCONJ
ejpam-3478	346	13	εu1	εu1	X
ejpam-3478	346	14	+	+	CCONJ
ejpam-3478	346	15	ε2u2	ε2u2	PROPN
ejpam-3478	346	16	]	]	PUNCT
ejpam-3478	346	17	(	(	PUNCT
ejpam-3478	346	18	a.1	a.1	NOUN
ejpam-3478	346	19	)	)	PUNCT
ejpam-3478	346	20	and	and	CCONJ
ejpam-3478	346	21	0	0	NUM
ejpam-3478	346	22	=	=	SYM
ejpam-3478	346	23	c	c	X
ejpam-3478	346	24	[	[	PUNCT
ejpam-3478	346	25	j0l	j0l	X
ejpam-3478	346	26	+	+	CCONJ
ejpam-3478	346	27	εj1l	εj1l	PROPN
ejpam-3478	346	28	+	+	CCONJ
ejpam-3478	346	29	ε2j2l	ε2j2l	NUM
ejpam-3478	346	30	]	]	PUNCT
ejpam-3478	347	1	+	+	NUM
ejpam-3478	347	2	q2	q2	NOUN
ejpam-3478	347	3	[	[	PUNCT
ejpam-3478	347	4	j0ll	j0ll	PUNCT
ejpam-3478	347	5	+	+	CCONJ
ejpam-3478	347	6	εj1ll	εj1ll	X
ejpam-3478	347	7	+	+	CCONJ
ejpam-3478	347	8	ε2j2ll	ε2j2ll	NOUN
ejpam-3478	347	9	]	]	PUNCT
ejpam-3478	348	1	[	[	PUNCT
ejpam-3478	348	2	u0	u0	X
ejpam-3478	348	3	+	+	CCONJ
ejpam-3478	348	4	εu1	εu1	X
ejpam-3478	349	1	+	+	CCONJ
ejpam-3478	349	2	ε2u2	ε2u2	PROPN
ejpam-3478	349	3	]	]	PUNCT
ejpam-3478	349	4	+	+	CCONJ
ejpam-3478	349	5	qσρ	qσρ	X
ejpam-3478	349	6	[	[	PUNCT
ejpam-3478	349	7	j0lw	j0lw	X
ejpam-3478	349	8	+	+	X
ejpam-3478	349	9	εj1lw	εj1lw	NOUN
ejpam-3478	349	10	+	+	CCONJ
ejpam-3478	349	11	ε2j2lw	ε2j2lw	NOUN
ejpam-3478	349	12	]	]	PUNCT
ejpam-3478	349	13	[	[	PUNCT
ejpam-3478	349	14	w0	w0	X
ejpam-3478	349	15	+	+	CCONJ
ejpam-3478	349	16	εw1	εw1	NOUN
ejpam-3478	349	17	+	+	NUM
ejpam-3478	349	18	ε2w2	ε2w2	X
ejpam-3478	349	19	]	]	PUNCT
ejpam-3478	349	20	.	.	PUNCT
ejpam-3478	350	1	(	(	PUNCT
ejpam-3478	350	2	a.2	a.2	SYM
ejpam-3478	350	3	)	)	PUNCT
ejpam-3478	350	4	so	so	SCONJ
ejpam-3478	350	5	we	we	PRON
ejpam-3478	350	6	have	have	VERB
ejpam-3478	350	7	for	for	ADP
ejpam-3478	350	8	o	o	PROPN
ejpam-3478	350	9	(	(	PUNCT
ejpam-3478	350	10	1	1	NUM
ejpam-3478	350	11	)	)	PUNCT
ejpam-3478	350	12	0	0	NUM
ejpam-3478	351	1	=	=	SYM
ejpam-3478	351	2	(	(	PUNCT
ejpam-3478	351	3	α−	α−	ADP
ejpam-3478	351	4	ra	ra	NOUN
ejpam-3478	351	5	)	)	PUNCT
ejpam-3478	351	6	j0w	j0w	PROPN
ejpam-3478	352	1	+	+	CCONJ
ejpam-3478	352	2	σ2w0j0ww	σ2w0j0ww	PROPN
ejpam-3478	352	3	+	+	CCONJ
ejpam-3478	352	4	qσρu0j0lw	qσρu0j0lw	ADJ
ejpam-3478	352	5	and	and	CCONJ
ejpam-3478	352	6	0	0	NUM
ejpam-3478	353	1	=	=	SYM
ejpam-3478	353	2	cj0l	cj0l	X
ejpam-3478	353	3	+	+	CCONJ
ejpam-3478	353	4	q2u0j0ll	q2u0j0ll	PROPN
ejpam-3478	353	5	+	+	NUM
ejpam-3478	353	6	qσρw0j0lw	qσρw0j0lw	ADJ
ejpam-3478	353	7	.	.	PUNCT
ejpam-3478	354	1	for	for	ADP
ejpam-3478	354	2	o	o	PROPN
ejpam-3478	354	3	(	(	PUNCT
ejpam-3478	354	4	ε	ε	PROPN
ejpam-3478	354	5	)	)	PUNCT
ejpam-3478	354	6	0	0	NUM
ejpam-3478	355	1	=	=	SYM
ejpam-3478	355	2	(	(	PUNCT
ejpam-3478	355	3	α−	α−	ADP
ejpam-3478	355	4	ra	ra	NOUN
ejpam-3478	355	5	)	)	PUNCT
ejpam-3478	355	6	j1w	j1w	PROPN
ejpam-3478	356	1	+	+	CCONJ
ejpam-3478	356	2	σ2w0j1ww	σ2w0j1ww	PROPN
ejpam-3478	356	3	+	+	CCONJ
ejpam-3478	356	4	qσρu0j1lw	qσρu0j1lw	NOUN
ejpam-3478	356	5	+	+	CCONJ
ejpam-3478	356	6	σ2w1j0ww	σ2w1j0ww	PROPN
ejpam-3478	356	7	+	+	CCONJ
ejpam-3478	356	8	qσρu1j0lw	qσρu1j0lw	NOUN
ejpam-3478	356	9	and	and	CCONJ
ejpam-3478	356	10	0	0	NUM
ejpam-3478	356	11	=	=	SYM
ejpam-3478	356	12	cj1l	cj1l	PROPN
ejpam-3478	357	1	+	+	CCONJ
ejpam-3478	357	2	q2u0j1ll	q2u0j1ll	PROPN
ejpam-3478	358	1	+	+	CCONJ
ejpam-3478	358	2	qσρw0j1lw	qσρw0j1lw	X
ejpam-3478	358	3	+	+	X
ejpam-3478	358	4	q2u1j0ll	q2u1j0ll	PROPN
ejpam-3478	358	5	+	+	ADV
ejpam-3478	358	6	qσρw1j0lw	qσρw1j0lw	ADJ
ejpam-3478	358	7	.	.	PUNCT
ejpam-3478	359	1	appendix	appendix	NOUN
ejpam-3478	359	2	1334	1334	NUM
ejpam-3478	359	3	for	for	ADP
ejpam-3478	359	4	o	o	PROPN
ejpam-3478	359	5	(	(	PUNCT
ejpam-3478	359	6	ε2	ε2	ADJ
ejpam-3478	359	7	)	)	PUNCT
ejpam-3478	359	8	0	0	PUNCT
ejpam-3478	360	1	=	=	NUM
ejpam-3478	360	2	w2σ	w2σ	ADP
ejpam-3478	360	3	2j0ww	2j0ww	NUM
ejpam-3478	361	1	+	+	CCONJ
ejpam-3478	361	2	u2qσρj0lw	u2qσρj0lw	PROPN
ejpam-3478	361	3	(	(	PUNCT
ejpam-3478	361	4	α−	α−	ADP
ejpam-3478	361	5	ra	ra	NOUN
ejpam-3478	361	6	)	)	PUNCT
ejpam-3478	361	7	j2w	j2w	NOUN
ejpam-3478	362	1	+	+	CCONJ
ejpam-3478	362	2	σ2w0j2ww	σ2w0j2ww	PROPN
ejpam-3478	362	3	+	+	CCONJ
ejpam-3478	362	4	qσρu0j2lw	qσρu0j2lw	NOUN
ejpam-3478	362	5	+	+	CCONJ
ejpam-3478	363	1	σ2w1j1ww	σ2w1j1ww	ADP
ejpam-3478	363	2	+	+	CCONJ
ejpam-3478	363	3	qσρu1j1lw	qσρu1j1lw	NOUN
ejpam-3478	363	4	and	and	CCONJ
ejpam-3478	363	5	0	0	NUM
ejpam-3478	363	6	=	=	SYM
ejpam-3478	363	7	w2qσρj0lw	w2qσρj0lw	PROPN
ejpam-3478	363	8	+	+	CCONJ
ejpam-3478	363	9	u2σ	u2σ	NUM
ejpam-3478	363	10	2j0ll	2j0ll	NUM
ejpam-3478	363	11	cj2l	cj2l	PROPN
ejpam-3478	363	12	+	+	NUM
ejpam-3478	363	13	qσρw0j2lw	qσρw0j2lw	ADJ
ejpam-3478	363	14	+	+	CCONJ
ejpam-3478	363	15	q2u0j2ll	q2u0j2ll	PROPN
ejpam-3478	363	16	+	+	CCONJ
ejpam-3478	363	17	qσρw1j1lw	qσρw1j1lw	NOUN
ejpam-3478	363	18	+	+	X
ejpam-3478	363	19	q2u1j1ll	q2u1j1ll	PROPN
ejpam-3478	363	20	.	.	PUNCT
ejpam-3478	364	1	our	our	PRON
ejpam-3478	364	2	equation	equation	NOUN
ejpam-3478	364	3	(	(	PUNCT
ejpam-3478	364	4	9	9	NUM
ejpam-3478	364	5	)	)	PUNCT
ejpam-3478	364	6	can	can	AUX
ejpam-3478	364	7	be	be	AUX
ejpam-3478	364	8	written	write	VERB
ejpam-3478	364	9	as	as	ADP
ejpam-3478	364	10	(	(	PUNCT
ejpam-3478	364	11	or	or	CCONJ
ejpam-3478	364	12	alternatively	alternatively	ADV
ejpam-3478	364	13	one	one	NUM
ejpam-3478	364	14	can	can	AUX
ejpam-3478	364	15	use	use	VERB
ejpam-3478	364	16	the	the	DET
ejpam-3478	364	17	version	version	NOUN
ejpam-3478	364	18	in	in	ADP
ejpam-3478	364	19	(	(	PUNCT
ejpam-3478	364	20	14	14	NUM
ejpam-3478	364	21	)	)	PUNCT
ejpam-3478	364	22	)	)	PUNCT
ejpam-3478	364	23	,	,	PUNCT
ejpam-3478	364	24	0	0	X
ejpam-3478	365	1	=	=	SYM
ejpam-3478	365	2	u	u	X
ejpam-3478	365	3	[	[	X
ejpam-3478	365	4	e	e	X
ejpam-3478	365	5	]	]	X
ejpam-3478	366	1	+	+	CCONJ
ejpam-3478	366	2	∂j	∂j	PROPN
ejpam-3478	366	3	∂t	∂t	PROPN
ejpam-3478	366	4	+	+	CCONJ
ejpam-3478	366	5	cu	cu	PROPN
ejpam-3478	366	6	∂j	∂j	PROPN
ejpam-3478	367	1	∂l	∂l	PROPN
ejpam-3478	368	1	+	+	CCONJ
ejpam-3478	368	2	(	(	PUNCT
ejpam-3478	368	3	α−	α−	ADP
ejpam-3478	368	4	ra)w	ra)w	NOUN
ejpam-3478	368	5	∂j	∂j	NOUN
ejpam-3478	369	1	∂w	∂w	NOUN
ejpam-3478	369	2	+	+	CCONJ
ejpam-3478	369	3	(	(	PUNCT
ejpam-3478	369	4	raw	raw	ADJ
ejpam-3478	369	5	∂j	∂j	NOUN
ejpam-3478	370	1	∂w	∂w	PROPN
ejpam-3478	370	2	+	+	NUM
ejpam-3478	370	3	rll	rll	NOUN
ejpam-3478	370	4	∂j	∂j	PROPN
ejpam-3478	370	5	∂l	∂l	PROPN
ejpam-3478	370	6	)	)	PUNCT
ejpam-3478	371	1	+	+	CCONJ
ejpam-3478	371	2	1	1	NUM
ejpam-3478	371	3	2	2	NUM
ejpam-3478	371	4	σ2w2	σ2w2	NOUN
ejpam-3478	371	5	∂	∂	NUM
ejpam-3478	371	6	2j	2j	X
ejpam-3478	371	7	∂w	∂w	PROPN
ejpam-3478	371	8	2	2	NUM
ejpam-3478	371	9	+	+	NOUN
ejpam-3478	371	10	qσρuw	qσρuw	NOUN
ejpam-3478	371	11	∂2j	∂2j	PROPN
ejpam-3478	371	12	∂l∂w	∂l∂w	NOUN
ejpam-3478	371	13	+	+	CCONJ
ejpam-3478	371	14	1	1	NUM
ejpam-3478	371	15	2	2	NUM
ejpam-3478	371	16	q2u2	q2u2	NOUN
ejpam-3478	371	17	∂2j	∂2j	PROPN
ejpam-3478	371	18	∂l2	∂l2	PROPN
ejpam-3478	371	19	,	,	PUNCT
ejpam-3478	371	20	(	(	PUNCT
ejpam-3478	371	21	a.3	a.3	NOUN
ejpam-3478	371	22	)	)	PUNCT
ejpam-3478	371	23	where	where	SCONJ
ejpam-3478	371	24	u	u	NOUN
ejpam-3478	371	25	=	=	PROPN
ejpam-3478	371	26	ul	ul	INTJ
ejpam-3478	371	27	,	,	PUNCT
ejpam-3478	371	28	w	w	PROPN
ejpam-3478	371	29	=	=	SYM
ejpam-3478	371	30	ww	ww	PROPN
ejpam-3478	371	31	.	.	PROPN
ejpam-3478	372	1	for	for	ADP
ejpam-3478	372	2	o	o	PROPN
ejpam-3478	372	3	(	(	PUNCT
ejpam-3478	372	4	i	i	NOUN
ejpam-3478	372	5	)	)	PUNCT
ejpam-3478	372	6	0	0	PUNCT
ejpam-3478	373	1	=	=	SYM
ejpam-3478	373	2	1	1	NUM
ejpam-3478	373	3	2	2	NUM
ejpam-3478	373	4	σ2w2	σ2w2	X
ejpam-3478	373	5	0jiww	0jiww	PUNCT
ejpam-3478	373	6	+	+	CCONJ
ejpam-3478	373	7	qσρu0w0jilw	qσρu0w0jilw	PROPN
ejpam-3478	373	8	+	+	CCONJ
ejpam-3478	373	9	1	1	NUM
ejpam-3478	373	10	2	2	NUM
ejpam-3478	373	11	q2u20jill	q2u20jill	NOUN
ejpam-3478	373	12	+	+	CCONJ
ejpam-3478	373	13	cu0jil	cu0jil	NOUN
ejpam-3478	373	14	+	+	CCONJ
ejpam-3478	373	15	(	(	PUNCT
ejpam-3478	373	16	α−	α−	ADP
ejpam-3478	373	17	ra)w0jiw	ra)w0jiw	PROPN
ejpam-3478	373	18	+	+	CCONJ
ejpam-3478	373	19	jit	jit	PROPN
ejpam-3478	373	20	+	+	CCONJ
ejpam-3478	373	21	other	other	ADJ
ejpam-3478	373	22	terms	term	NOUN
ejpam-3478	373	23	(	(	PUNCT
ejpam-3478	373	24	involving	involve	VERB
ejpam-3478	373	25	ji−1	ji−1	PROPN
ejpam-3478	373	26	,	,	PUNCT
ejpam-3478	373	27	etc	etc	X
ejpam-3478	373	28	.	.	X
ejpam-3478	373	29	)	)	PUNCT
ejpam-3478	373	30	.	.	PUNCT
ejpam-3478	374	1	so	so	ADV
ejpam-3478	374	2	write	write	VERB
ejpam-3478	374	3	l	l	PROPN
ejpam-3478	374	4	(	(	PUNCT
ejpam-3478	374	5	ji	ji	NOUN
ejpam-3478	374	6	)	)	PUNCT
ejpam-3478	374	7	=	=	SYM
ejpam-3478	375	1	(	(	PUNCT
ejpam-3478	375	2	1	1	NUM
ejpam-3478	375	3	2	2	NUM
ejpam-3478	375	4	σ2w2	σ2w2	SYM
ejpam-3478	375	5	0	0	NUM
ejpam-3478	375	6	∂2	∂2	NOUN
ejpam-3478	375	7	∂w	∂w	PROPN
ejpam-3478	375	8	2	2	NUM
ejpam-3478	375	9	+	+	CCONJ
ejpam-3478	375	10	qσρu0w0	qσρu0w0	PROPN
ejpam-3478	375	11	∂2	∂2	PROPN
ejpam-3478	375	12	∂l∂w	∂l∂w	NOUN
ejpam-3478	375	13	+	+	CCONJ
ejpam-3478	375	14	1	1	NUM
ejpam-3478	375	15	2	2	NUM
ejpam-3478	375	16	q2u0	q2u0	NOUN
ejpam-3478	375	17	∂2	∂2	NOUN
ejpam-3478	375	18	∂l2	∂l2	PROPN
ejpam-3478	375	19	+	+	NOUN
ejpam-3478	375	20	cu0	cu0	NOUN
ejpam-3478	375	21	∂	∂	NOUN
ejpam-3478	375	22	∂l	∂l	NOUN
ejpam-3478	376	1	+	+	CCONJ
ejpam-3478	376	2	(	(	PUNCT
ejpam-3478	376	3	α−	α−	ADP
ejpam-3478	376	4	ra)w0	ra)w0	PROPN
ejpam-3478	376	5	∂	∂	NOUN
ejpam-3478	377	1	∂w	∂w	PROPN
ejpam-3478	378	1	+	+	CCONJ
ejpam-3478	378	2	∂	∂	NOUN
ejpam-3478	378	3	∂t	∂t	PROPN
ejpam-3478	378	4	)	)	PUNCT
ejpam-3478	378	5	ji	ji	PROPN
ejpam-3478	379	1	and	and	CCONJ
ejpam-3478	379	2	note	note	VERB
ejpam-3478	379	3	if	if	SCONJ
ejpam-3478	379	4	rl	rl	VERB
ejpam-3478	379	5	=	=	SYM
ejpam-3478	379	6	ra	ra	PROPN
ejpam-3478	380	1	+	+	CCONJ
ejpam-3478	380	2	ε	ε	PROPN
ejpam-3478	380	3	then	then	ADV
ejpam-3478	380	4	raw	raw	ADJ
ejpam-3478	380	5	∂j	∂j	PROPN
ejpam-3478	381	1	∂w	∂w	PROPN
ejpam-3478	381	2	+	+	NUM
ejpam-3478	381	3	rll	rll	NOUN
ejpam-3478	381	4	∂j	∂j	NOUN
ejpam-3478	382	1	∂l	∂l	PROPN
ejpam-3478	382	2	=	=	SYM
ejpam-3478	382	3	ra	ra	PROPN
ejpam-3478	382	4	(	(	PUNCT
ejpam-3478	382	5	w	w	PROPN
ejpam-3478	382	6	∂j	∂j	PROPN
ejpam-3478	382	7	∂w	∂w	PROPN
ejpam-3478	383	1	+	+	NUM
ejpam-3478	383	2	l	l	NOUN
ejpam-3478	383	3	∂j	∂j	NOUN
ejpam-3478	383	4	∂l	∂l	NOUN
ejpam-3478	383	5	)	)	PUNCT
ejpam-3478	384	1	+	+	CCONJ
ejpam-3478	384	2	εl	εl	ADP
ejpam-3478	384	3	∂j	∂j	NOUN
ejpam-3478	384	4	∂l	∂l	PROPN
ejpam-3478	384	5	.	.	PUNCT
ejpam-3478	385	1	we	we	PRON
ejpam-3478	385	2	have	have	VERB
ejpam-3478	385	3	u	u	NOUN
ejpam-3478	385	4	(	(	PUNCT
ejpam-3478	385	5	e	e	NOUN
ejpam-3478	385	6	)	)	PUNCT
ejpam-3478	385	7	=	=	PUNCT
ejpam-3478	385	8	eγ	eγ	ADP
ejpam-3478	385	9	γ	γ	X
ejpam-3478	385	10	=	=	PUNCT
ejpam-3478	385	11	(	(	PUNCT
ejpam-3478	385	12	w−l)γ	w−l)γ	PROPN
ejpam-3478	385	13	γ	γ	X
ejpam-3478	385	14	with	with	ADP
ejpam-3478	385	15	j0	j0	PROPN
ejpam-3478	385	16	=	=	SYM
ejpam-3478	385	17	a	a	DET
ejpam-3478	385	18	(	(	PUNCT
ejpam-3478	385	19	t	t	NOUN
ejpam-3478	385	20	)	)	PUNCT
ejpam-3478	385	21	(	(	PUNCT
ejpam-3478	385	22	w−l)γ	w−l)γ	NOUN
ejpam-3478	385	23	γ	γ	X
ejpam-3478	385	24	w	w	VERB
ejpam-3478	385	25	∂j0	∂j0	PROPN
ejpam-3478	385	26	∂w	∂w	PROPN
ejpam-3478	386	1	+	+	NUM
ejpam-3478	386	2	l	l	NOUN
ejpam-3478	386	3	∂j0	∂j0	ADV
ejpam-3478	386	4	∂l	∂l	VERB
ejpam-3478	386	5	=	=	PUNCT
ejpam-3478	386	6	a	a	DET
ejpam-3478	386	7	(	(	PUNCT
ejpam-3478	386	8	t	t	NOUN
ejpam-3478	386	9	)	)	PUNCT
ejpam-3478	386	10	(	(	PUNCT
ejpam-3478	386	11	w	w	NOUN
ejpam-3478	386	12	−	−	PROPN
ejpam-3478	386	13	l)γ	l)γ	NOUN
ejpam-3478	386	14	appendix	appendix	VERB
ejpam-3478	386	15	1335	1335	NUM
ejpam-3478	386	16	and	and	CCONJ
ejpam-3478	386	17	raw	raw	ADJ
ejpam-3478	386	18	∂j	∂j	NOUN
ejpam-3478	387	1	∂w	∂w	PROPN
ejpam-3478	387	2	+	+	NUM
ejpam-3478	387	3	rll	rll	NOUN
ejpam-3478	387	4	∂j	∂j	PROPN
ejpam-3478	387	5	∂w	∂w	PROPN
ejpam-3478	387	6	=	=	SYM
ejpam-3478	387	7	ral1	ral1	PROPN
ejpam-3478	387	8	(	(	PUNCT
ejpam-3478	387	9	j	j	NOUN
ejpam-3478	387	10	)	)	PUNCT
ejpam-3478	388	1	+	+	CCONJ
ejpam-3478	388	2	εl	εl	ADP
ejpam-3478	388	3	∂j	∂j	NOUN
ejpam-3478	388	4	∂l	∂l	PROPN
ejpam-3478	388	5	,	,	PUNCT
ejpam-3478	388	6	where	where	SCONJ
ejpam-3478	388	7	l1	l1	PROPN
ejpam-3478	388	8	(	(	PUNCT
ejpam-3478	388	9	j	j	PROPN
ejpam-3478	388	10	)	)	PUNCT
ejpam-3478	388	11	≡	≡	PROPN
ejpam-3478	388	12	(	(	PUNCT
ejpam-3478	388	13	w	w	NOUN
ejpam-3478	388	14	∂	∂	NOUN
ejpam-3478	389	1	∂w	∂w	PROPN
ejpam-3478	389	2	+	+	NUM
ejpam-3478	389	3	l	l	NOUN
ejpam-3478	389	4	∂	∂	X
ejpam-3478	389	5	∂l	∂l	NOUN
ejpam-3478	389	6	)	)	PUNCT
ejpam-3478	390	1	j	j	PROPN
ejpam-3478	391	1	so	so	ADV
ejpam-3478	391	2	from	from	ADP
ejpam-3478	391	3	our	our	PRON
ejpam-3478	391	4	equation	equation	NOUN
ejpam-3478	391	5	we	we	PRON
ejpam-3478	391	6	have	have	VERB
ejpam-3478	391	7	o	o	NOUN
ejpam-3478	391	8	(	(	PUNCT
ejpam-3478	391	9	1	1	NUM
ejpam-3478	391	10	)	)	PUNCT
ejpam-3478	391	11	u	u	NOUN
ejpam-3478	391	12	(	(	PUNCT
ejpam-3478	391	13	e	e	NOUN
ejpam-3478	391	14	)	)	PUNCT
ejpam-3478	392	1	+	+	NUM
ejpam-3478	392	2	l	l	NOUN
ejpam-3478	392	3	(	(	PUNCT
ejpam-3478	392	4	j0	j0	PROPN
ejpam-3478	392	5	)	)	PUNCT
ejpam-3478	392	6	+	+	CCONJ
ejpam-3478	392	7	ral1	ral1	PROPN
ejpam-3478	392	8	(	(	PUNCT
ejpam-3478	392	9	j0	j0	PROPN
ejpam-3478	392	10	)	)	PUNCT
ejpam-3478	392	11	=	=	SYM
ejpam-3478	392	12	0	0	NUM
ejpam-3478	392	13	and	and	CCONJ
ejpam-3478	392	14	o	o	PROPN
ejpam-3478	392	15	(	(	PUNCT
ejpam-3478	392	16	ε	ε	PROPN
ejpam-3478	392	17	)	)	PUNCT
ejpam-3478	392	18	0	0	NUM
ejpam-3478	393	1	=	=	SYM
ejpam-3478	393	2	l	l	NOUN
ejpam-3478	393	3	(	(	PUNCT
ejpam-3478	393	4	j1	j1	PROPN
ejpam-3478	393	5	)	)	PUNCT
ejpam-3478	393	6	+	+	CCONJ
ejpam-3478	393	7	ral1	ral1	ADJ
ejpam-3478	393	8	(	(	PUNCT
ejpam-3478	393	9	j1	j1	PROPN
ejpam-3478	393	10	)	)	PUNCT
ejpam-3478	394	1	+	+	NUM
ejpam-3478	394	2	l	l	NOUN
ejpam-3478	394	3	∂j0	∂j0	ADV
ejpam-3478	394	4	∂l	∂l	VERB
ejpam-3478	394	5	+	+	CCONJ
ejpam-3478	394	6	cu1j0l	cu1j0l	PROPN
ejpam-3478	394	7	+	+	CCONJ
ejpam-3478	394	8	(	(	PUNCT
ejpam-3478	394	9	α−	α−	ADP
ejpam-3478	394	10	ra)w1j0w	ra)w1j0w	NOUN
ejpam-3478	394	11	+	+	NOUN
ejpam-3478	394	12	1	1	NUM
ejpam-3478	394	13	2	2	NUM
ejpam-3478	394	14	σ2	σ2	PROPN
ejpam-3478	394	15	(	(	PUNCT
ejpam-3478	394	16	2w1w0	2w1w0	NUM
ejpam-3478	394	17	)	)	PUNCT
ejpam-3478	394	18	j0ww	j0ww	PUNCT
ejpam-3478	395	1	+	+	PUNCT
ejpam-3478	395	2	qσρ	qσρ	NOUN
ejpam-3478	395	3	(	(	PUNCT
ejpam-3478	395	4	u0w1	u0w1	NOUN
ejpam-3478	395	5	+	+	X
ejpam-3478	395	6	u1w0	u1w0	NOUN
ejpam-3478	395	7	)	)	PUNCT
ejpam-3478	395	8	j0lw	j0lw	NOUN
ejpam-3478	396	1	+	+	CCONJ
ejpam-3478	396	2	1	1	NUM
ejpam-3478	396	3	2	2	NUM
ejpam-3478	396	4	q2	q2	NOUN
ejpam-3478	396	5	(	(	PUNCT
ejpam-3478	396	6	2u1u0	2u1u0	NUM
ejpam-3478	396	7	)	)	PUNCT
ejpam-3478	396	8	j0ll	j0ll	NOUN
ejpam-3478	396	9	call	call	VERB
ejpam-3478	396	10	this	this	DET
ejpam-3478	396	11	lij	lij	NOUN
ejpam-3478	396	12	(	(	PUNCT
ejpam-3478	396	13	j0	j0	PROPN
ejpam-3478	396	14	)	)	PUNCT
ejpam-3478	396	15	,	,	PUNCT
ejpam-3478	397	1	therefore	therefore	ADV
ejpam-3478	397	2	,	,	PUNCT
ejpam-3478	397	3	0	0	X
ejpam-3478	397	4	=	=	SYM
ejpam-3478	397	5	l10	l10	PROPN
ejpam-3478	397	6	(	(	PUNCT
ejpam-3478	397	7	j0	j0	PROPN
ejpam-3478	397	8	)	)	PUNCT
ejpam-3478	397	9	o	o	NOUN
ejpam-3478	398	1	(	(	PUNCT
ejpam-3478	398	2	ε2	ε2	ADJ
ejpam-3478	398	3	)	)	PUNCT
ejpam-3478	398	4	0	0	NUM
ejpam-3478	399	1	=	=	SYM
ejpam-3478	399	2	l	l	NOUN
ejpam-3478	399	3	(	(	PUNCT
ejpam-3478	399	4	j2	j2	PROPN
ejpam-3478	399	5	)	)	PUNCT
ejpam-3478	399	6	+	+	CCONJ
ejpam-3478	399	7	ral1	ral1	PROPN
ejpam-3478	399	8	(	(	PUNCT
ejpam-3478	399	9	j2	j2	PROPN
ejpam-3478	399	10	)	)	PUNCT
ejpam-3478	400	1	+	+	NUM
ejpam-3478	400	2	l	l	NOUN
ejpam-3478	400	3	∂j1	∂j1	NOUN
ejpam-3478	400	4	∂l	∂l	NOUN
ejpam-3478	400	5	+	+	CCONJ
ejpam-3478	400	6	ral20	ral20	PROPN
ejpam-3478	400	7	(	(	PUNCT
ejpam-3478	400	8	j0	j0	PROPN
ejpam-3478	400	9	)	)	PUNCT
ejpam-3478	400	10	+	+	CCONJ
ejpam-3478	400	11	l10	l10	PROPN
ejpam-3478	400	12	(	(	PUNCT
ejpam-3478	400	13	j1	j1	PROPN
ejpam-3478	400	14	)	)	PUNCT
ejpam-3478	400	15	,	,	PUNCT
ejpam-3478	400	16	where	where	SCONJ
ejpam-3478	400	17	l20	l20	PROPN
ejpam-3478	400	18	(	(	PUNCT
ejpam-3478	400	19	j0	j0	PROPN
ejpam-3478	400	20	)	)	PUNCT
ejpam-3478	400	21	=	=	SYM
ejpam-3478	400	22	cu2j0l	cu2j0l	PROPN
ejpam-3478	400	23	+	+	CCONJ
ejpam-3478	400	24	(	(	PUNCT
ejpam-3478	400	25	α−	α−	ADP
ejpam-3478	400	26	ra)w2j0w	ra)w2j0w	PROPN
ejpam-3478	400	27	+	+	CCONJ
ejpam-3478	400	28	σ2	σ2	PROPN
ejpam-3478	400	29	(	(	PUNCT
ejpam-3478	400	30	w2w0	w2w0	PROPN
ejpam-3478	400	31	+	+	CCONJ
ejpam-3478	400	32	w2	w2	NOUN
ejpam-3478	400	33	1	1	NUM
ejpam-3478	400	34	2	2	NUM
ejpam-3478	400	35	)	)	PUNCT
ejpam-3478	400	36	j0ww	j0ww	PUNCT
ejpam-3478	401	1	+	+	PUNCT
ejpam-3478	401	2	qσρ	qσρ	NOUN
ejpam-3478	401	3	(	(	PUNCT
ejpam-3478	401	4	u0w2	u0w2	PROPN
ejpam-3478	401	5	+	+	CCONJ
ejpam-3478	401	6	u2w0	u2w0	PROPN
ejpam-3478	401	7	+	+	CCONJ
ejpam-3478	401	8	u1w1	u1w1	X
ejpam-3478	401	9	)	)	PUNCT
ejpam-3478	401	10	j0lw	j0lw	NOUN
ejpam-3478	402	1	+	+	CCONJ
ejpam-3478	402	2	q2	q2	NOUN
ejpam-3478	402	3	(	(	PUNCT
ejpam-3478	402	4	u2u0	u2u0	PROPN
ejpam-3478	402	5	+	+	CCONJ
ejpam-3478	402	6	u21	u21	PROPN
ejpam-3478	402	7	2	2	NUM
ejpam-3478	402	8	)	)	PUNCT
ejpam-3478	402	9	j0ll	j0ll	PROPN
ejpam-3478	402	10	and	and	CCONJ
ejpam-3478	402	11	l10	l10	PROPN
ejpam-3478	402	12	(	(	PUNCT
ejpam-3478	402	13	j0	j0	PROPN
ejpam-3478	402	14	)	)	PUNCT
ejpam-3478	402	15	=	=	SYM
ejpam-3478	402	16	cu1j0l	cu1j0l	PROPN
ejpam-3478	402	17	+	+	CCONJ
ejpam-3478	402	18	(	(	PUNCT
ejpam-3478	402	19	α−	α−	ADP
ejpam-3478	402	20	ra)w1j0w	ra)w1j0w	NOUN
ejpam-3478	402	21	+	+	PROPN
ejpam-3478	402	22	σ2w1w0j0ww	σ2w1w0j0ww	PROPN
ejpam-3478	402	23	+	+	CCONJ
ejpam-3478	402	24	qσρ	qσρ	NOUN
ejpam-3478	402	25	(	(	PUNCT
ejpam-3478	402	26	u0w1	u0w1	NOUN
ejpam-3478	402	27	+	+	X
ejpam-3478	402	28	u1w0	u1w0	NOUN
ejpam-3478	402	29	)	)	PUNCT
ejpam-3478	402	30	j0lw	j0lw	NOUN
ejpam-3478	402	31	+	+	CCONJ
ejpam-3478	402	32	q2u1u0j0ll	q2u1u0j0ll	VERB
ejpam-3478	402	33	.	.	PUNCT
ejpam-3478	402	34	with	with	ADP
ejpam-3478	402	35	the	the	DET
ejpam-3478	402	36	choice	choice	NOUN
ejpam-3478	402	37	j0	j0	PROPN
ejpam-3478	402	38	=	=	PROPN
ejpam-3478	402	39	a	a	DET
ejpam-3478	402	40	(	(	PUNCT
ejpam-3478	402	41	t	t	NOUN
ejpam-3478	402	42	)	)	PUNCT
ejpam-3478	402	43	(	(	PUNCT
ejpam-3478	402	44	w	w	NOUN
ejpam-3478	402	45	−	−	PROPN
ejpam-3478	402	46	l)γ	l)γ	NOUN
ejpam-3478	402	47	γ	γ	X
ejpam-3478	402	48	,	,	PUNCT
ejpam-3478	402	49	appendix	appendix	VERB
ejpam-3478	402	50	1336	1336	NUM
ejpam-3478	402	51	the	the	DET
ejpam-3478	402	52	o	o	X
ejpam-3478	402	53	(	(	PUNCT
ejpam-3478	402	54	1	1	NUM
ejpam-3478	402	55	)	)	PUNCT
ejpam-3478	402	56	equation	equation	NOUN
ejpam-3478	402	57	reduces	reduce	VERB
ejpam-3478	402	58	to	to	ADP
ejpam-3478	402	59	the	the	DET
ejpam-3478	402	60	equation	equation	NOUN
ejpam-3478	402	61	we	we	PRON
ejpam-3478	402	62	had	have	VERB
ejpam-3478	402	63	previously	previously	ADV
ejpam-3478	402	64	,	,	PUNCT
ejpam-3478	402	65	which	which	PRON
ejpam-3478	402	66	has	have	VERB
ejpam-3478	402	67	the	the	DET
ejpam-3478	402	68	form	form	NOUN
ejpam-3478	402	69	ȧ	ȧ	PROPN
ejpam-3478	402	70	(	(	PUNCT
ejpam-3478	402	71	t	t	PROPN
ejpam-3478	402	72	)	)	PUNCT
ejpam-3478	402	73	γ	γ	NOUN
ejpam-3478	402	74	+	+	NOUN
ejpam-3478	402	75	1	1	NUM
ejpam-3478	402	76	γ	γ	X
ejpam-3478	402	77	+	+	PROPN
ejpam-3478	402	78	da	da	NOUN
ejpam-3478	402	79	=	=	SYM
ejpam-3478	402	80	0	0	NUM
ejpam-3478	402	81	,	,	PUNCT
ejpam-3478	402	82	where	where	SCONJ
ejpam-3478	402	83	d	d	NOUN
ejpam-3478	402	84	is	be	AUX
ejpam-3478	402	85	constant	constant	ADJ
ejpam-3478	402	86	and	and	CCONJ
ejpam-3478	402	87	equals	equal	VERB
ejpam-3478	402	88	κ	κ	PROPN
ejpam-3478	402	89	γ	γ	NOUN
ejpam-3478	402	90	.	.	PUNCT
ejpam-3478	403	1	thus	thus	ADV
ejpam-3478	403	2	a	a	DET
ejpam-3478	403	3	(	(	PUNCT
ejpam-3478	403	4	t	t	NOUN
ejpam-3478	403	5	)	)	PUNCT
ejpam-3478	403	6	=	=	PUNCT
ejpam-3478	404	1	−	−	PROPN
ejpam-3478	404	2	1	1	NUM
ejpam-3478	404	3	γd	γd	ADP
ejpam-3478	404	4	+	+	NUM
ejpam-3478	404	5	1	1	NUM
ejpam-3478	404	6	γd	γd	ADV
ejpam-3478	404	7	e(−κ(t−t	e(−κ(t−t	ADV
ejpam-3478	404	8	)	)	PUNCT
ejpam-3478	404	9	)	)	PUNCT
ejpam-3478	405	1	with	with	ADP
ejpam-3478	405	2	a	a	DET
ejpam-3478	405	3	(	(	PUNCT
ejpam-3478	405	4	t	t	NOUN
ejpam-3478	405	5	)	)	PUNCT
ejpam-3478	405	6	=	=	PUNCT
ejpam-3478	406	1	0	0	X
ejpam-3478	406	2	.	.	PUNCT
ejpam-3478	407	1	from	from	ADP
ejpam-3478	407	2	the	the	DET
ejpam-3478	407	3	o	o	PROPN
ejpam-3478	407	4	(	(	PUNCT
ejpam-3478	407	5	1	1	NUM
ejpam-3478	407	6	)	)	PUNCT
ejpam-3478	407	7	equations	equation	NOUN
ejpam-3478	407	8	for	for	ADP
ejpam-3478	407	9	w0	w0	PROPN
ejpam-3478	407	10	and	and	CCONJ
ejpam-3478	407	11	u0	u0	ADJ
ejpam-3478	407	12	we	we	PRON
ejpam-3478	407	13	find	find	VERB
ejpam-3478	407	14	that	that	SCONJ
ejpam-3478	407	15	w0	w0	PROPN
ejpam-3478	407	16	and	and	CCONJ
ejpam-3478	407	17	u0	u0	PROPN
ejpam-3478	407	18	are	be	AUX
ejpam-3478	407	19	both	both	PRON
ejpam-3478	407	20	proportional	proportional	ADJ
ejpam-3478	407	21	to	to	ADP
ejpam-3478	407	22	(	(	PUNCT
ejpam-3478	407	23	w	w	PROPN
ejpam-3478	407	24	−	−	PROPN
ejpam-3478	407	25	l	l	NOUN
ejpam-3478	407	26	)	)	PUNCT
ejpam-3478	407	27	.	.	PUNCT
ejpam-3478	408	1	when	when	SCONJ
ejpam-3478	408	2	we	we	PRON
ejpam-3478	408	3	come	come	VERB
ejpam-3478	408	4	to	to	ADP
ejpam-3478	408	5	the	the	DET
ejpam-3478	408	6	o	o	NOUN
ejpam-3478	408	7	(	(	PUNCT
ejpam-3478	408	8	ε	ε	PROPN
ejpam-3478	408	9	)	)	PUNCT
ejpam-3478	408	10	equations	equation	NOUN
ejpam-3478	408	11	,	,	PUNCT
ejpam-3478	408	12	we	we	PRON
ejpam-3478	408	13	write	write	VERB
ejpam-3478	408	14	j1	j1	PROPN
ejpam-3478	408	15	=	=	SYM
ejpam-3478	408	16	(	(	PUNCT
ejpam-3478	408	17	bl+b1w	bl+b1w	PROPN
ejpam-3478	408	18	)	)	PUNCT
ejpam-3478	409	1	(	(	PUNCT
ejpam-3478	409	2	w	w	NOUN
ejpam-3478	409	3	−	−	PROPN
ejpam-3478	409	4	l)γ−1	l)γ−1	VERB
ejpam-3478	409	5	and	and	CCONJ
ejpam-3478	409	6	note	note	VERB
ejpam-3478	409	7	that	that	SCONJ
ejpam-3478	409	8	l10	l10	PROPN
ejpam-3478	409	9	(	(	PUNCT
ejpam-3478	409	10	j0	j0	PROPN
ejpam-3478	409	11	)	)	PUNCT
ejpam-3478	409	12	will	will	AUX
ejpam-3478	409	13	have	have	VERB
ejpam-3478	409	14	terms	term	NOUN
ejpam-3478	409	15	like	like	ADP
ejpam-3478	409	16	(	(	PUNCT
ejpam-3478	409	17	w	w	NOUN
ejpam-3478	409	18	−	−	PROPN
ejpam-3478	409	19	l)γ−1	l)γ−1	NOUN
ejpam-3478	409	20	multiplying	multiply	VERB
ejpam-3478	409	21	a	a	DET
ejpam-3478	409	22	linear	linear	ADJ
ejpam-3478	409	23	combination	combination	NOUN
ejpam-3478	409	24	of	of	ADP
ejpam-3478	409	25	terms	term	NOUN
ejpam-3478	409	26	involving	involve	VERB
ejpam-3478	409	27	u1	u1	NOUN
ejpam-3478	409	28	and	and	CCONJ
ejpam-3478	409	29	w1	w1	NOUN
ejpam-3478	409	30	.	.	PUNCT
ejpam-3478	410	1	the	the	DET
ejpam-3478	410	2	term	term	NOUN
ejpam-3478	410	3	l∂j0∂l	l∂j0∂l	PRON
ejpam-3478	410	4	is	be	AUX
ejpam-3478	410	5	again	again	ADV
ejpam-3478	410	6	of	of	ADP
ejpam-3478	410	7	the	the	DET
ejpam-3478	410	8	form	form	NOUN
ejpam-3478	410	9	(	(	PUNCT
ejpam-3478	410	10	w	w	NOUN
ejpam-3478	410	11	−	−	PROPN
ejpam-3478	410	12	l)γ−1	l)γ−1	PROPN
ejpam-3478	410	13	(	(	PUNCT
ejpam-3478	410	14	l	l	NOUN
ejpam-3478	410	15	)	)	PUNCT
ejpam-3478	410	16	.	.	PUNCT
ejpam-3478	411	1	then	then	ADV
ejpam-3478	411	2	l1	l1	PROPN
ejpam-3478	411	3	(	(	PUNCT
ejpam-3478	411	4	j1	j1	PROPN
ejpam-3478	411	5	)	)	PUNCT
ejpam-3478	411	6	has	have	VERB
ejpam-3478	411	7	this	this	DET
ejpam-3478	411	8	form	form	NOUN
ejpam-3478	411	9	also	also	ADV
ejpam-3478	411	10	on	on	ADP
ejpam-3478	411	11	account	account	NOUN
ejpam-3478	411	12	of	of	ADP
ejpam-3478	411	13	(	(	PUNCT
ejpam-3478	411	14	w	w	PROPN
ejpam-3478	411	15	∂	∂	NOUN
ejpam-3478	411	16	∂w	∂w	PROPN
ejpam-3478	411	17	+	+	NUM
ejpam-3478	411	18	l	l	NOUN
ejpam-3478	411	19	∂	∂	X
ejpam-3478	411	20	∂l	∂l	NOUN
ejpam-3478	411	21	)	)	PUNCT
ejpam-3478	412	1	(	(	PUNCT
ejpam-3478	412	2	w	w	NOUN
ejpam-3478	412	3	−	−	NOUN
ejpam-3478	412	4	l)γ−1	l)γ−1	PROPN
ejpam-3478	412	5	=	=	PUNCT
ejpam-3478	412	6	(	(	PUNCT
ejpam-3478	412	7	γ	γ	X
ejpam-3478	412	8	−	−	PROPN
ejpam-3478	412	9	1	1	NUM
ejpam-3478	412	10	)	)	PUNCT
ejpam-3478	412	11	(	(	PUNCT
ejpam-3478	412	12	w	w	NOUN
ejpam-3478	412	13	−	−	PROPN
ejpam-3478	412	14	l)γ−1	l)γ−1	PROPN
ejpam-3478	412	15	,	,	PUNCT
ejpam-3478	412	16	l	l	PROPN
ejpam-3478	412	17	(	(	PUNCT
ejpam-3478	412	18	j1	j1	PROPN
ejpam-3478	412	19	)	)	PUNCT
ejpam-3478	412	20	will	will	AUX
ejpam-3478	412	21	also	also	ADV
ejpam-3478	412	22	have	have	VERB
ejpam-3478	412	23	this	this	DET
ejpam-3478	412	24	form	form	NOUN
ejpam-3478	412	25	.	.	PUNCT
ejpam-3478	413	1	so	so	ADV
ejpam-3478	413	2	if	if	SCONJ
ejpam-3478	413	3	u1	u1	NOUN
ejpam-3478	413	4	and	and	CCONJ
ejpam-3478	413	5	w1	w1	NOUN
ejpam-3478	413	6	turn	turn	VERB
ejpam-3478	413	7	out	out	ADP
ejpam-3478	413	8	to	to	PART
ejpam-3478	413	9	be	be	AUX
ejpam-3478	413	10	proportional	proportional	ADJ
ejpam-3478	413	11	to	to	ADP
ejpam-3478	413	12	a	a	DET
ejpam-3478	413	13	linear	linear	ADJ
ejpam-3478	413	14	combination	combination	NOUN
ejpam-3478	413	15	of	of	ADP
ejpam-3478	413	16	l	l	NOUN
ejpam-3478	413	17	and	and	CCONJ
ejpam-3478	413	18	w	w	NOUN
ejpam-3478	413	19	we	we	PRON
ejpam-3478	413	20	get	get	VERB
ejpam-3478	413	21	the	the	DET
ejpam-3478	413	22	coupled	couple	VERB
ejpam-3478	413	23	ode’1	ode’1	NOUN
ejpam-3478	413	24	for	for	ADP
ejpam-3478	413	25	b	b	PROPN
ejpam-3478	413	26	and	and	CCONJ
ejpam-3478	413	27	b1	b1	NOUN
ejpam-3478	413	28	by	by	ADP
ejpam-3478	413	29	equating	equate	VERB
ejpam-3478	413	30	to	to	ADP
ejpam-3478	413	31	zero	zero	NUM
ejpam-3478	413	32	coefficients	coefficient	NOUN
ejpam-3478	413	33	of	of	ADP
ejpam-3478	413	34	l	l	NOUN
ejpam-3478	413	35	and	and	CCONJ
ejpam-3478	413	36	w	w	NOUN
ejpam-3478	413	37	.	.	PUNCT
ejpam-3478	414	1	this	this	DET
ejpam-3478	414	2	behaviour	behaviour	NOUN
ejpam-3478	414	3	of	of	ADP
ejpam-3478	414	4	u1	u1	NOUN
ejpam-3478	414	5	and	and	CCONJ
ejpam-3478	414	6	w1	w1	NOUN
ejpam-3478	414	7	follows	follow	VERB
ejpam-3478	414	8	from	from	ADP
ejpam-3478	414	9	the	the	DET
ejpam-3478	414	10	o	o	PROPN
ejpam-3478	414	11	(	(	PUNCT
ejpam-3478	414	12	ε	ε	PROPN
ejpam-3478	414	13	)	)	PUNCT
ejpam-3478	414	14	equations	equation	NOUN
ejpam-3478	414	15	of	of	ADP
ejpam-3478	414	16	(	(	PUNCT
ejpam-3478	414	17	a.1	a.1	NOUN
ejpam-3478	414	18	)	)	PUNCT
ejpam-3478	414	19	and	and	CCONJ
ejpam-3478	414	20	(	(	PUNCT
ejpam-3478	414	21	a.2	a.2	NOUN
ejpam-3478	414	22	)	)	PUNCT
ejpam-3478	414	23	.	.	PUNCT
ejpam-3478	415	1	for	for	ADP
ejpam-3478	415	2	the	the	DET
ejpam-3478	415	3	o	o	PROPN
ejpam-3478	415	4	(	(	PUNCT
ejpam-3478	415	5	ε	ε	PROPN
ejpam-3478	415	6	)	)	PUNCT
ejpam-3478	415	7	equations	equation	NOUN
ejpam-3478	415	8	,	,	PUNCT
ejpam-3478	415	9	note	note	VERB
ejpam-3478	415	10	that	that	SCONJ
ejpam-3478	415	11	l10	l10	PROPN
ejpam-3478	415	12	(	(	PUNCT
ejpam-3478	415	13	j1	j1	PROPN
ejpam-3478	415	14	)	)	PUNCT
ejpam-3478	415	15	will	will	AUX
ejpam-3478	415	16	be	be	AUX
ejpam-3478	415	17	of	of	ADP
ejpam-3478	415	18	the	the	DET
ejpam-3478	415	19	form	form	NOUN
ejpam-3478	415	20	(	(	PUNCT
ejpam-3478	415	21	w	w	NOUN
ejpam-3478	415	22	−	−	PROPN
ejpam-3478	415	23	l)γ−2	l)γ−2	NOUN
ejpam-3478	415	24	.	.	PUNCT
ejpam-3478	416	1	similarly	similarly	ADV
ejpam-3478	416	2	l∂j1∂l	l∂j1∂l	PUNCT
ejpam-3478	416	3	has	have	VERB
ejpam-3478	416	4	the	the	DET
ejpam-3478	416	5	same	same	ADJ
ejpam-3478	416	6	form	form	NOUN
ejpam-3478	416	7	.	.	PUNCT
ejpam-3478	417	1	l20	l20	PROPN
ejpam-3478	417	2	(	(	PUNCT
ejpam-3478	417	3	j0	j0	PROPN
ejpam-3478	417	4	)	)	PUNCT
ejpam-3478	417	5	has	have	VERB
ejpam-3478	417	6	the	the	DET
ejpam-3478	417	7	form	form	NOUN
ejpam-3478	417	8	u2	u2	NOUN
ejpam-3478	417	9	(	(	PUNCT
ejpam-3478	417	10	)	)	PUNCT
ejpam-3478	417	11	(	(	PUNCT
ejpam-3478	417	12	w	w	NOUN
ejpam-3478	417	13	−	−	PROPN
ejpam-3478	417	14	l)γ−1	l)γ−1	PROPN
ejpam-3478	417	15	+	+	NUM
ejpam-3478	417	16	w2	w2	NOUN
ejpam-3478	417	17	(	(	PUNCT
ejpam-3478	417	18	)	)	PUNCT
ejpam-3478	417	19	(	(	PUNCT
ejpam-3478	417	20	w	w	NOUN
ejpam-3478	417	21	−	−	PROPN
ejpam-3478	417	22	l)γ−1	l)γ−1	PROPN
ejpam-3478	417	23	and	and	CCONJ
ejpam-3478	417	24	the	the	DET
ejpam-3478	417	25	determined	determined	ADJ
ejpam-3478	417	26	terms	term	NOUN
ejpam-3478	417	27	w2	w2	NOUN
ejpam-3478	417	28	1	1	NUM
ejpam-3478	417	29	2	2	NUM
ejpam-3478	417	30	j0ww	j0ww	X
ejpam-3478	417	31	etc	etc	X
ejpam-3478	417	32	are	be	AUX
ejpam-3478	417	33	of	of	ADP
ejpam-3478	417	34	the	the	DET
ejpam-3478	417	35	quadratic×	quadratic×	PROPN
ejpam-3478	417	36	(	(	PUNCT
ejpam-3478	417	37	w	w	PROPN
ejpam-3478	417	38	−	−	PROPN
ejpam-3478	417	39	l)γ−2	l)γ−2	NOUN
ejpam-3478	417	40	.	.	PUNCT
ejpam-3478	418	1	if	if	SCONJ
ejpam-3478	418	2	we	we	PRON
ejpam-3478	418	3	assume	assume	VERB
ejpam-3478	418	4	j2	j2	PROPN
ejpam-3478	418	5	=	=	SYM
ejpam-3478	418	6	(	(	PUNCT
ejpam-3478	418	7	c1w	c1w	NOUN
ejpam-3478	418	8	2	2	NUM
ejpam-3478	418	9	+	+	CCONJ
ejpam-3478	418	10	c2lw	c2lw	X
ejpam-3478	418	11	+	+	CCONJ
ejpam-3478	418	12	c3l	c3l	X
ejpam-3478	418	13	2	2	NUM
ejpam-3478	418	14	)	)	PUNCT
ejpam-3478	418	15	(	(	PUNCT
ejpam-3478	418	16	w	w	NOUN
ejpam-3478	418	17	−	−	PROPN
ejpam-3478	418	18	l)γ−2	l)γ−2	NOUN
ejpam-3478	418	19	,	,	PUNCT
ejpam-3478	418	20	then	then	ADV
ejpam-3478	418	21	l	l	PROPN
ejpam-3478	418	22	(	(	PUNCT
ejpam-3478	418	23	j2	j2	PROPN
ejpam-3478	418	24	)	)	PUNCT
ejpam-3478	419	1	=	=	SYM
ejpam-3478	419	2	quadratic×	quadratic×	PROPN
ejpam-3478	419	3	(	(	PUNCT
ejpam-3478	419	4	w	w	NOUN
ejpam-3478	419	5	−	−	PROPN
ejpam-3478	419	6	l)γ−2	l)γ−2	NOUN
ejpam-3478	419	7	+	+	CCONJ
ejpam-3478	419	8	(	(	PUNCT
ejpam-3478	419	9	c	c	PROPN
ejpam-3478	419	10	′1w	′1w	ADJ
ejpam-3478	419	11	2	2	NUM
ejpam-3478	419	12	+	+	CCONJ
ejpam-3478	419	13	c	c	NOUN
ejpam-3478	419	14	′2lw	′2lw	ADV
ejpam-3478	419	15	+	+	CCONJ
ejpam-3478	419	16	c	c	X
ejpam-3478	419	17	′3l	′3l	X
ejpam-3478	419	18	2	2	NUM
ejpam-3478	419	19	)	)	PUNCT
ejpam-3478	419	20	(	(	PUNCT
ejpam-3478	419	21	w	w	NOUN
ejpam-3478	419	22	−	−	PROPN
ejpam-3478	419	23	l)γ−2	l)γ−2	NOUN
ejpam-3478	419	24	similarly	similarly	ADV
ejpam-3478	419	25	,	,	PUNCT
ejpam-3478	419	26	rl1	rl1	NOUN
ejpam-3478	419	27	(	(	PUNCT
ejpam-3478	419	28	j2	j2	PROPN
ejpam-3478	419	29	)	)	PUNCT
ejpam-3478	419	30	is	be	AUX
ejpam-3478	419	31	quadratic×	quadratic×	PROPN
ejpam-3478	419	32	(	(	PUNCT
ejpam-3478	419	33	w	w	PROPN
ejpam-3478	419	34	−	−	PROPN
ejpam-3478	419	35	l)γ−2	l)γ−2	NOUN
ejpam-3478	419	36	.	.	PUNCT
ejpam-3478	420	1	finally	finally	ADV
ejpam-3478	420	2	the	the	DET
ejpam-3478	420	3	o	o	X
ejpam-3478	420	4	(	(	PUNCT
ejpam-3478	420	5	ε2	ε2	ADJ
ejpam-3478	420	6	)	)	PUNCT
ejpam-3478	420	7	equation	equation	NOUN
ejpam-3478	420	8	gives	give	VERB
ejpam-3478	420	9	(	(	PUNCT
ejpam-3478	420	10	w	w	NOUN
ejpam-3478	420	11	−	−	PROPN
ejpam-3478	420	12	l)γ−2	l)γ−2	NOUN
ejpam-3478	420	13	(	(	PUNCT
ejpam-3478	420	14	·	·	PUNCT
ejpam-3478	420	15	·	·	PUNCT
ejpam-3478	420	16	·	·	PUNCT
ejpam-3478	420	17	·	·	PUNCT
ejpam-3478	420	18	·	·	PUNCT
ejpam-3478	420	19	·	·	PUNCT
ejpam-3478	420	20	·	·	PUNCT
ejpam-3478	420	21	·	·	PUNCT
ejpam-3478	420	22	·	·	PUNCT
ejpam-3478	420	23	·	·	PUNCT
ejpam-3478	420	24	·	·	PUNCT
ejpam-3478	420	25	·	·	PUNCT
ejpam-3478	420	26	)	)	PUNCT
ejpam-3478	421	1	(	(	PUNCT
ejpam-3478	421	2	w2	w2	NOUN
ejpam-3478	421	3	u2	u2	PROPN
ejpam-3478	421	4	)	)	PUNCT
ejpam-3478	421	5	=	=	SYM
ejpam-3478	421	6	(	(	PUNCT
ejpam-3478	421	7	quadratic	quadratic	NOUN
ejpam-3478	421	8	)	)	PUNCT
ejpam-3478	421	9	(	(	PUNCT
ejpam-3478	421	10	w	w	NOUN
ejpam-3478	421	11	−	−	NOUN
ejpam-3478	421	12	l)γ−3	l)γ−3	NOUN
ejpam-3478	421	13	.	.	PUNCT
ejpam-3478	422	1	this	this	PRON
ejpam-3478	422	2	gives	give	VERB
ejpam-3478	422	3	w2	w2	NOUN
ejpam-3478	422	4	and	and	CCONJ
ejpam-3478	422	5	u2	u2	NOUN
ejpam-3478	422	6	as	as	ADP
ejpam-3478	422	7	quadratic	quadratic	ADJ
ejpam-3478	422	8	(	(	PUNCT
ejpam-3478	422	9	w−l	w−l	NOUN
ejpam-3478	422	10	)	)	PUNCT
ejpam-3478	422	11	.	.	PUNCT
ejpam-3478	423	1	thus	thus	ADV
ejpam-3478	423	2	the	the	DET
ejpam-3478	423	3	term	term	NOUN
ejpam-3478	423	4	in	in	ADP
ejpam-3478	423	5	l20	l20	PROPN
ejpam-3478	423	6	(	(	PUNCT
ejpam-3478	423	7	j0	j0	PROPN
ejpam-3478	423	8	)	)	PUNCT
ejpam-3478	423	9	has	have	VERB
ejpam-3478	423	10	the	the	DET
ejpam-3478	423	11	form	form	NOUN
ejpam-3478	423	12	(	(	PUNCT
ejpam-3478	423	13	quadratic)(w	quadratic)(w	NOUN
ejpam-3478	423	14	−	−	PROPN
ejpam-3478	423	15	l)γ−2	l)γ−2	NOUN
ejpam-3478	423	16	.	.	PUNCT
ejpam-3478	424	1	finally	finally	ADV
ejpam-3478	424	2	equating	equate	VERB
ejpam-3478	424	3	coefficients	coefficient	NOUN
ejpam-3478	424	4	of	of	ADP
ejpam-3478	424	5	w	w	NOUN
ejpam-3478	424	6	2	2	NUM
ejpam-3478	424	7	,	,	PUNCT
ejpam-3478	424	8	lw	lw	NOUN
ejpam-3478	424	9	and	and	CCONJ
ejpam-3478	424	10	l2	l2	NOUN
ejpam-3478	424	11	gives	give	VERB
ejpam-3478	424	12	3	3	NUM
ejpam-3478	424	13	ode	ode	NOUN
ejpam-3478	424	14	for	for	ADP
ejpam-3478	424	15	c1	c1	PROPN
ejpam-3478	424	16	,	,	PUNCT
ejpam-3478	424	17	c2	c2	PROPN
ejpam-3478	424	18	and	and	CCONJ
ejpam-3478	424	19	c3	c3	PROPN
ejpam-3478	424	20	.	.	PUNCT