id	sid	tid	token	lemma	pos
ejpam-3347	1	1	european	european	PROPN
ejpam-3347	1	2	journal	journal	PROPN
ejpam-3347	1	3	of	of	ADP
ejpam-3347	1	4	pure	pure	ADJ
ejpam-3347	1	5	and	and	CCONJ
ejpam-3347	1	6	applied	apply	VERB
ejpam-3347	1	7	mathematics	mathematic	NOUN
ejpam-3347	1	8	vol	vol	NOUN
ejpam-3347	1	9	.	.	PROPN
ejpam-3347	2	1	12	12	NUM
ejpam-3347	2	2	,	,	PUNCT
ejpam-3347	2	3	no	no	INTJ
ejpam-3347	2	4	.	.	NOUN
ejpam-3347	2	5	1	1	NUM
ejpam-3347	2	6	,	,	PUNCT
ejpam-3347	2	7	2019	2019	NUM
ejpam-3347	2	8	,	,	PUNCT
ejpam-3347	2	9	194	194	NUM
ejpam-3347	2	10	-	-	SYM
ejpam-3347	2	11	207	207	NUM
ejpam-3347	2	12	issn	issn	PROPN
ejpam-3347	2	13	1307	1307	NUM
ejpam-3347	2	14	-	-	SYM
ejpam-3347	2	15	5543	5543	NUM
ejpam-3347	2	16	–	–	PUNCT
ejpam-3347	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3347	3	2	published	publish	VERB
ejpam-3347	3	3	by	by	ADP
ejpam-3347	3	4	new	new	PROPN
ejpam-3347	3	5	york	york	PROPN
ejpam-3347	3	6	business	business	PROPN
ejpam-3347	3	7	global	global	ADJ
ejpam-3347	3	8	value	value	NOUN
ejpam-3347	3	9	-	-	PUNCT
ejpam-3347	3	10	at	at	ADP
ejpam-3347	3	11	-	-	PUNCT
ejpam-3347	3	12	risk	risk	NOUN
ejpam-3347	3	13	modeling	modeling	NOUN
ejpam-3347	3	14	with	with	ADP
ejpam-3347	3	15	conditional	conditional	ADJ
ejpam-3347	3	16	copulas	copula	NOUN
ejpam-3347	3	17	in	in	ADP
ejpam-3347	3	18	euclidean	euclidean	ADJ
ejpam-3347	3	19	space	space	NOUN
ejpam-3347	3	20	framework	framework	NOUN
ejpam-3347	3	21	vini	vini	NOUN
ejpam-3347	3	22	yves	yve	NOUN
ejpam-3347	3	23	bernadin	bernadin	VERB
ejpam-3347	3	24	loyara1	loyara1	NOUN
ejpam-3347	3	25	,	,	PUNCT
ejpam-3347	3	26	diakarya	diakarya	NOUN
ejpam-3347	3	27	barro2,∗	barro2,∗	VERB
ejpam-3347	3	28	1	1	NUM
ejpam-3347	3	29	espk	espk	PROPN
ejpam-3347	3	30	,	,	PUNCT
ejpam-3347	3	31	bp	bp	PROPN
ejpam-3347	3	32	174	174	NUM
ejpam-3347	3	33	kaya	kaya	PROPN
ejpam-3347	3	34	,	,	PUNCT
ejpam-3347	3	35	burkina	burkina	PROPN
ejpam-3347	3	36	faso	faso	PROPN
ejpam-3347	3	37	2	2	NUM
ejpam-3347	3	38	ufr	ufr	PROPN
ejpam-3347	3	39	-	-	PUNCT
ejpam-3347	3	40	seg	seg	NOUN
ejpam-3347	3	41	,	,	PUNCT
ejpam-3347	3	42	u.o2	u.o2	ADJ
ejpam-3347	3	43	,	,	PUNCT
ejpam-3347	3	44	12	12	NUM
ejpam-3347	3	45	bp:417	bp:417	NUM
ejpam-3347	3	46	ouaga	ouaga	NOUN
ejpam-3347	3	47	12	12	NUM
ejpam-3347	3	48	,	,	PUNCT
ejpam-3347	3	49	burkina	burkina	PROPN
ejpam-3347	3	50	faso	faso	PROPN
ejpam-3347	3	51	abstract	abstract	PROPN
ejpam-3347	3	52	.	.	PUNCT
ejpam-3347	4	1	this	this	DET
ejpam-3347	4	2	paper	paper	NOUN
ejpam-3347	4	3	aims	aim	VERB
ejpam-3347	4	4	to	to	PART
ejpam-3347	4	5	establish	establish	VERB
ejpam-3347	4	6	an	an	DET
ejpam-3347	4	7	analytic	analytic	ADJ
ejpam-3347	4	8	relation	relation	NOUN
ejpam-3347	4	9	between	between	ADP
ejpam-3347	4	10	a	a	DET
ejpam-3347	4	11	time	time	NOUN
ejpam-3347	4	12	-	-	PUNCT
ejpam-3347	4	13	varying	vary	VERB
ejpam-3347	4	14	conditional	conditional	ADJ
ejpam-3347	4	15	copula	copula	NOUN
ejpam-3347	4	16	and	and	CCONJ
ejpam-3347	4	17	the	the	DET
ejpam-3347	4	18	value	value	NOUN
ejpam-3347	4	19	at	at	ADP
ejpam-3347	4	20	risk	risk	NOUN
ejpam-3347	4	21	modeled	model	VERB
ejpam-3347	4	22	by	by	ADP
ejpam-3347	4	23	the	the	DET
ejpam-3347	4	24	underlying	underlying	NOUN
ejpam-3347	4	25	.	.	PUNCT
ejpam-3347	5	1	specically	specically	ADV
ejpam-3347	5	2	,	,	PUNCT
ejpam-3347	5	3	under	under	ADP
ejpam-3347	5	4	the	the	DET
ejpam-3347	5	5	assumption	assumption	NOUN
ejpam-3347	5	6	that	that	SCONJ
ejpam-3347	5	7	the	the	DET
ejpam-3347	5	8	space	space	NOUN
ejpam-3347	5	9	is	be	AUX
ejpam-3347	5	10	euclidean	euclidean	ADJ
ejpam-3347	5	11	we	we	PRON
ejpam-3347	5	12	use	use	VERB
ejpam-3347	5	13	scalar	scalar	ADJ
ejpam-3347	5	14	product	product	NOUN
ejpam-3347	5	15	to	to	PART
ejpam-3347	5	16	clarify	clarify	VERB
ejpam-3347	5	17	a	a	DET
ejpam-3347	5	18	link	link	NOUN
ejpam-3347	5	19	between	between	ADP
ejpam-3347	5	20	the	the	DET
ejpam-3347	5	21	conditional	conditional	ADJ
ejpam-3347	5	22	copula	copula	NOUN
ejpam-3347	5	23	varying	vary	VERB
ejpam-3347	5	24	with	with	ADP
ejpam-3347	5	25	time	time	NOUN
ejpam-3347	5	26	and	and	CCONJ
ejpam-3347	5	27	norms	norm	NOUN
ejpam-3347	5	28	.	.	PUNCT
ejpam-3347	6	1	it	it	PRON
ejpam-3347	6	2	is	be	AUX
ejpam-3347	6	3	then	then	ADV
ejpam-3347	6	4	established	establish	VERB
ejpam-3347	6	5	a	a	DET
ejpam-3347	6	6	new	new	ADJ
ejpam-3347	6	7	expression	expression	NOUN
ejpam-3347	6	8	on	on	ADP
ejpam-3347	6	9	the	the	DET
ejpam-3347	6	10	geometric	geometric	ADJ
ejpam-3347	6	11	yield	yield	NOUN
ejpam-3347	6	12	.	.	PUNCT
ejpam-3347	7	1	2010	2010	NUM
ejpam-3347	7	2	mathematics	mathematic	NOUN
ejpam-3347	7	3	subject	subject	NOUN
ejpam-3347	7	4	classifications	classification	NOUN
ejpam-3347	7	5	:	:	PUNCT
ejpam-3347	7	6	51a50	51a50	NUM
ejpam-3347	7	7	,	,	PUNCT
ejpam-3347	7	8	91c15	91c15	NUM
ejpam-3347	7	9	,	,	PUNCT
ejpam-3347	7	10	60g57	60g57	NUM
ejpam-3347	7	11	,	,	PUNCT
ejpam-3347	7	12	60h30	60h30	NUM
ejpam-3347	7	13	,	,	PUNCT
ejpam-3347	7	14	62h00	62h00	NUM
ejpam-3347	7	15	key	key	ADJ
ejpam-3347	7	16	words	word	NOUN
ejpam-3347	7	17	and	and	CCONJ
ejpam-3347	7	18	phrases	phrase	NOUN
ejpam-3347	7	19	:	:	PUNCT
ejpam-3347	7	20	copulas	copula	NOUN
ejpam-3347	7	21	,	,	PUNCT
ejpam-3347	7	22	euclidean	euclidean	ADJ
ejpam-3347	7	23	space	space	NOUN
ejpam-3347	7	24	,	,	PUNCT
ejpam-3347	7	25	scalar	scalar	ADJ
ejpam-3347	7	26	product	product	NOUN
ejpam-3347	7	27	,	,	PUNCT
ejpam-3347	7	28	var	var	NOUN
ejpam-3347	7	29	1	1	NUM
ejpam-3347	7	30	.	.	PUNCT
ejpam-3347	8	1	introduction	introduction	NOUN
ejpam-3347	8	2	modeling	model	VERB
ejpam-3347	8	3	the	the	DET
ejpam-3347	8	4	risk	risk	NOUN
ejpam-3347	8	5	of	of	ADP
ejpam-3347	8	6	portfolio	portfolio	NOUN
ejpam-3347	8	7	is	be	AUX
ejpam-3347	8	8	to	to	PART
ejpam-3347	8	9	highlight	highlight	VERB
ejpam-3347	8	10	the	the	DET
ejpam-3347	8	11	different	different	ADJ
ejpam-3347	8	12	methods	method	NOUN
ejpam-3347	8	13	or	or	CCONJ
ejpam-3347	8	14	protocols	protocol	NOUN
ejpam-3347	8	15	to	to	PART
ejpam-3347	8	16	minimize	minimize	VERB
ejpam-3347	8	17	the	the	DET
ejpam-3347	8	18	loss	loss	NOUN
ejpam-3347	8	19	of	of	ADP
ejpam-3347	8	20	values	value	NOUN
ejpam-3347	8	21	of	of	ADP
ejpam-3347	8	22	a	a	DET
ejpam-3347	8	23	portfolio	portfolio	NOUN
ejpam-3347	8	24	.	.	PUNCT
ejpam-3347	9	1	the	the	DET
ejpam-3347	9	2	use	use	NOUN
ejpam-3347	9	3	of	of	ADP
ejpam-3347	9	4	multivariate	multivariate	NOUN
ejpam-3347	9	5	copulas	copula	NOUN
ejpam-3347	9	6	in	in	ADP
ejpam-3347	9	7	this	this	DET
ejpam-3347	9	8	modeling	modeling	NOUN
ejpam-3347	9	9	,	,	PUNCT
ejpam-3347	9	10	is	be	AUX
ejpam-3347	9	11	a	a	DET
ejpam-3347	9	12	contemporary	contemporary	ADJ
ejpam-3347	9	13	approach	approach	NOUN
ejpam-3347	9	14	,	,	PUNCT
ejpam-3347	9	15	to	to	PART
ejpam-3347	9	16	develop	develop	VERB
ejpam-3347	9	17	indicators	indicator	NOUN
ejpam-3347	9	18	for	for	ADP
ejpam-3347	9	19	the	the	DET
ejpam-3347	9	20	evaluation	evaluation	NOUN
ejpam-3347	9	21	of	of	ADP
ejpam-3347	9	22	the	the	DET
ejpam-3347	9	23	dependence	dependence	NOUN
ejpam-3347	9	24	between	between	ADP
ejpam-3347	9	25	the	the	DET
ejpam-3347	9	26	different	different	ADJ
ejpam-3347	9	27	assets	asset	NOUN
ejpam-3347	9	28	of	of	ADP
ejpam-3347	9	29	this	this	DET
ejpam-3347	9	30	portfolio	portfolio	NOUN
ejpam-3347	9	31	.	.	PUNCT
ejpam-3347	10	1	in	in	ADP
ejpam-3347	10	2	multivariate	multivariate	NOUN
ejpam-3347	10	3	theory	theory	NOUN
ejpam-3347	10	4	of	of	ADP
ejpam-3347	10	5	probability	probability	NOUN
ejpam-3347	10	6	a	a	DET
ejpam-3347	10	7	pioneer	pioneer	NOUN
ejpam-3347	10	8	theorem	theorem	NOUN
ejpam-3347	10	9	(	(	PUNCT
ejpam-3347	10	10	sklar,1959	sklar,1959	NOUN
ejpam-3347	10	11	)	)	PUNCT
ejpam-3347	10	12	.	.	PUNCT
ejpam-3347	11	1	abe	abe	PROPN
ejpam-3347	11	2	sklar	sklar	PROPN
ejpam-3347	11	3	showed	show	VERB
ejpam-3347	11	4	that	that	SCONJ
ejpam-3347	11	5	the	the	DET
ejpam-3347	11	6	copula	copula	NOUN
ejpam-3347	11	7	function	function	NOUN
ejpam-3347	11	8	enables	enable	VERB
ejpam-3347	11	9	to	to	PART
ejpam-3347	11	10	capture	capture	VERB
ejpam-3347	11	11	and	and	CCONJ
ejpam-3347	11	12	to	to	PART
ejpam-3347	11	13	piece	piece	VERB
ejpam-3347	11	14	together	together	ADV
ejpam-3347	11	15	the	the	DET
ejpam-3347	11	16	univariate	univariate	ADJ
ejpam-3347	11	17	models	model	NOUN
ejpam-3347	11	18	(	(	PUNCT
ejpam-3347	11	19	sklar	sklar	PROPN
ejpam-3347	11	20	’s	’s	PART
ejpam-3347	11	21	theorem	theorem	NOUN
ejpam-3347	11	22	)	)	PUNCT
ejpam-3347	11	23	.	.	PUNCT
ejpam-3347	12	1	therefore	therefore	ADV
ejpam-3347	12	2	,	,	PUNCT
ejpam-3347	12	3	every	every	DET
ejpam-3347	12	4	n	n	ADV
ejpam-3347	12	5	-	-	PUNCT
ejpam-3347	12	6	dimensional	dimensional	ADJ
ejpam-3347	12	7	continuous	continuous	ADJ
ejpam-3347	12	8	distribution	distribution	NOUN
ejpam-3347	12	9	h	h	NOUN
ejpam-3347	12	10	can	can	AUX
ejpam-3347	12	11	be	be	AUX
ejpam-3347	12	12	canonically	canonically	ADV
ejpam-3347	12	13	parameterized	parameterized	ADJ
ejpam-3347	12	14	by	by	ADP
ejpam-3347	12	15	its	its	PRON
ejpam-3347	12	16	univariate	univariate	ADJ
ejpam-3347	12	17	marginal	marginal	ADJ
ejpam-3347	12	18	h1	h1	NOUN
ejpam-3347	12	19	;	;	PUNCT
ejpam-3347	12	20	...	...	PUNCT
ejpam-3347	12	21	;	;	PUNCT
ejpam-3347	12	22	hn	hn	PROPN
ejpam-3347	12	23	using	use	VERB
ejpam-3347	12	24	[	[	X
ejpam-3347	12	25	0	0	NUM
ejpam-3347	12	26	,	,	PUNCT
ejpam-3347	12	27	1]n	1]n	NUM
ejpam-3347	12	28	a	a	DET
ejpam-3347	12	29	copula	copula	NOUN
ejpam-3347	12	30	c	c	PROPN
ejpam-3347	12	31	defined	define	VERB
ejpam-3347	12	32	on	on	ADP
ejpam-3347	12	33	the	the	DET
ejpam-3347	12	34	unit	unit	NOUN
ejpam-3347	12	35	cube	cube	NOUN
ejpam-3347	12	36	[	[	X
ejpam-3347	12	37	0	0	NUM
ejpam-3347	12	38	;	;	PUNCT
ejpam-3347	12	39	1	1	NUM
ejpam-3347	12	40	]	]	PUNCT
ejpam-3347	12	41	,	,	PUNCT
ejpam-3347	12	42	such	such	ADJ
ejpam-3347	12	43	as	as	ADP
ejpam-3347	12	44	h	h	NOUN
ejpam-3347	12	45	(	(	PUNCT
ejpam-3347	12	46	x1	x1	PROPN
ejpam-3347	12	47	,	,	PUNCT
ejpam-3347	12	48	...	...	PUNCT
ejpam-3347	12	49	,	,	PUNCT
ejpam-3347	12	50	xn	xn	PROPN
ejpam-3347	12	51	)	)	PUNCT
ejpam-3347	12	52	=	=	PUNCT
ejpam-3347	13	1	c	c	NOUN
ejpam-3347	14	1	[	[	X
ejpam-3347	14	2	h	h	X
ejpam-3347	14	3	(	(	PUNCT
ejpam-3347	14	4	x1	x1	PROPN
ejpam-3347	14	5	)	)	PUNCT
ejpam-3347	14	6	,	,	PUNCT
ejpam-3347	14	7	...	...	PUNCT
ejpam-3347	14	8	,	,	PUNCT
ejpam-3347	14	9	hn	hn	PROPN
ejpam-3347	14	10	(	(	PUNCT
ejpam-3347	14	11	xn	xn	PROPN
ejpam-3347	14	12	)	)	PUNCT
ejpam-3347	14	13	]	]	PUNCT
ejpam-3347	14	14	;	;	PUNCT
ejpam-3347	14	15	with	with	ADP
ejpam-3347	14	16	(	(	PUNCT
ejpam-3347	14	17	x1	x1	ADJ
ejpam-3347	14	18	,	,	PUNCT
ejpam-3347	14	19	...	...	PUNCT
ejpam-3347	14	20	,	,	PUNCT
ejpam-3347	14	21	xn	xn	X
ejpam-3347	14	22	)	)	PUNCT
ejpam-3347	14	23	∈	∈	NOUN
ejpam-3347	14	24	r̄n	r̄n	NOUN
ejpam-3347	14	25	=	=	PUNCT
ejpam-3347	15	1	[	[	X
ejpam-3347	15	2	−∞,+∞]n	−∞,+∞]n	X
ejpam-3347	15	3	.	.	PUNCT
ejpam-3347	16	1	(	(	PUNCT
ejpam-3347	16	2	1	1	X
ejpam-3347	16	3	)	)	PUNCT
ejpam-3347	16	4	under	under	ADP
ejpam-3347	16	5	additional	additional	ADJ
ejpam-3347	16	6	assumptions	assumption	NOUN
ejpam-3347	16	7	,	,	PUNCT
ejpam-3347	16	8	differentiating	differentiate	VERB
ejpam-3347	16	9	the	the	DET
ejpam-3347	16	10	formula	formula	NOUN
ejpam-3347	16	11	(	(	PUNCT
ejpam-3347	16	12	1	1	X
ejpam-3347	16	13	)	)	PUNCT
ejpam-3347	16	14	shows	show	VERB
ejpam-3347	16	15	that	that	SCONJ
ejpam-3347	16	16	the	the	DET
ejpam-3347	16	17	density	density	NOUN
ejpam-3347	16	18	function	function	NOUN
ejpam-3347	16	19	of	of	ADP
ejpam-3347	16	20	the	the	DET
ejpam-3347	16	21	copula	copula	NOUN
ejpam-3347	16	22	is	be	AUX
ejpam-3347	16	23	equal	equal	ADJ
ejpam-3347	16	24	to	to	ADP
ejpam-3347	16	25	the	the	DET
ejpam-3347	16	26	ratio	ratio	NOUN
ejpam-3347	16	27	of	of	ADP
ejpam-3347	16	28	the	the	DET
ejpam-3347	16	29	joint	joint	ADJ
ejpam-3347	16	30	density	density	NOUN
ejpam-3347	16	31	h	h	NOUN
ejpam-3347	16	32	of	of	ADP
ejpam-3347	16	33	h	h	NOUN
ejpam-3347	16	34	to	to	ADP
ejpam-3347	16	35	the	the	DET
ejpam-3347	16	36	product	product	NOUN
ejpam-3347	16	37	of	of	ADP
ejpam-3347	16	38	n	n	DET
ejpam-3347	16	39	marginal	marginal	ADJ
ejpam-3347	16	40	densities	density	NOUN
ejpam-3347	16	41	hi	hi	INTJ
ejpam-3347	16	42	such	such	ADJ
ejpam-3347	16	43	as	as	ADP
ejpam-3347	16	44	,	,	PUNCT
ejpam-3347	16	45	for	for	ADP
ejpam-3347	16	46	all	all	DET
ejpam-3347	16	47	(	(	PUNCT
ejpam-3347	16	48	u1	u1	NOUN
ejpam-3347	16	49	,	,	PUNCT
ejpam-3347	16	50	...	...	PUNCT
ejpam-3347	16	51	,	,	PUNCT
ejpam-3347	16	52	un	un	PROPN
ejpam-3347	16	53	)	)	PUNCT
ejpam-3347	16	54	∈	∈	PROPN
ejpam-3347	17	1	[	[	X
ejpam-3347	17	2	0	0	NUM
ejpam-3347	17	3	,	,	PUNCT
ejpam-3347	17	4	1]n	1]n	NUM
ejpam-3347	17	5	,	,	PUNCT
ejpam-3347	17	6	c	c	PROPN
ejpam-3347	17	7	(	(	PUNCT
ejpam-3347	17	8	u1	u1	PROPN
ejpam-3347	17	9	,	,	PUNCT
ejpam-3347	17	10	...	...	PUNCT
ejpam-3347	17	11	,	,	PUNCT
ejpam-3347	17	12	un	un	PROPN
ejpam-3347	17	13	)	)	PUNCT
ejpam-3347	17	14	=	=	SYM
ejpam-3347	18	1	∂nc	∂nc	PROPN
ejpam-3347	18	2	(	(	PUNCT
ejpam-3347	18	3	u1	u1	NOUN
ejpam-3347	18	4	,	,	PUNCT
ejpam-3347	18	5	...	...	PUNCT
ejpam-3347	18	6	,	,	PUNCT
ejpam-3347	18	7	un	un	PROPN
ejpam-3347	18	8	)	)	PUNCT
ejpam-3347	18	9	∂u1	∂u1	PROPN
ejpam-3347	18	10	×	×	NOUN
ejpam-3347	18	11	...	...	PUNCT
ejpam-3347	18	12	×	×	NOUN
ejpam-3347	18	13	∂un	∂un	NOUN
ejpam-3347	18	14	=	=	PUNCT
ejpam-3347	18	15	h	h	NOUN
ejpam-3347	18	16	[	[	PUNCT
ejpam-3347	18	17	h−1	h−1	PROPN
ejpam-3347	18	18	n	n	CCONJ
ejpam-3347	18	19	(	(	PUNCT
ejpam-3347	18	20	u1	u1	PROPN
ejpam-3347	18	21	)	)	PUNCT
ejpam-3347	18	22	,	,	PUNCT
ejpam-3347	18	23	...	...	PUNCT
ejpam-3347	18	24	,	,	PUNCT
ejpam-3347	18	25	h−1	h−1	PROPN
ejpam-3347	18	26	n	n	PROPN
ejpam-3347	18	27	(	(	PUNCT
ejpam-3347	18	28	un	un	PROPN
ejpam-3347	18	29	)	)	PUNCT
ejpam-3347	18	30	]	]	PUNCT
ejpam-3347	19	1	h1	h1	PROPN
ejpam-3347	19	2	[	[	PUNCT
ejpam-3347	19	3	h−1	h−1	PROPN
ejpam-3347	19	4	1	1	NUM
ejpam-3347	19	5	(	(	PUNCT
ejpam-3347	19	6	u1)×	u1)×	PROPN
ejpam-3347	19	7	...	...	PUNCT
ejpam-3347	19	8	×h−1	×h−1	PROPN
ejpam-3347	19	9	n	n	CCONJ
ejpam-3347	19	10	(	(	PUNCT
ejpam-3347	19	11	un	un	PROPN
ejpam-3347	19	12	)	)	PUNCT
ejpam-3347	19	13	]	]	PUNCT
ejpam-3347	19	14	.	.	PUNCT
ejpam-3347	20	1	(	(	PUNCT
ejpam-3347	20	2	2	2	X
ejpam-3347	20	3	)	)	PUNCT
ejpam-3347	20	4	∗corresponding	∗corresponde	VERB
ejpam-3347	20	5	author	author	NOUN
ejpam-3347	20	6	.	.	PUNCT
ejpam-3347	21	1	doi	doi	NOUN
ejpam-3347	21	2	:	:	PUNCT
ejpam-3347	21	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3347	https://doi.org/10.29020/nybg.ejpam.v12i1.3347	ADJ
ejpam-3347	21	4	email	email	NOUN
ejpam-3347	21	5	addresses	address	VERB
ejpam-3347	21	6	:	:	PUNCT
ejpam-3347	22	1	loyarayves@outlook.com	loyarayves@outlook.com	X
ejpam-3347	22	2	(	(	PUNCT
ejpam-3347	22	3	v.	v.	ADP
ejpam-3347	22	4	y.	y.	PROPN
ejpam-3347	22	5	b.	b.	PROPN
ejpam-3347	23	1	loyara	loyara	PROPN
ejpam-3347	23	2	)	)	PUNCT
ejpam-3347	23	3	,	,	PUNCT
ejpam-3347	24	1	dbarro2@gmail.com	dbarro2@gmail.com	X
ejpam-3347	24	2	(	(	PUNCT
ejpam-3347	24	3	d.	d.	NOUN
ejpam-3347	24	4	barro	barro	PROPN
ejpam-3347	24	5	)	)	PUNCT
ejpam-3347	24	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3347	25	1	194	194	NUM
ejpam-3347	25	2	c	c	X
ejpam-3347	25	3	©	©	PROPN
ejpam-3347	25	4	2019	2019	NUM
ejpam-3347	25	5	ejpam	ejpam	NOUN
ejpam-3347	25	6	all	all	DET
ejpam-3347	25	7	rights	right	NOUN
ejpam-3347	25	8	reserved	reserve	VERB
ejpam-3347	25	9	.	.	PUNCT
ejpam-3347	26	1	v.	v.	PROPN
ejpam-3347	26	2	y.	y.	PROPN
ejpam-3347	26	3	b.	b.	PROPN
ejpam-3347	27	1	loyara	loyara	PROPN
ejpam-3347	27	2	,	,	PUNCT
ejpam-3347	27	3	d.	d.	PROPN
ejpam-3347	27	4	barro	barro	PROPN
ejpam-3347	27	5	/	/	SYM
ejpam-3347	27	6	eur	eur	PROPN
ejpam-3347	27	7	.	.	PUNCT
ejpam-3347	28	1	j.	j.	PROPN
ejpam-3347	28	2	pure	pure	PROPN
ejpam-3347	28	3	appl	appl	PROPN
ejpam-3347	28	4	.	.	PROPN
ejpam-3347	28	5	math	math	PROPN
ejpam-3347	28	6	,	,	PUNCT
ejpam-3347	28	7	12	12	NUM
ejpam-3347	28	8	(	(	PUNCT
ejpam-3347	28	9	1	1	NUM
ejpam-3347	28	10	)	)	PUNCT
ejpam-3347	28	11	(	(	PUNCT
ejpam-3347	28	12	2019	2019	NUM
ejpam-3347	28	13	)	)	PUNCT
ejpam-3347	28	14	,	,	PUNCT
ejpam-3347	28	15	194	194	NUM
ejpam-3347	28	16	-	-	SYM
ejpam-3347	28	17	207	207	NUM
ejpam-3347	28	18	195	195	NUM
ejpam-3347	28	19	where	where	SCONJ
ejpam-3347	28	20	h−1	h−1	PROPN
ejpam-3347	28	21	i	i	PRON
ejpam-3347	28	22	is	be	AUX
ejpam-3347	28	23	the	the	DET
ejpam-3347	28	24	quantile	quantile	ADJ
ejpam-3347	28	25	function	function	NOUN
ejpam-3347	28	26	of	of	ADP
ejpam-3347	28	27	hi	hi	INTJ
ejpam-3347	28	28	;	;	PUNCT
ejpam-3347	28	29	that	that	PRON
ejpam-3347	28	30	is	is	ADV
ejpam-3347	28	31	,	,	PUNCT
ejpam-3347	29	1	h−1	h−1	PROPN
ejpam-3347	29	2	i	i	PRON
ejpam-3347	29	3	(	(	PUNCT
ejpam-3347	29	4	u	u	NOUN
ejpam-3347	29	5	)	)	PUNCT
ejpam-3347	29	6	=	=	SYM
ejpam-3347	29	7	inf	inf	NOUN
ejpam-3347	29	8	{	{	PUNCT
ejpam-3347	29	9	x	x	SYM
ejpam-3347	29	10	∈	∈	PROPN
ejpam-3347	29	11	r	r	NOUN
ejpam-3347	29	12	,	,	PUNCT
ejpam-3347	29	13	h	h	NOUN
ejpam-3347	29	14	(	(	PUNCT
ejpam-3347	29	15	xi	xi	PROPN
ejpam-3347	29	16	)	)	PUNCT
ejpam-3347	29	17	≥	≥	NOUN
ejpam-3347	29	18	u	u	NOUN
ejpam-3347	29	19	}	}	PUNCT
ejpam-3347	29	20	.	.	PUNCT
ejpam-3347	30	1	in	in	ADP
ejpam-3347	30	2	stochastic	stochastic	ADJ
ejpam-3347	30	3	financial	financial	ADJ
ejpam-3347	30	4	analysis	analysis	NOUN
ejpam-3347	30	5	,	,	PUNCT
ejpam-3347	30	6	from	from	ADP
ejpam-3347	30	7	the	the	DET
ejpam-3347	30	8	definition	definition	NOUN
ejpam-3347	30	9	in	in	ADP
ejpam-3347	30	10	the	the	DET
ejpam-3347	30	11	univariate	univariate	ADJ
ejpam-3347	30	12	case	case	NOUN
ejpam-3347	30	13	we	we	PRON
ejpam-3347	30	14	know	know	VERB
ejpam-3347	30	15	that	that	SCONJ
ejpam-3347	30	16	the	the	DET
ejpam-3347	30	17	quantile	quantile	ADJ
ejpam-3347	30	18	function	function	NOUN
ejpam-3347	30	19	provides	provide	VERB
ejpam-3347	30	20	a	a	DET
ejpam-3347	30	21	point	point	NOUN
ejpam-3347	30	22	that	that	PRON
ejpam-3347	30	23	accumulates	accumulate	VERB
ejpam-3347	30	24	a	a	DET
ejpam-3347	30	25	probability	probability	NOUN
ejpam-3347	30	26	for	for	ADP
ejpam-3347	30	27	the	the	DET
ejpam-3347	30	28	left	left	ADJ
ejpam-3347	30	29	tail	tail	NOUN
ejpam-3347	30	30	and	and	CCONJ
ejpam-3347	30	31	for	for	ADP
ejpam-3347	30	32	the	the	DET
ejpam-3347	30	33	right	right	ADJ
ejpam-3347	30	34	tail	tail	NOUN
ejpam-3347	30	35	.	.	PUNCT
ejpam-3347	31	1	the	the	DET
ejpam-3347	31	2	univariate	univariate	ADJ
ejpam-3347	31	3	quantile	quantile	ADJ
ejpam-3347	31	4	function	function	NOUN
ejpam-3347	31	5	qx	qx	PROPN
ejpam-3347	31	6	(	(	PUNCT
ejpam-3347	31	7	α	α	NOUN
ejpam-3347	31	8	)	)	PUNCT
ejpam-3347	31	9	is	be	AUX
ejpam-3347	31	10	used	use	VERB
ejpam-3347	31	11	in	in	ADP
ejpam-3347	31	12	the	the	DET
ejpam-3347	31	13	risk	risk	NOUN
ejpam-3347	31	14	theory	theory	NOUN
ejpam-3347	31	15	to	to	PART
ejpam-3347	31	16	define	define	VERB
ejpam-3347	31	17	the	the	DET
ejpam-3347	31	18	univariate	univariate	ADJ
ejpam-3347	31	19	risk	risk	NOUN
ejpam-3347	31	20	measure	measure	NOUN
ejpam-3347	31	21	:	:	PUNCT
ejpam-3347	31	22	the	the	DET
ejpam-3347	31	23	value	value	NOUN
ejpam-3347	31	24	at	at	ADP
ejpam-3347	31	25	risk	risk	NOUN
ejpam-3347	31	26	is	be	AUX
ejpam-3347	31	27	defined	define	VERB
ejpam-3347	31	28	.	.	PUNCT
ejpam-3347	32	1	more	more	ADV
ejpam-3347	32	2	generally	generally	ADV
ejpam-3347	32	3	in	in	ADP
ejpam-3347	32	4	multivariate	multivariate	NOUN
ejpam-3347	32	5	study	study	NOUN
ejpam-3347	32	6	,	,	PUNCT
ejpam-3347	32	7	for	for	ADP
ejpam-3347	32	8	a	a	DET
ejpam-3347	32	9	random	random	ADJ
ejpam-3347	32	10	vector	vector	NOUN
ejpam-3347	32	11	x	x	PUNCT
ejpam-3347	32	12	satisfying	satisfy	VERB
ejpam-3347	32	13	the	the	DET
ejpam-3347	32	14	regularity	regularity	NOUN
ejpam-3347	32	15	conditions	condition	NOUN
ejpam-3347	32	16	,	,	PUNCT
ejpam-3347	32	17	we	we	PRON
ejpam-3347	32	18	define	define	VERB
ejpam-3347	32	19	the	the	DET
ejpam-3347	32	20	multidimensional	multidimensional	ADJ
ejpam-3347	32	21	var	var	NOUN
ejpam-3347	32	22	at	at	ADP
ejpam-3347	32	23	probability	probability	NOUN
ejpam-3347	32	24	level	level	NOUN
ejpam-3347	32	25	α	α	NOUN
ejpam-3347	32	26	by	by	ADP
ejpam-3347	32	27	:	:	PUNCT
ejpam-3347	32	28	v	v	NUM
ejpam-3347	32	29	arα	arα	NOUN
ejpam-3347	32	30	(	(	PUNCT
ejpam-3347	32	31	x	x	NOUN
ejpam-3347	32	32	)	)	PUNCT
ejpam-3347	32	33	=	=	SYM
ejpam-3347	33	1	e	e	X
ejpam-3347	34	1	[	[	X
ejpam-3347	34	2	x	x	X
ejpam-3347	34	3	|	|	ADV
ejpam-3347	34	4	x	x	SYM
ejpam-3347	34	5	∈	∈	NOUN
ejpam-3347	34	6	∂l	∂l	PROPN
ejpam-3347	34	7	(	(	PUNCT
ejpam-3347	34	8	α	α	NOUN
ejpam-3347	34	9	)	)	PUNCT
ejpam-3347	34	10	]	]	PUNCT
ejpam-3347	34	11	(	(	PUNCT
ejpam-3347	34	12	3	3	X
ejpam-3347	34	13	)	)	PUNCT
ejpam-3347	34	14	where	where	SCONJ
ejpam-3347	34	15	∂l	∂l	PROPN
ejpam-3347	34	16	(	(	PUNCT
ejpam-3347	34	17	α	α	NOUN
ejpam-3347	34	18	)	)	PUNCT
ejpam-3347	34	19	is	be	AUX
ejpam-3347	34	20	the	the	DET
ejpam-3347	34	21	boundary	boundary	NOUN
ejpam-3347	34	22	of	of	ADP
ejpam-3347	34	23	the	the	DET
ejpam-3347	34	24	α	α	NOUN
ejpam-3347	34	25	−	−	NOUN
ejpam-3347	34	26	level	level	NOUN
ejpam-3347	34	27	set	set	NOUN
ejpam-3347	34	28	of	of	ADP
ejpam-3347	34	29	f	f	PROPN
ejpam-3347	34	30	,	,	PUNCT
ejpam-3347	34	31	the	the	DET
ejpam-3347	34	32	univariate	univariate	ADJ
ejpam-3347	34	33	component	component	NOUN
ejpam-3347	34	34	of	of	ADP
ejpam-3347	34	35	the	the	DET
ejpam-3347	34	36	vector	vector	NOUN
ejpam-3347	34	37	:	:	PUNCT
ejpam-3347	34	38	v	v	NUM
ejpam-3347	34	39	arα	arα	NOUN
ejpam-3347	34	40	(	(	PUNCT
ejpam-3347	34	41	x	x	X
ejpam-3347	34	42	)	)	PUNCT
ejpam-3347	34	43	are	be	AUX
ejpam-3347	34	44	such	such	ADJ
ejpam-3347	34	45	as	as	ADP
ejpam-3347	34	46	,	,	PUNCT
ejpam-3347	34	47	for	for	ADP
ejpam-3347	34	48	all	all	DET
ejpam-3347	34	49	portfolio	portfolio	NOUN
ejpam-3347	34	50	xi;v	xi;v	PUNCT
ejpam-3347	34	51	arα	arα	NOUN
ejpam-3347	34	52	(	(	PUNCT
ejpam-3347	34	53	x	x	NOUN
ejpam-3347	34	54	)	)	PUNCT
ejpam-3347	34	55	=	=	SYM
ejpam-3347	34	56	{	{	PUNCT
ejpam-3347	34	57	z	z	NOUN
ejpam-3347	34	58	/	/	SYM
ejpam-3347	34	59	fxi	fxi	NOUN
ejpam-3347	34	60	(	(	PUNCT
ejpam-3347	34	61	z	z	NOUN
ejpam-3347	34	62	)	)	PUNCT
ejpam-3347	34	63	≥	≥	NOUN
ejpam-3347	34	64	α	α	NOUN
ejpam-3347	34	65	}	}	PUNCT
ejpam-3347	34	66	=	=	SYM
ejpam-3347	34	67	f−1	f−1	PROPN
ejpam-3347	34	68	xi	xi	X
ejpam-3347	34	69	(	(	PUNCT
ejpam-3347	34	70	α	α	NOUN
ejpam-3347	34	71	)	)	PUNCT
ejpam-3347	34	72	,	,	PUNCT
ejpam-3347	34	73	f−1	f−1	PROPN
ejpam-3347	34	74	xi	xi	VERB
ejpam-3347	34	75	being	be	AUX
ejpam-3347	34	76	the	the	DET
ejpam-3347	34	77	right	right	ADJ
ejpam-3347	34	78	continuous	continuous	ADJ
ejpam-3347	34	79	inverse	inverse	NOUN
ejpam-3347	34	80	of	of	ADP
ejpam-3347	34	81	fx	fx	PROPN
ejpam-3347	34	82	.	.	PUNCT
ejpam-3347	35	1	in	in	ADP
ejpam-3347	35	2	this	this	DET
ejpam-3347	35	3	paper	paper	NOUN
ejpam-3347	35	4	,	,	PUNCT
ejpam-3347	35	5	it	it	PRON
ejpam-3347	35	6	is	be	AUX
ejpam-3347	35	7	matter	matter	NOUN
ejpam-3347	35	8	of	of	ADP
ejpam-3347	35	9	the	the	DET
ejpam-3347	35	10	notion	notion	NOUN
ejpam-3347	35	11	of	of	ADP
ejpam-3347	35	12	multivariate	multivariate	NOUN
ejpam-3347	35	13	risk	risk	NOUN
ejpam-3347	35	14	coupled	couple	VERB
ejpam-3347	35	15	with	with	ADP
ejpam-3347	35	16	that	that	PRON
ejpam-3347	35	17	of	of	ADP
ejpam-3347	35	18	conditional	conditional	ADJ
ejpam-3347	35	19	copula	copula	NOUN
ejpam-3347	35	20	varying	vary	VERB
ejpam-3347	35	21	with	with	ADP
ejpam-3347	35	22	time	time	NOUN
ejpam-3347	35	23	.	.	PUNCT
ejpam-3347	36	1	we	we	PRON
ejpam-3347	36	2	have	have	AUX
ejpam-3347	36	3	established	establish	VERB
ejpam-3347	36	4	,	,	PUNCT
ejpam-3347	36	5	subject	subject	ADJ
ejpam-3347	36	6	of	of	ADP
ejpam-3347	36	7	being	be	AUX
ejpam-3347	36	8	in	in	ADP
ejpam-3347	36	9	a	a	DET
ejpam-3347	36	10	euclidean	euclidean	ADJ
ejpam-3347	36	11	space	space	NOUN
ejpam-3347	36	12	,	,	PUNCT
ejpam-3347	36	13	a	a	DET
ejpam-3347	36	14	relation	relation	NOUN
ejpam-3347	36	15	between	between	ADP
ejpam-3347	36	16	the	the	DET
ejpam-3347	36	17	conditional	conditional	ADJ
ejpam-3347	36	18	copula	copula	NOUN
ejpam-3347	36	19	varying	vary	VERB
ejpam-3347	36	20	with	with	ADP
ejpam-3347	36	21	time	time	NOUN
ejpam-3347	36	22	and	and	CCONJ
ejpam-3347	36	23	the	the	DET
ejpam-3347	36	24	scalar	scalar	ADJ
ejpam-3347	36	25	product	product	NOUN
ejpam-3347	36	26	or	or	CCONJ
ejpam-3347	36	27	norm	norm	NOUN
ejpam-3347	36	28	.	.	PUNCT
ejpam-3347	37	1	we	we	PRON
ejpam-3347	37	2	are	be	AUX
ejpam-3347	37	3	inspired	inspire	VERB
ejpam-3347	37	4	by	by	ADP
ejpam-3347	37	5	patton	patton	PROPN
ejpam-3347	37	6	’s	’s	PART
ejpam-3347	37	7	work	work	NOUN
ejpam-3347	37	8	on	on	ADP
ejpam-3347	37	9	conditional	conditional	ADJ
ejpam-3347	37	10	copulas	copula	NOUN
ejpam-3347	37	11	varying	vary	VERB
ejpam-3347	37	12	with	with	ADP
ejpam-3347	37	13	time	time	NOUN
ejpam-3347	37	14	.	.	PUNCT
ejpam-3347	38	1	indeed	indeed	ADV
ejpam-3347	38	2	,	,	PUNCT
ejpam-3347	38	3	from	from	ADP
ejpam-3347	38	4	proposition	proposition	NOUN
ejpam-3347	38	5	and	and	CCONJ
ejpam-3347	38	6	sklar	sklar	PROPN
ejpam-3347	38	7	’s	’s	PART
ejpam-3347	38	8	theorem	theorem	NOUN
ejpam-3347	38	9	adapted	adapt	VERB
ejpam-3347	38	10	to	to	ADP
ejpam-3347	38	11	the	the	DET
ejpam-3347	38	12	conditional	conditional	ADJ
ejpam-3347	38	13	copula	copula	NOUN
ejpam-3347	38	14	(	(	PUNCT
ejpam-3347	38	15	which	which	PRON
ejpam-3347	38	16	are	be	AUX
ejpam-3347	38	17	all	all	ADV
ejpam-3347	38	18	from	from	ADP
ejpam-3347	38	19	patton	patton	PROPN
ejpam-3347	38	20	)	)	PUNCT
ejpam-3347	38	21	we	we	PRON
ejpam-3347	38	22	use	use	VERB
ejpam-3347	38	23	the	the	DET
ejpam-3347	38	24	relation	relation	NOUN
ejpam-3347	38	25	(	(	PUNCT
ejpam-3347	38	26	5	5	NUM
ejpam-3347	38	27	)	)	PUNCT
ejpam-3347	38	28	to	to	PART
ejpam-3347	38	29	obtain	obtain	VERB
ejpam-3347	38	30	our	our	PRON
ejpam-3347	38	31	different	different	ADJ
ejpam-3347	38	32	results	result	NOUN
ejpam-3347	38	33	.	.	PUNCT
ejpam-3347	39	1	finally	finally	ADV
ejpam-3347	39	2	,	,	PUNCT
ejpam-3347	39	3	a	a	DET
ejpam-3347	39	4	new	new	ADJ
ejpam-3347	39	5	expression	expression	NOUN
ejpam-3347	39	6	on	on	ADP
ejpam-3347	39	7	the	the	DET
ejpam-3347	39	8	geometric	geometric	ADJ
ejpam-3347	39	9	yield	yield	NOUN
ejpam-3347	39	10	is	be	AUX
ejpam-3347	39	11	established	establish	VERB
ejpam-3347	39	12	.	.	PUNCT
ejpam-3347	40	1	2	2	X
ejpam-3347	40	2	.	.	NUM
ejpam-3347	40	3	preliminaries	preliminary	NOUN
ejpam-3347	40	4	in	in	ADP
ejpam-3347	40	5	this	this	DET
ejpam-3347	40	6	section	section	NOUN
ejpam-3347	40	7	we	we	PRON
ejpam-3347	40	8	have	have	AUX
ejpam-3347	40	9	grouped	group	VERB
ejpam-3347	40	10	together	together	ADV
ejpam-3347	40	11	the	the	DET
ejpam-3347	40	12	different	different	ADJ
ejpam-3347	40	13	notion	notion	NOUN
ejpam-3347	40	14	definitions	definition	NOUN
ejpam-3347	40	15	,	,	PUNCT
ejpam-3347	40	16	propositions	proposition	NOUN
ejpam-3347	40	17	and	and	CCONJ
ejpam-3347	40	18	theorems	theorem	NOUN
ejpam-3347	40	19	which	which	PRON
ejpam-3347	40	20	will	will	AUX
ejpam-3347	40	21	be	be	AUX
ejpam-3347	40	22	useful	useful	ADJ
ejpam-3347	40	23	thereafter	thereafter	ADV
ejpam-3347	40	24	.	.	PUNCT
ejpam-3347	41	1	we	we	PRON
ejpam-3347	41	2	need	need	VERB
ejpam-3347	41	3	sklar	sklar	PROPN
ejpam-3347	41	4	’s	’s	PART
ejpam-3347	41	5	theorem	theorem	NOUN
ejpam-3347	41	6	and	and	CCONJ
ejpam-3347	41	7	its	its	PRON
ejpam-3347	41	8	adaptation	adaptation	NOUN
ejpam-3347	41	9	in	in	ADP
ejpam-3347	41	10	the	the	DET
ejpam-3347	41	11	conditional	conditional	ADJ
ejpam-3347	41	12	case	case	NOUN
ejpam-3347	41	13	proposed	propose	VERB
ejpam-3347	41	14	by	by	ADP
ejpam-3347	41	15	patton	patton	PROPN
ejpam-3347	41	16	(	(	PUNCT
ejpam-3347	41	17	2006	2006	NUM
ejpam-3347	41	18	)	)	PUNCT
ejpam-3347	41	19	to	to	PART
ejpam-3347	41	20	elaborate	elaborate	VERB
ejpam-3347	41	21	the	the	DET
ejpam-3347	41	22	different	different	ADJ
ejpam-3347	41	23	results	result	NOUN
ejpam-3347	41	24	we	we	PRON
ejpam-3347	41	25	found	find	VERB
ejpam-3347	41	26	.	.	PUNCT
ejpam-3347	42	1	2.1	2.1	NUM
ejpam-3347	42	2	.	.	PUNCT
ejpam-3347	43	1	a	a	DET
ejpam-3347	43	2	survey	survey	NOUN
ejpam-3347	43	3	of	of	ADP
ejpam-3347	43	4	conditional	conditional	ADJ
ejpam-3347	43	5	copulas	copula	NOUN
ejpam-3347	43	6	in	in	ADP
ejpam-3347	43	7	copulas	copula	NOUN
ejpam-3347	43	8	theory	theory	NOUN
ejpam-3347	43	9	joe	joe	PROPN
ejpam-3347	43	10	(	(	PUNCT
ejpam-3347	43	11	1997	1997	NUM
ejpam-3347	43	12	)	)	PUNCT
ejpam-3347	43	13	or	or	CCONJ
ejpam-3347	43	14	nelsen	nelsen	NOUN
ejpam-3347	43	15	(	(	PUNCT
ejpam-3347	43	16	2007	2007	NUM
ejpam-3347	43	17	)	)	PUNCT
ejpam-3347	43	18	provide	provide	VERB
ejpam-3347	43	19	detailed	detailed	ADJ
ejpam-3347	43	20	and	and	CCONJ
ejpam-3347	43	21	readable	readable	ADJ
ejpam-3347	43	22	introductions	introduction	NOUN
ejpam-3347	43	23	to	to	ADP
ejpam-3347	43	24	copulas	copula	NOUN
ejpam-3347	43	25	and	and	CCONJ
ejpam-3347	43	26	their	their	PRON
ejpam-3347	43	27	statistical	statistical	ADJ
ejpam-3347	43	28	and	and	CCONJ
ejpam-3347	43	29	mathematical	mathematical	ADJ
ejpam-3347	43	30	foundations	foundation	NOUN
ejpam-3347	43	31	while	while	SCONJ
ejpam-3347	43	32	bouy	bouy	PROPN
ejpam-3347	43	33	et	et	PROPN
ejpam-3347	43	34	al	al	PROPN
ejpam-3347	43	35	.	.	PROPN
ejpam-3347	44	1	(	(	PUNCT
ejpam-3347	44	2	2000	2000	NUM
ejpam-3347	44	3	)	)	PUNCT
ejpam-3347	44	4	or	or	CCONJ
ejpam-3347	44	5	cherubini	cherubini	NOUN
ejpam-3347	44	6	et	et	PROPN
ejpam-3347	44	7	al	al	PROPN
ejpam-3347	44	8	.	.	PROPN
ejpam-3347	45	1	(	(	PUNCT
ejpam-3347	45	2	2004	2004	NUM
ejpam-3347	45	3	)	)	PUNCT
ejpam-3347	45	4	deal	deal	NOUN
ejpam-3347	45	5	with	with	ADP
ejpam-3347	45	6	applications	application	NOUN
ejpam-3347	45	7	of	of	ADP
ejpam-3347	45	8	copulas	copula	NOUN
ejpam-3347	45	9	to	to	ADP
ejpam-3347	45	10	different	different	ADJ
ejpam-3347	45	11	levels	level	NOUN
ejpam-3347	45	12	of	of	ADP
ejpam-3347	45	13	financial	financial	ADJ
ejpam-3347	45	14	issues	issue	NOUN
ejpam-3347	45	15	and	and	CCONJ
ejpam-3347	45	16	derivatives	derivative	NOUN
ejpam-3347	45	17	pricing	pricing	NOUN
ejpam-3347	45	18	.	.	PUNCT
ejpam-3347	46	1	a	a	DET
ejpam-3347	46	2	n−	n−	NOUN
ejpam-3347	46	3	dimensional	dimensional	ADJ
ejpam-3347	46	4	copula	copula	NOUN
ejpam-3347	46	5	is	be	AUX
ejpam-3347	46	6	a	a	DET
ejpam-3347	46	7	multivariate	multivariate	NOUN
ejpam-3347	46	8	distribution	distribution	NOUN
ejpam-3347	46	9	function	function	NOUN
ejpam-3347	46	10	c	c	NOUN
ejpam-3347	46	11	:	:	PUNCT
ejpam-3347	47	1	[	[	X
ejpam-3347	47	2	0	0	NUM
ejpam-3347	47	3	,	,	PUNCT
ejpam-3347	47	4	1]n	1]n	NOUN
ejpam-3347	47	5	−→	−→	ADJ
ejpam-3347	47	6	[	[	X
ejpam-3347	47	7	0	0	NUM
ejpam-3347	47	8	,	,	PUNCT
ejpam-3347	47	9	1	1	NUM
ejpam-3347	47	10	]	]	PUNCT
ejpam-3347	47	11	satisfying	satisfy	VERB
ejpam-3347	47	12	the	the	DET
ejpam-3347	47	13	following	follow	VERB
ejpam-3347	47	14	properties	property	NOUN
ejpam-3347	47	15	i	i	PRON
ejpam-3347	47	16	)	)	PUNCT
ejpam-3347	47	17	grounded	ground	VERB
ejpam-3347	47	18	:	:	PUNCT
ejpam-3347	47	19	c	c	X
ejpam-3347	47	20	(	(	PUNCT
ejpam-3347	47	21	u1	u1	PROPN
ejpam-3347	47	22	,	,	PUNCT
ejpam-3347	47	23	...	...	PUNCT
ejpam-3347	47	24	,	,	PUNCT
ejpam-3347	47	25	ui−1	ui−1	PROPN
ejpam-3347	47	26	,	,	PUNCT
ejpam-3347	47	27	0	0	NUM
ejpam-3347	47	28	,	,	PUNCT
ejpam-3347	47	29	ui+1	ui+1	PROPN
ejpam-3347	47	30	,	,	PUNCT
ejpam-3347	47	31	...	...	PUNCT
ejpam-3347	47	32	,	,	PUNCT
ejpam-3347	47	33	un	un	PROPN
ejpam-3347	47	34	)	)	PUNCT
ejpam-3347	47	35	=	=	SYM
ejpam-3347	47	36	0	0	NUM
ejpam-3347	47	37	for	for	ADP
ejpam-3347	47	38	all	all	DET
ejpam-3347	47	39	i	i	PRON
ejpam-3347	47	40	and	and	CCONJ
ejpam-3347	47	41	all	all	PRON
ejpam-3347	47	42	(	(	PUNCT
ejpam-3347	47	43	u1	u1	NOUN
ejpam-3347	47	44	,	,	PUNCT
ejpam-3347	47	45	...	...	PUNCT
ejpam-3347	47	46	,	,	PUNCT
ejpam-3347	47	47	ui−1	ui−1	PROPN
ejpam-3347	47	48	,	,	PUNCT
ejpam-3347	47	49	ui+1	ui+1	PROPN
ejpam-3347	47	50	,	,	PUNCT
ejpam-3347	47	51	...	...	PUNCT
ejpam-3347	47	52	,	,	PUNCT
ejpam-3347	47	53	un	un	PROPN
ejpam-3347	47	54	)	)	PUNCT
ejpam-3347	47	55	∈	∈	PROPN
ejpam-3347	48	1	[	[	X
ejpam-3347	48	2	0	0	NUM
ejpam-3347	48	3	,	,	PUNCT
ejpam-3347	48	4	1]n−1	1]n−1	NUM
ejpam-3347	48	5	.	.	PUNCT
ejpam-3347	48	6	ii	ii	PROPN
ejpam-3347	48	7	)	)	PUNCT
ejpam-3347	48	8	copula	copula	NOUN
ejpam-3347	48	9	marginal	marginal	NOUN
ejpam-3347	48	10	:	:	PUNCT
ejpam-3347	48	11	c	c	X
ejpam-3347	48	12	(	(	PUNCT
ejpam-3347	48	13	u1	u1	PROPN
ejpam-3347	48	14	,	,	PUNCT
ejpam-3347	48	15	...	...	PUNCT
ejpam-3347	48	16	,	,	PUNCT
ejpam-3347	49	1	ui−1	ui−1	PROPN
ejpam-3347	49	2	,	,	PUNCT
ejpam-3347	49	3	1	1	NUM
ejpam-3347	49	4	,	,	PUNCT
ejpam-3347	49	5	ui+1	ui+1	ADJ
ejpam-3347	49	6	,	,	PUNCT
ejpam-3347	49	7	...	...	PUNCT
ejpam-3347	49	8	,	,	PUNCT
ejpam-3347	49	9	un	un	PROPN
ejpam-3347	49	10	)	)	PUNCT
ejpam-3347	49	11	is	be	AUX
ejpam-3347	49	12	an	an	DET
ejpam-3347	49	13	(	(	PUNCT
ejpam-3347	49	14	n−	n−	NOUN
ejpam-3347	49	15	1	1	NUM
ejpam-3347	49	16	)	)	PUNCT
ejpam-3347	49	17	copula	copula	NOUN
ejpam-3347	49	18	for	for	ADP
ejpam-3347	49	19	all	all	DET
ejpam-3347	49	20	i	i	PRON
ejpam-3347	49	21	∈	∈	PROPN
ejpam-3347	49	22	{	{	PUNCT
ejpam-3347	49	23	1	1	NUM
ejpam-3347	49	24	,	,	PUNCT
ejpam-3347	49	25	...	...	PUNCT
ejpam-3347	49	26	,	,	PUNCT
ejpam-3347	49	27	n	n	CCONJ
ejpam-3347	49	28	}	}	PUNCT
ejpam-3347	49	29	.	.	PUNCT
ejpam-3347	50	1	iii	iii	X
ejpam-3347	50	2	)	)	PUNCT
ejpam-3347	50	3	n−	n−	NOUN
ejpam-3347	50	4	increasingness	increasingness	VERB
ejpam-3347	50	5	:	:	PUNCT
ejpam-3347	50	6	the	the	DET
ejpam-3347	50	7	volume	volume	NOUN
ejpam-3347	50	8	vb	vb	NOUN
ejpam-3347	50	9	of	of	ADP
ejpam-3347	50	10	any	any	DET
ejpam-3347	50	11	rectangle	rectangle	NOUN
ejpam-3347	50	12	b	b	NOUN
ejpam-3347	51	1	=	=	PUNCT
ejpam-3347	52	1	[	[	X
ejpam-3347	52	2	a	a	X
ejpam-3347	52	3	,	,	PUNCT
ejpam-3347	52	4	b	b	NOUN
ejpam-3347	52	5	]	]	X
ejpam-3347	52	6	⊆	⊆	NUM
ejpam-3347	52	7	[	[	X
ejpam-3347	52	8	0	0	NUM
ejpam-3347	52	9	,	,	PUNCT
ejpam-3347	52	10	1]n	1]n	NUM
ejpam-3347	52	11	is	be	AUX
ejpam-3347	52	12	positive	positive	ADJ
ejpam-3347	52	13	,	,	PUNCT
ejpam-3347	52	14	vb	vb	NOUN
ejpam-3347	52	15	=	=	SYM
ejpam-3347	52	16	∫	∫	PROPN
ejpam-3347	52	17	b	b	PROPN
ejpam-3347	52	18	dc	dc	PROPN
ejpam-3347	52	19	(	(	PUNCT
ejpam-3347	52	20	u1	u1	PROPN
ejpam-3347	52	21	,	,	PUNCT
ejpam-3347	52	22	...	...	PUNCT
ejpam-3347	52	23	,	,	PUNCT
ejpam-3347	52	24	un	un	PROPN
ejpam-3347	52	25	)	)	PUNCT
ejpam-3347	53	1	=	=	NOUN
ejpam-3347	53	2	[	[	PUNCT
ejpam-3347	53	3	i1=1]2	i1=1]2	PROPN
ejpam-3347	53	4	∑	∑	PUNCT
ejpam-3347	53	5	...	...	PUNCT
ejpam-3347	54	1	[	[	PUNCT
ejpam-3347	54	2	in=1]2	in=1]2	ADV
ejpam-3347	54	3	∑	∑	PUNCT
ejpam-3347	54	4	(	(	PUNCT
ejpam-3347	54	5	−1)i1+	−1)i1+	ADJ
ejpam-3347	54	6	...	...	PUNCT
ejpam-3347	54	7	+in	+in	NOUN
ejpam-3347	55	1	c	c	NOUN
ejpam-3347	55	2	(	(	PUNCT
ejpam-3347	55	3	ui1	ui1	PROPN
ejpam-3347	55	4	,	,	PUNCT
ejpam-3347	55	5	...	...	PUNCT
ejpam-3347	55	6	,	,	PUNCT
ejpam-3347	55	7	uin	uin	PROPN
ejpam-3347	55	8	)	)	PUNCT
ejpam-3347	55	9	≥	≥	NOUN
ejpam-3347	55	10	0	0	NUM
ejpam-3347	55	11	.	.	PUNCT
ejpam-3347	56	1	(	(	PUNCT
ejpam-3347	56	2	4	4	X
ejpam-3347	56	3	)	)	PUNCT
ejpam-3347	56	4	v.	v.	ADP
ejpam-3347	56	5	y.	y.	PROPN
ejpam-3347	56	6	b.	b.	PROPN
ejpam-3347	57	1	loyara	loyara	PROPN
ejpam-3347	57	2	,	,	PUNCT
ejpam-3347	57	3	d.	d.	PROPN
ejpam-3347	57	4	barro	barro	PROPN
ejpam-3347	57	5	/	/	SYM
ejpam-3347	57	6	eur	eur	PROPN
ejpam-3347	57	7	.	.	PUNCT
ejpam-3347	58	1	j.	j.	PROPN
ejpam-3347	58	2	pure	pure	PROPN
ejpam-3347	58	3	appl	appl	PROPN
ejpam-3347	58	4	.	.	PROPN
ejpam-3347	58	5	math	math	PROPN
ejpam-3347	58	6	,	,	PUNCT
ejpam-3347	58	7	12	12	NUM
ejpam-3347	58	8	(	(	PUNCT
ejpam-3347	58	9	1	1	NUM
ejpam-3347	58	10	)	)	PUNCT
ejpam-3347	58	11	(	(	PUNCT
ejpam-3347	58	12	2019	2019	NUM
ejpam-3347	58	13	)	)	PUNCT
ejpam-3347	58	14	,	,	PUNCT
ejpam-3347	58	15	194	194	NUM
ejpam-3347	58	16	-	-	SYM
ejpam-3347	58	17	207	207	NUM
ejpam-3347	58	18	196	196	NUM
ejpam-3347	58	19	using	use	VERB
ejpam-3347	58	20	the	the	DET
ejpam-3347	58	21	above	above	ADJ
ejpam-3347	58	22	relation	relation	NOUN
ejpam-3347	58	23	(	(	PUNCT
ejpam-3347	58	24	4	4	NUM
ejpam-3347	58	25	)	)	PUNCT
ejpam-3347	58	26	(	(	PUNCT
ejpam-3347	58	27	positiveness	positiveness	NOUN
ejpam-3347	58	28	of	of	ADP
ejpam-3347	58	29	the	the	DET
ejpam-3347	58	30	volume	volume	NOUN
ejpam-3347	58	31	of	of	ADP
ejpam-3347	58	32	any	any	DET
ejpam-3347	58	33	hyper	hyper	NOUN
ejpam-3347	58	34	-	-	NOUN
ejpam-3347	58	35	rectangle	rectangle	NOUN
ejpam-3347	58	36	of	of	ADP
ejpam-3347	58	37	r̄n	r̄n	NOUN
ejpam-3347	58	38	)	)	PUNCT
ejpam-3347	59	1	barro	barro	PROPN
ejpam-3347	59	2	et	et	PROPN
ejpam-3347	59	3	all.(2012	all.(2012	PROPN
ejpam-3347	59	4	)	)	PUNCT
ejpam-3347	59	5	provide	provide	VERB
ejpam-3347	59	6	the	the	DET
ejpam-3347	59	7	following	follow	VERB
ejpam-3347	59	8	result	result	NOUN
ejpam-3347	59	9	by	by	ADP
ejpam-3347	59	10	extending	extend	VERB
ejpam-3347	59	11	a	a	DET
ejpam-3347	59	12	proposition	proposition	NOUN
ejpam-3347	59	13	of	of	ADP
ejpam-3347	59	14	patton	patton	PROPN
ejpam-3347	59	15	(	(	PUNCT
ejpam-3347	59	16	2002	2002	NUM
ejpam-3347	59	17	)	)	PUNCT
ejpam-3347	59	18	both	both	PRON
ejpam-3347	59	19	to	to	ADP
ejpam-3347	59	20	space	space	NOUN
ejpam-3347	59	21	-	-	PUNCT
ejpam-3347	59	22	varying	vary	VERB
ejpam-3347	59	23	case	case	NOUN
ejpam-3347	59	24	and	and	CCONJ
ejpam-3347	59	25	to	to	ADP
ejpam-3347	59	26	higher	high	ADJ
ejpam-3347	59	27	dimensional	dimensional	ADJ
ejpam-3347	59	28	framework	framework	NOUN
ejpam-3347	59	29	.	.	PUNCT
ejpam-3347	60	1	proposition	proposition	NOUN
ejpam-3347	60	2	1	1	NUM
ejpam-3347	60	3	.	.	PUNCT
ejpam-3347	61	1	let	let	VERB
ejpam-3347	61	2	ft	ft	PRON
ejpam-3347	61	3	,	,	PUNCT
ejpam-3347	61	4	wt	wt	PROPN
ejpam-3347	61	5	denote	denote	VERB
ejpam-3347	61	6	the	the	DET
ejpam-3347	61	7	joint	joint	ADJ
ejpam-3347	61	8	distribution	distribution	NOUN
ejpam-3347	61	9	of	of	ADP
ejpam-3347	61	10	(	(	PUNCT
ejpam-3347	61	11	x̃t	x̃t	PROPN
ejpam-3347	61	12	,	,	PUNCT
ejpam-3347	61	13	n−1,wt	n−1,wt	NOUN
ejpam-3347	61	14	)	)	PUNCT
ejpam-3347	61	15	,	,	PUNCT
ejpam-3347	61	16	t	t	PROPN
ejpam-3347	61	17	∈	∈	PROPN
ejpam-3347	61	18	t	t	PROPN
ejpam-3347	61	19	with	with	ADP
ejpam-3347	61	20	x̃t	x̃t	PROPN
ejpam-3347	61	21	,	,	PUNCT
ejpam-3347	61	22	n−1	n−1	PROPN
ejpam-3347	61	23	=	=	SYM
ejpam-3347	61	24	(	(	PUNCT
ejpam-3347	61	25	xt,1	xt,1	PROPN
ejpam-3347	61	26	,	,	PUNCT
ejpam-3347	61	27	...	...	PUNCT
ejpam-3347	61	28	,	,	PUNCT
ejpam-3347	61	29	xt	xt	X
ejpam-3347	61	30	,	,	PUNCT
ejpam-3347	61	31	n−1	n−1	PROPN
ejpam-3347	61	32	)	)	PUNCT
ejpam-3347	61	33	,	,	PUNCT
ejpam-3347	61	34	then	then	ADV
ejpam-3347	61	35	the	the	DET
ejpam-3347	61	36	conditional	conditional	ADJ
ejpam-3347	61	37	time	time	NOUN
ejpam-3347	61	38	-	-	PUNCT
ejpam-3347	61	39	varying	vary	VERB
ejpam-3347	61	40	distribution	distribution	NOUN
ejpam-3347	61	41	of	of	ADP
ejpam-3347	61	42	(	(	PUNCT
ejpam-3347	61	43	x̃t	x̃t	PROPN
ejpam-3347	61	44	,	,	PUNCT
ejpam-3347	61	45	n−1,wt	n−1,wt	NOUN
ejpam-3347	61	46	)	)	PUNCT
ejpam-3347	61	47	is	be	AUX
ejpam-3347	61	48	given	give	VERB
ejpam-3347	61	49	,	,	PUNCT
ejpam-3347	61	50	for	for	ADP
ejpam-3347	61	51	all	all	DET
ejpam-3347	61	52	ỹt	ỹt	PROPN
ejpam-3347	61	53	∈	∈	PROPN
ejpam-3347	61	54	(	(	PUNCT
ejpam-3347	61	55	r̄	r̄	NOUN
ejpam-3347	61	56	)	)	PUNCT
ejpam-3347	61	57	n−1	n−1	PROPN
ejpam-3347	61	58	by	by	ADP
ejpam-3347	61	59	ht	ht	PROPN
ejpam-3347	61	60	,	,	PUNCT
ejpam-3347	61	61	wt	wt	PROPN
ejpam-3347	61	62	(	(	PUNCT
ejpam-3347	61	63	xt	xt	NOUN
ejpam-3347	61	64	/	/	SYM
ejpam-3347	61	65	wt	wt	NOUN
ejpam-3347	61	66	)	)	PUNCT
ejpam-3347	61	67	=	=	SYM
ejpam-3347	61	68	f−1	f−1	PROPN
ejpam-3347	61	69	w	w	ADP
ejpam-3347	61	70	(	(	PUNCT
ejpam-3347	61	71	wt	wt	NOUN
ejpam-3347	61	72	)	)	PUNCT
ejpam-3347	61	73	∂ht	∂ht	NOUN
ejpam-3347	61	74	,	,	PUNCT
ejpam-3347	61	75	wt	wt	INTJ
ejpam-3347	61	76	(	(	PUNCT
ejpam-3347	61	77	xt,1	xt,1	PROPN
ejpam-3347	61	78	,	,	PUNCT
ejpam-3347	61	79	...	...	PUNCT
ejpam-3347	61	80	,	,	PUNCT
ejpam-3347	61	81	xt	xt	X
ejpam-3347	61	82	,	,	PUNCT
ejpam-3347	61	83	n−1	n−1	PROPN
ejpam-3347	61	84	,	,	PUNCT
ejpam-3347	61	85	wt	wt	NOUN
ejpam-3347	61	86	)	)	PUNCT
ejpam-3347	61	87	∂wt	∂wt	PROPN
ejpam-3347	61	88	(	(	PUNCT
ejpam-3347	61	89	5	5	NUM
ejpam-3347	61	90	)	)	PUNCT
ejpam-3347	61	91	where	where	SCONJ
ejpam-3347	61	92	fw	fw	PROPN
ejpam-3347	61	93	is	be	AUX
ejpam-3347	61	94	the	the	DET
ejpam-3347	61	95	spacial	spacial	ADJ
ejpam-3347	61	96	density	density	NOUN
ejpam-3347	61	97	of	of	ADP
ejpam-3347	61	98	the	the	DET
ejpam-3347	61	99	law	law	NOUN
ejpam-3347	61	100	of	of	ADP
ejpam-3347	61	101	wt	wt	PROPN
ejpam-3347	61	102	.	.	PUNCT
ejpam-3347	62	1	moreover	moreover	ADV
ejpam-3347	62	2	,	,	PUNCT
ejpam-3347	62	3	the	the	DET
ejpam-3347	62	4	following	follow	VERB
ejpam-3347	62	5	properties	property	NOUN
ejpam-3347	62	6	are	be	AUX
ejpam-3347	62	7	satisfied	satisfied	ADJ
ejpam-3347	62	8	(	(	PUNCT
ejpam-3347	62	9	i	i	NOUN
ejpam-3347	62	10	)	)	PUNCT
ejpam-3347	62	11	ht	ht	PROPN
ejpam-3347	62	12	,	,	PUNCT
ejpam-3347	62	13	wt	wt	PROPN
ejpam-3347	62	14	(	(	PUNCT
ejpam-3347	62	15	xt,1	xt,1	PROPN
ejpam-3347	62	16	,	,	PUNCT
ejpam-3347	62	17	...	...	PUNCT
ejpam-3347	62	18	,	,	PUNCT
ejpam-3347	62	19	−∞	−∞	NOUN
ejpam-3347	62	20	,	,	PUNCT
ejpam-3347	62	21	...	...	PUNCT
ejpam-3347	62	22	,	,	PUNCT
ejpam-3347	62	23	xt	xt	X
ejpam-3347	62	24	,	,	PUNCT
ejpam-3347	62	25	n−1	n−1	PROPN
ejpam-3347	62	26	,	,	PUNCT
ejpam-3347	62	27	wt	wt	NOUN
ejpam-3347	62	28	)	)	PUNCT
ejpam-3347	62	29	=	=	SYM
ejpam-3347	62	30	0	0	NUM
ejpam-3347	62	31	for	for	ADP
ejpam-3347	62	32	all	all	DET
ejpam-3347	62	33	ỹt	ỹt	PROPN
ejpam-3347	62	34	∈	∈	PROPN
ejpam-3347	62	35	(	(	PUNCT
ejpam-3347	62	36	r̄	r̄	NOUN
ejpam-3347	62	37	)	)	PUNCT
ejpam-3347	62	38	n−1	n−1	PROPN
ejpam-3347	62	39	.	.	PUNCT
ejpam-3347	63	1	(	(	PUNCT
ejpam-3347	63	2	ii	ii	NOUN
ejpam-3347	63	3	)	)	PUNCT
ejpam-3347	63	4	h	h	NOUN
ejpam-3347	63	5	(	(	PUNCT
ejpam-3347	63	6	∞	∞	PROPN
ejpam-3347	63	7	,	,	PUNCT
ejpam-3347	63	8	...	...	PUNCT
ejpam-3347	63	9	,	,	PUNCT
ejpam-3347	63	10	∞/wt	∞/wt	PROPN
ejpam-3347	63	11	)	)	PUNCT
ejpam-3347	64	1	=	=	SYM
ejpam-3347	64	2	1	1	NUM
ejpam-3347	64	3	for	for	ADP
ejpam-3347	64	4	all	all	DET
ejpam-3347	64	5	ỹt	ỹt	PROPN
ejpam-3347	64	6	∈	∈	PROPN
ejpam-3347	64	7	(	(	PUNCT
ejpam-3347	64	8	r̄	r̄	NOUN
ejpam-3347	64	9	)	)	PUNCT
ejpam-3347	64	10	n−1	n−1	PROPN
ejpam-3347	64	11	.	.	PUNCT
ejpam-3347	65	1	(	(	PUNCT
ejpam-3347	65	2	iii	iii	NOUN
ejpam-3347	65	3	)	)	PUNCT
ejpam-3347	65	4	for	for	ADP
ejpam-3347	65	5	all	all	DET
ejpam-3347	65	6	x̃	x̃	PROPN
ejpam-3347	65	7	(	(	PUNCT
ejpam-3347	65	8	1	1	X
ejpam-3347	65	9	)	)	PUNCT
ejpam-3347	65	10	t	t	NOUN
ejpam-3347	65	11	=	=	SYM
ejpam-3347	66	1	(	(	PUNCT
ejpam-3347	66	2	x	x	SYM
ejpam-3347	66	3	(	(	PUNCT
ejpam-3347	66	4	1	1	NUM
ejpam-3347	66	5	)	)	PUNCT
ejpam-3347	66	6	t,1	t,1	NOUN
ejpam-3347	66	7	,	,	PUNCT
ejpam-3347	66	8	...	...	PUNCT
ejpam-3347	66	9	,	,	PUNCT
ejpam-3347	66	10	x	x	X
ejpam-3347	66	11	(	(	PUNCT
ejpam-3347	66	12	1	1	X
ejpam-3347	66	13	)	)	PUNCT
ejpam-3347	66	14	t	t	PROPN
ejpam-3347	66	15	,	,	PUNCT
ejpam-3347	66	16	n−1	n−1	PROPN
ejpam-3347	66	17	)	)	PUNCT
ejpam-3347	66	18	∈	∈	PROPN
ejpam-3347	66	19	(	(	PUNCT
ejpam-3347	66	20	r̄	r̄	NOUN
ejpam-3347	66	21	)	)	PUNCT
ejpam-3347	66	22	n−1	n−1	PROPN
ejpam-3347	66	23	and	and	CCONJ
ejpam-3347	66	24	ỹ	ỹ	PROPN
ejpam-3347	66	25	(	(	PUNCT
ejpam-3347	66	26	1	1	NUM
ejpam-3347	66	27	)	)	PUNCT
ejpam-3347	66	28	t	t	NOUN
ejpam-3347	67	1	=	=	SYM
ejpam-3347	67	2	(	(	PUNCT
ejpam-3347	67	3	x	x	X
ejpam-3347	67	4	(	(	PUNCT
ejpam-3347	67	5	2	2	NUM
ejpam-3347	67	6	)	)	PUNCT
ejpam-3347	67	7	t,1	t,1	NOUN
ejpam-3347	67	8	,	,	PUNCT
ejpam-3347	67	9	...	...	PUNCT
ejpam-3347	67	10	,	,	PUNCT
ejpam-3347	67	11	x	x	X
ejpam-3347	67	12	(	(	PUNCT
ejpam-3347	67	13	2	2	X
ejpam-3347	67	14	)	)	PUNCT
ejpam-3347	67	15	t	t	PROPN
ejpam-3347	67	16	,	,	PUNCT
ejpam-3347	67	17	n−1	n−1	PROPN
ejpam-3347	67	18	)	)	PUNCT
ejpam-3347	67	19	∈	∈	PROPN
ejpam-3347	67	20	(	(	PUNCT
ejpam-3347	67	21	r̄	r̄	NOUN
ejpam-3347	67	22	)	)	PUNCT
ejpam-3347	67	23	n−1	n−1	PROPN
ejpam-3347	67	24	such	such	ADJ
ejpam-3347	67	25	as	as	ADP
ejpam-3347	67	26	x	x	X
ejpam-3347	67	27	(	(	PUNCT
ejpam-3347	67	28	1	1	NUM
ejpam-3347	67	29	)	)	PUNCT
ejpam-3347	67	30	t	t	PROPN
ejpam-3347	67	31	,	,	PUNCT
ejpam-3347	67	32	j	j	PROPN
ejpam-3347	67	33	≤	≤	NUM
ejpam-3347	67	34	x	x	SYM
ejpam-3347	67	35	(	(	PUNCT
ejpam-3347	67	36	2	2	NUM
ejpam-3347	67	37	)	)	PUNCT
ejpam-3347	67	38	t	t	PROPN
ejpam-3347	67	39	,	,	PUNCT
ejpam-3347	67	40	j	j	PROPN
ejpam-3347	67	41	then	then	ADV
ejpam-3347	67	42	∑	∑	INTJ
ejpam-3347	67	43	(	(	PUNCT
ejpam-3347	67	44	i1,	i1,	NOUN
ejpam-3347	67	45	...	...	PUNCT
ejpam-3347	67	46	,in)∈{1,2}n	,in)∈{1,2}n	PUNCT
ejpam-3347	67	47	(	(	PUNCT
ejpam-3347	67	48	−1	−1	NOUN
ejpam-3347	67	49	)	)	PUNCT
ejpam-3347	67	50	[	[	PUNCT
ejpam-3347	67	51	j=1]n	j=1]n	NUM
ejpam-3347	67	52	∑	∑	PROPN
ejpam-3347	67	53	jj	jj	PROPN
ejpam-3347	67	54	hn−1,wt	hn−1,wt	PROPN
ejpam-3347	67	55	(	(	PUNCT
ejpam-3347	67	56	x	x	X
ejpam-3347	67	57	(	(	PUNCT
ejpam-3347	67	58	i1	i1	PROPN
ejpam-3347	67	59	)	)	PUNCT
ejpam-3347	67	60	t,1	t,1	NOUN
ejpam-3347	67	61	,	,	PUNCT
ejpam-3347	67	62	...	...	PUNCT
ejpam-3347	67	63	,	,	PUNCT
ejpam-3347	67	64	x	x	X
ejpam-3347	67	65	(	(	PUNCT
ejpam-3347	67	66	in−1	in−1	ADJ
ejpam-3347	67	67	)	)	PUNCT
ejpam-3347	67	68	t	t	PROPN
ejpam-3347	67	69	,	,	PUNCT
ejpam-3347	67	70	n−1	n−1	PROPN
ejpam-3347	67	71	,	,	PUNCT
ejpam-3347	67	72	wt	wt	PROPN
ejpam-3347	67	73	)	)	PUNCT
ejpam-3347	67	74	≥	≥	NOUN
ejpam-3347	67	75	0	0	NUM
ejpam-3347	67	76	.	.	PUNCT
ejpam-3347	68	1	(	(	PUNCT
ejpam-3347	68	2	6	6	X
ejpam-3347	68	3	)	)	PUNCT
ejpam-3347	68	4	let	let	VERB
ejpam-3347	68	5	’s	’s	NOUN
ejpam-3347	68	6	consider	consider	VERB
ejpam-3347	68	7	a	a	DET
ejpam-3347	68	8	linear	linear	ADJ
ejpam-3347	68	9	portfolio	portfolio	NOUN
ejpam-3347	68	10	of	of	ADP
ejpam-3347	68	11	consisting	consist	VERB
ejpam-3347	68	12	of	of	ADP
ejpam-3347	68	13	n	n	CCONJ
ejpam-3347	68	14	different	different	ADJ
ejpam-3347	68	15	financial	financial	ADJ
ejpam-3347	68	16	instruments	instrument	NOUN
ejpam-3347	68	17	(	(	PUNCT
ejpam-3347	68	18	risks	risk	NOUN
ejpam-3347	68	19	,	,	PUNCT
ejpam-3347	68	20	actions	action	NOUN
ejpam-3347	68	21	)	)	PUNCT
ejpam-3347	68	22	x	x	X
ejpam-3347	69	1	=	=	PUNCT
ejpam-3347	69	2	(	(	PUNCT
ejpam-3347	69	3	x1	x1	PROPN
ejpam-3347	69	4	,	,	PUNCT
ejpam-3347	69	5	...	...	PUNCT
ejpam-3347	69	6	,	,	PUNCT
ejpam-3347	69	7	xn	xn	PROPN
ejpam-3347	69	8	)	)	PUNCT
ejpam-3347	69	9	.	.	PUNCT
ejpam-3347	70	1	further	far	ADV
ejpam-3347	70	2	,	,	PUNCT
ejpam-3347	70	3	let	let	VERB
ejpam-3347	70	4	p0	p0	NOUN
ejpam-3347	70	5	=	=	SYM
ejpam-3347	70	6	(	(	PUNCT
ejpam-3347	70	7	p0,1	p0,1	PROPN
ejpam-3347	70	8	,	,	PUNCT
ejpam-3347	70	9	...	...	PUNCT
ejpam-3347	70	10	,	,	PUNCT
ejpam-3347	70	11	p0,n	p0,n	PROPN
ejpam-3347	70	12	)	)	PUNCT
ejpam-3347	70	13	the	the	DET
ejpam-3347	70	14	initial	initial	ADJ
ejpam-3347	70	15	value	value	NOUN
ejpam-3347	70	16	of	of	ADP
ejpam-3347	70	17	the	the	DET
ejpam-3347	70	18	portfolio	portfolio	NOUN
ejpam-3347	70	19	is	be	AUX
ejpam-3347	70	20	given	give	VERB
ejpam-3347	70	21	by	by	ADP
ejpam-3347	70	22	v0	v0	NOUN
ejpam-3347	70	23	=	=	PUNCT
ejpam-3347	70	24	[	[	PUNCT
ejpam-3347	70	25	i=	i=	PROPN
ejpam-3347	70	26	1]n	1]n	NUM
ejpam-3347	70	27	∑	∑	PUNCT
ejpam-3347	70	28	xip0,i	xip0,i	PROPN
ejpam-3347	70	29	for	for	ADP
ejpam-3347	70	30	a	a	DET
ejpam-3347	70	31	realization	realization	NOUN
ejpam-3347	70	32	x	x	PUNCT
ejpam-3347	70	33	=	=	SYM
ejpam-3347	70	34	(	(	PUNCT
ejpam-3347	70	35	x1	x1	PROPN
ejpam-3347	70	36	,	,	PUNCT
ejpam-3347	70	37	...	...	PUNCT
ejpam-3347	70	38	,	,	PUNCT
ejpam-3347	70	39	xn	xn	PROPN
ejpam-3347	70	40	)	)	PUNCT
ejpam-3347	70	41	of	of	ADP
ejpam-3347	70	42	x.	x.	NOUN
ejpam-3347	70	43	at	at	ADP
ejpam-3347	70	44	the	the	DET
ejpam-3347	70	45	next	next	ADJ
ejpam-3347	70	46	date	date	NOUN
ejpam-3347	70	47	t	t	X
ejpam-3347	70	48	the	the	DET
ejpam-3347	70	49	uncertain	uncertain	ADJ
ejpam-3347	70	50	profit	profit	NOUN
ejpam-3347	70	51	and	and	CCONJ
ejpam-3347	70	52	loss	loss	NOUN
ejpam-3347	70	53	function	function	NOUN
ejpam-3347	70	54	of	of	ADP
ejpam-3347	70	55	the	the	DET
ejpam-3347	70	56	portfolio	portfolio	NOUN
ejpam-3347	70	57	is	be	AUX
ejpam-3347	70	58	given	give	VERB
ejpam-3347	70	59	by	by	ADP
ejpam-3347	70	60	ft	ft	X
ejpam-3347	70	61	(	(	PUNCT
ejpam-3347	70	62	x1	x1	PROPN
ejpam-3347	70	63	,	,	PUNCT
ejpam-3347	70	64	...	...	PUNCT
ejpam-3347	70	65	,	,	PUNCT
ejpam-3347	70	66	xn	xn	PROPN
ejpam-3347	70	67	)	)	PUNCT
ejpam-3347	71	1	=	=	PRON
ejpam-3347	71	2	[	[	PUNCT
ejpam-3347	71	3	i=1]n	i=1]n	NOUN
ejpam-3347	71	4	∑	∑	PROPN
ejpam-3347	71	5	xi	xi	X
ejpam-3347	71	6	(	(	PUNCT
ejpam-3347	71	7	p0,i	p0,i	PROPN
ejpam-3347	71	8	−	−	PROPN
ejpam-3347	71	9	pt	pt	PROPN
ejpam-3347	71	10	,	,	PUNCT
ejpam-3347	71	11	i	i	NOUN
ejpam-3347	71	12	)	)	PUNCT
ejpam-3347	71	13	=	=	PUNCT
ejpam-3347	72	1	[	[	PUNCT
ejpam-3347	72	2	i=1]n	i=1]n	NOUN
ejpam-3347	72	3	∑	∑	SYM
ejpam-3347	72	4	xipt	xipt	PROPN
ejpam-3347	72	5	,	,	PUNCT
ejpam-3347	72	6	i	i	PRON
ejpam-3347	72	7	(	(	PUNCT
ejpam-3347	72	8	ezt	ezt	PROPN
ejpam-3347	72	9	,	,	PUNCT
ejpam-3347	72	10	i	i	PRON
ejpam-3347	72	11	−	−	PROPN
ejpam-3347	72	12	1	1	NUM
ejpam-3347	72	13	)	)	PUNCT
ejpam-3347	72	14	.	.	PUNCT
ejpam-3347	73	1	(	(	PUNCT
ejpam-3347	73	2	7	7	X
ejpam-3347	73	3	)	)	PUNCT
ejpam-3347	73	4	where	where	SCONJ
ejpam-3347	73	5	zt	zt	PROPN
ejpam-3347	73	6	=	=	PRON
ejpam-3347	73	7	(	(	PUNCT
ejpam-3347	73	8	zt	zt	PROPN
ejpam-3347	73	9	,	,	PUNCT
ejpam-3347	73	10	i	i	PRON
ejpam-3347	73	11	,	,	PUNCT
ejpam-3347	73	12	...	...	PUNCT
ejpam-3347	73	13	,	,	PUNCT
ejpam-3347	73	14	zt	zt	PROPN
ejpam-3347	73	15	,	,	PUNCT
ejpam-3347	73	16	n	n	CCONJ
ejpam-3347	73	17	)	)	PUNCT
ejpam-3347	73	18	is	be	AUX
ejpam-3347	73	19	the	the	DET
ejpam-3347	73	20	log	log	NOUN
ejpam-3347	73	21	price	price	NOUN
ejpam-3347	73	22	vector	vector	NOUN
ejpam-3347	73	23	such	such	ADJ
ejpam-3347	73	24	as	as	ADP
ejpam-3347	73	25	zt	zt	PROPN
ejpam-3347	73	26	,	,	PUNCT
ejpam-3347	73	27	i	i	PROPN
ejpam-3347	73	28	=	=	NOUN
ejpam-3347	73	29	logpt	logpt	NOUN
ejpam-3347	73	30	,	,	PUNCT
ejpam-3347	73	31	i	i	PRON
ejpam-3347	73	32	.	.	PUNCT
ejpam-3347	74	1	particularly	particularly	ADV
ejpam-3347	74	2	,	,	PUNCT
ejpam-3347	74	3	from	from	ADP
ejpam-3347	74	4	the	the	DET
ejpam-3347	74	5	integral	integral	ADJ
ejpam-3347	74	6	probability	probability	NOUN
ejpam-3347	74	7	transforms	transform	VERB
ejpam-3347	74	8	we	we	PRON
ejpam-3347	74	9	can	can	AUX
ejpam-3347	74	10	associate	associate	VERB
ejpam-3347	74	11	to	to	ADP
ejpam-3347	74	12	ft	ft	PRON
ejpam-3347	74	13	,	,	PUNCT
ejpam-3347	74	14	a	a	DET
ejpam-3347	74	15	parametric	parametric	ADJ
ejpam-3347	74	16	copula	copula	NOUN
ejpam-3347	74	17	ct	ct	PRON
ejpam-3347	74	18	such	such	ADJ
ejpam-3347	74	19	as	as	ADP
ejpam-3347	74	20	,	,	PUNCT
ejpam-3347	74	21	for	for	ADP
ejpam-3347	74	22	all	all	DET
ejpam-3347	74	23	(	(	PUNCT
ejpam-3347	74	24	ut,1	ut,1	PROPN
ejpam-3347	74	25	,	,	PUNCT
ejpam-3347	74	26	...	...	PUNCT
ejpam-3347	74	27	,	,	PUNCT
ejpam-3347	74	28	ut	ut	PROPN
ejpam-3347	74	29	,	,	PUNCT
ejpam-3347	74	30	n	n	CCONJ
ejpam-3347	74	31	)	)	PUNCT
ejpam-3347	74	32	∈	∈	PROPN
ejpam-3347	75	1	[	[	X
ejpam-3347	75	2	0	0	NUM
ejpam-3347	75	3	,	,	PUNCT
ejpam-3347	75	4	1]n	1]n	NUM
ejpam-3347	75	5	,	,	PUNCT
ejpam-3347	75	6	ct	ct	PROPN
ejpam-3347	75	7	(	(	PUNCT
ejpam-3347	75	8	ut,1	ut,1	PROPN
ejpam-3347	75	9	,	,	PUNCT
ejpam-3347	75	10	...	...	PUNCT
ejpam-3347	75	11	,	,	PUNCT
ejpam-3347	75	12	ut	ut	PROPN
ejpam-3347	75	13	,	,	PUNCT
ejpam-3347	75	14	n	n	CCONJ
ejpam-3347	75	15	)	)	PUNCT
ejpam-3347	76	1	=	=	SYM
ejpam-3347	76	2	p	p	X
ejpam-3347	76	3	(	(	PUNCT
ejpam-3347	76	4	ft,1	ft,1	PROPN
ejpam-3347	76	5	(	(	PUNCT
ejpam-3347	76	6	x1	x1	PROPN
ejpam-3347	76	7	)	)	PUNCT
ejpam-3347	76	8	≤	≤	NOUN
ejpam-3347	76	9	ut,1	ut,1	PROPN
ejpam-3347	76	10	,	,	PUNCT
ejpam-3347	76	11	...	...	PUNCT
ejpam-3347	76	12	,	,	PUNCT
ejpam-3347	76	13	ft	ft	PROPN
ejpam-3347	76	14	,	,	PUNCT
ejpam-3347	76	15	n	n	CCONJ
ejpam-3347	76	16	(	(	PUNCT
ejpam-3347	76	17	xn	xn	PROPN
ejpam-3347	76	18	)	)	PUNCT
ejpam-3347	76	19	≤	≤	NUM
ejpam-3347	76	20	ut	ut	PROPN
ejpam-3347	76	21	,	,	PUNCT
ejpam-3347	76	22	n	n	CCONJ
ejpam-3347	76	23	)	)	PUNCT
ejpam-3347	76	24	(	(	PUNCT
ejpam-3347	76	25	8)	8)	NUM
ejpam-3347	76	26	2.2	2.2	NUM
ejpam-3347	76	27	.	.	PUNCT
ejpam-3347	76	28	scalar	scalar	ADJ
ejpam-3347	76	29	product	product	NOUN
ejpam-3347	76	30	and	and	CCONJ
ejpam-3347	76	31	copulas	copula	NOUN
ejpam-3347	76	32	application	application	NOUN
ejpam-3347	76	33	on	on	ADP
ejpam-3347	76	34	var	var	NOUN
ejpam-3347	76	35	according	accord	VERB
ejpam-3347	76	36	to	to	ADP
ejpam-3347	76	37	karl	karl	PROPN
ejpam-3347	76	38	friedrich	friedrich	PROPN
ejpam-3347	76	39	siburg	siburg	PROPN
ejpam-3347	76	40	et	et	PROPN
ejpam-3347	76	41	al	al	PROPN
ejpam-3347	76	42	.	.	PUNCT
ejpam-3347	77	1	(	(	PUNCT
ejpam-3347	77	2	1975	1975	NUM
ejpam-3347	77	3	)	)	PUNCT
ejpam-3347	77	4	,	,	PUNCT
ejpam-3347	77	5	the	the	DET
ejpam-3347	77	6	restrictions	restriction	NOUN
ejpam-3347	77	7	of	of	ADP
ejpam-3347	77	8	〈	〈	PROPN
ejpam-3347	77	9	,	,	PUNCT
ejpam-3347	77	10	〉	〉	PROPN
ejpam-3347	77	11	,	,	PUNCT
ejpam-3347	77	12	‖‖	‖‖	NOUN
ejpam-3347	77	13	and	and	CCONJ
ejpam-3347	77	14	d	d	X
ejpam-3347	77	15	to	to	ADP
ejpam-3347	77	16	cn	cn	PROPN
ejpam-3347	77	17	are	be	AUX
ejpam-3347	77	18	called	call	VERB
ejpam-3347	77	19	the	the	DET
ejpam-3347	77	20	sobolev	sobolev	NOUN
ejpam-3347	77	21	scalar	scalar	ADJ
ejpam-3347	77	22	product	product	NOUN
ejpam-3347	77	23	,	,	PUNCT
ejpam-3347	77	24	the	the	DET
ejpam-3347	77	25	sobolev	sobolev	NOUN
ejpam-3347	77	26	norm	norm	NOUN
ejpam-3347	77	27	and	and	CCONJ
ejpam-3347	77	28	the	the	DET
ejpam-3347	77	29	sobolev	sobolev	NOUN
ejpam-3347	77	30	distance	distance	NOUN
ejpam-3347	77	31	function	function	NOUN
ejpam-3347	77	32	on	on	ADP
ejpam-3347	77	33	cn	cn	PROPN
ejpam-3347	77	34	,	,	PUNCT
ejpam-3347	77	35	respectively	respectively	ADV
ejpam-3347	77	36	.	.	PUNCT
ejpam-3347	78	1	but	but	CCONJ
ejpam-3347	78	2	we	we	PRON
ejpam-3347	78	3	suppose	suppose	VERB
ejpam-3347	78	4	a	a	DET
ejpam-3347	78	5	new	new	ADJ
ejpam-3347	78	6	norm	norm	NOUN
ejpam-3347	78	7	in	in	ADP
ejpam-3347	78	8	a	a	DET
ejpam-3347	78	9	space	space	NOUN
ejpam-3347	78	10	a	a	DET
ejpam-3347	78	11	euclidean	euclidean	ADJ
ejpam-3347	78	12	vector	vector	NOUN
ejpam-3347	78	13	space	space	NOUN
ejpam-3347	78	14	is	be	AUX
ejpam-3347	78	15	a	a	DET
ejpam-3347	78	16	prehilbert	prehilbert	ADJ
ejpam-3347	78	17	space	space	NOUN
ejpam-3347	78	18	of	of	ADP
ejpam-3347	78	19	finite	finite	ADJ
ejpam-3347	78	20	dimension	dimension	NOUN
ejpam-3347	78	21	.	.	PUNCT
ejpam-3347	79	1	it	it	PRON
ejpam-3347	79	2	is	be	AUX
ejpam-3347	79	3	complete	complete	ADJ
ejpam-3347	79	4	.	.	PUNCT
ejpam-3347	80	1	v.	v.	PROPN
ejpam-3347	80	2	y.	y.	PROPN
ejpam-3347	80	3	b.	b.	PROPN
ejpam-3347	81	1	loyara	loyara	PROPN
ejpam-3347	81	2	,	,	PUNCT
ejpam-3347	81	3	d.	d.	PROPN
ejpam-3347	81	4	barro	barro	PROPN
ejpam-3347	81	5	/	/	SYM
ejpam-3347	81	6	eur	eur	PROPN
ejpam-3347	81	7	.	.	PUNCT
ejpam-3347	82	1	j.	j.	PROPN
ejpam-3347	82	2	pure	pure	PROPN
ejpam-3347	82	3	appl	appl	PROPN
ejpam-3347	82	4	.	.	PROPN
ejpam-3347	82	5	math	math	PROPN
ejpam-3347	82	6	,	,	PUNCT
ejpam-3347	82	7	12	12	NUM
ejpam-3347	82	8	(	(	PUNCT
ejpam-3347	82	9	1	1	NUM
ejpam-3347	82	10	)	)	PUNCT
ejpam-3347	82	11	(	(	PUNCT
ejpam-3347	82	12	2019	2019	NUM
ejpam-3347	82	13	)	)	PUNCT
ejpam-3347	82	14	,	,	PUNCT
ejpam-3347	82	15	194	194	NUM
ejpam-3347	82	16	-	-	SYM
ejpam-3347	82	17	207	207	NUM
ejpam-3347	82	18	197	197	NUM
ejpam-3347	82	19	definition	definition	NOUN
ejpam-3347	82	20	1	1	NUM
ejpam-3347	82	21	.	.	PUNCT
ejpam-3347	82	22	consider	consider	VERB
ejpam-3347	82	23	e	e	PROPN
ejpam-3347	82	24	=	=	PROPN
ejpam-3347	82	25	rn	rn	PROPN
ejpam-3347	82	26	a	a	DET
ejpam-3347	82	27	vector	vector	NOUN
ejpam-3347	82	28	space	space	NOUN
ejpam-3347	82	29	with	with	ADP
ejpam-3347	82	30	the	the	DET
ejpam-3347	82	31	scalar	scalar	ADJ
ejpam-3347	82	32	product	product	NOUN
ejpam-3347	82	33	〈	〈	PROPN
ejpam-3347	82	34	,	,	PUNCT
ejpam-3347	82	35	〉	〉	PROPN
ejpam-3347	82	36	.	.	PUNCT
ejpam-3347	83	1	in	in	ADP
ejpam-3347	83	2	the	the	DET
ejpam-3347	83	3	following	following	NOUN
ejpam-3347	83	4	we	we	PRON
ejpam-3347	83	5	consider	consider	VERB
ejpam-3347	83	6	ourselves	ourselves	PRON
ejpam-3347	83	7	in	in	ADP
ejpam-3347	83	8	finite	finite	ADJ
ejpam-3347	83	9	dimension	dimension	NOUN
ejpam-3347	83	10	and	and	CCONJ
ejpam-3347	83	11	(	(	PUNCT
ejpam-3347	83	12	e	e	NOUN
ejpam-3347	83	13	,	,	PUNCT
ejpam-3347	83	14	〈	〈	PROPN
ejpam-3347	83	15	,	,	PUNCT
ejpam-3347	83	16	〉	〉	PROPN
ejpam-3347	83	17	)	)	PUNCT
ejpam-3347	83	18	is	be	AUX
ejpam-3347	83	19	euclidean	euclidean	ADJ
ejpam-3347	83	20	space	space	NOUN
ejpam-3347	83	21	.	.	PUNCT
ejpam-3347	84	1	the	the	DET
ejpam-3347	84	2	application	application	NOUN
ejpam-3347	84	3	x	x	PUNCT
ejpam-3347	84	4	7−→	7−→	NOUN
ejpam-3347	84	5	‖x‖	‖x‖	PROPN
ejpam-3347	84	6	=	=	PUNCT
ejpam-3347	84	7	√	√	ADP
ejpam-3347	84	8	〈	〈	PROPN
ejpam-3347	84	9	x	x	X
ejpam-3347	84	10	,	,	PUNCT
ejpam-3347	84	11	x	x	SYM
ejpam-3347	84	12	〉	〉	NOUN
ejpam-3347	84	13	defines	define	VERB
ejpam-3347	84	14	on	on	ADP
ejpam-3347	84	15	e	e	PROPN
ejpam-3347	84	16	a	a	DET
ejpam-3347	84	17	norm	norm	NOUN
ejpam-3347	84	18	,	,	PUNCT
ejpam-3347	84	19	called	call	VERB
ejpam-3347	84	20	euclidean	euclidean	ADJ
ejpam-3347	84	21	norm	norm	NOUN
ejpam-3347	84	22	and	and	CCONJ
ejpam-3347	84	23	noted	note	VERB
ejpam-3347	84	24	‖‖.	‖‖.	PUNCT
ejpam-3347	84	25	∀	∀	PUNCT
ejpam-3347	84	26	(	(	PUNCT
ejpam-3347	84	27	x	x	X
ejpam-3347	84	28	,	,	PUNCT
ejpam-3347	84	29	y	y	NOUN
ejpam-3347	84	30	)	)	PUNCT
ejpam-3347	84	31	∈	∈	PROPN
ejpam-3347	84	32	e2	e2	PROPN
ejpam-3347	84	33	we	we	PRON
ejpam-3347	84	34	have	have	VERB
ejpam-3347	84	35	:	:	PUNCT
ejpam-3347	84	36	•	•	NUM
ejpam-3347	84	37	cauchy	cauchy	PROPN
ejpam-3347	84	38	-	-	PUNCT
ejpam-3347	84	39	schwartz	schwartz	PROPN
ejpam-3347	84	40	inequality	inequality	NOUN
ejpam-3347	84	41	:	:	PUNCT
ejpam-3347	84	42	|〈x	|〈x	NOUN
ejpam-3347	84	43	,	,	PUNCT
ejpam-3347	85	1	y〉|	y〉|	NOUN
ejpam-3347	85	2	≤	≤	PUNCT
ejpam-3347	86	1	‖x‖	‖x‖	VERB
ejpam-3347	86	2	‖y‖	‖y‖	PROPN
ejpam-3347	86	3	(	(	PUNCT
ejpam-3347	86	4	9	9	NUM
ejpam-3347	86	5	)	)	PUNCT
ejpam-3347	86	6	•	•	NOUN
ejpam-3347	86	7	cauchy	cauchy	PROPN
ejpam-3347	86	8	-	-	PUNCT
ejpam-3347	86	9	schwartz	schwartz	NOUN
ejpam-3347	86	10	equality	equality	NOUN
ejpam-3347	86	11	(	(	PUNCT
ejpam-3347	86	12	in	in	ADP
ejpam-3347	86	13	the	the	DET
ejpam-3347	86	14	case	case	NOUN
ejpam-3347	86	15	where	where	SCONJ
ejpam-3347	86	16	(	(	PUNCT
ejpam-3347	86	17	x	x	NOUN
ejpam-3347	86	18	,	,	PUNCT
ejpam-3347	86	19	y	y	NOUN
ejpam-3347	86	20	)	)	PUNCT
ejpam-3347	86	21	do	do	AUX
ejpam-3347	86	22	not	not	PART
ejpam-3347	86	23	form	form	VERB
ejpam-3347	86	24	a	a	DET
ejpam-3347	86	25	free	free	ADJ
ejpam-3347	86	26	family	family	NOUN
ejpam-3347	86	27	):	):	PUNCT
ejpam-3347	86	28	|〈x	|〈x	NOUN
ejpam-3347	86	29	,	,	PUNCT
ejpam-3347	86	30	y〉|	y〉|	X
ejpam-3347	87	1	=	=	PUNCT
ejpam-3347	88	1	‖x‖	‖x‖	PROPN
ejpam-3347	88	2	‖y‖	‖y‖	PROPN
ejpam-3347	88	3	(	(	PUNCT
ejpam-3347	88	4	10	10	NUM
ejpam-3347	88	5	)	)	PUNCT
ejpam-3347	88	6	•	•	NUM
ejpam-3347	88	7	polarization	polarization	NOUN
ejpam-3347	88	8	identity	identity	NOUN
ejpam-3347	88	9	:	:	PUNCT
ejpam-3347	88	10	〈	〈	PROPN
ejpam-3347	88	11	x	x	X
ejpam-3347	88	12	,	,	PUNCT
ejpam-3347	88	13	y	y	PROPN
ejpam-3347	88	14	〉	〉	NUM
ejpam-3347	88	15	=	=	SYM
ejpam-3347	88	16	1	1	NUM
ejpam-3347	88	17	4	4	NUM
ejpam-3347	88	18	(	(	PUNCT
ejpam-3347	88	19	‖x+	‖x+	PROPN
ejpam-3347	88	20	y‖2	y‖2	PROPN
ejpam-3347	88	21	+	+	CCONJ
ejpam-3347	88	22	‖x−	‖x−	PROPN
ejpam-3347	88	23	y‖2	y‖2	PROPN
ejpam-3347	88	24	)	)	PUNCT
ejpam-3347	88	25	(	(	PUNCT
ejpam-3347	88	26	11	11	NUM
ejpam-3347	88	27	)	)	PUNCT
ejpam-3347	88	28	in	in	ADP
ejpam-3347	88	29	euclidean	euclidean	ADJ
ejpam-3347	88	30	space	space	NOUN
ejpam-3347	88	31	there	there	PRON
ejpam-3347	88	32	is	be	VERB
ejpam-3347	88	33	an	an	DET
ejpam-3347	88	34	orthogonal	orthogonal	ADJ
ejpam-3347	88	35	basis	basis	NOUN
ejpam-3347	88	36	and	and	CCONJ
ejpam-3347	88	37	the	the	DET
ejpam-3347	88	38	gram	gram	NOUN
ejpam-3347	88	39	-	-	PUNCT
ejpam-3347	88	40	schimdt	schimdt	NOUN
ejpam-3347	88	41	process	process	NOUN
ejpam-3347	88	42	allows	allow	VERB
ejpam-3347	88	43	to	to	PART
ejpam-3347	88	44	build	build	VERB
ejpam-3347	88	45	it	it	PRON
ejpam-3347	88	46	.	.	PUNCT
ejpam-3347	89	1	in	in	ADP
ejpam-3347	89	2	a	a	DET
ejpam-3347	89	3	euclidean	euclidean	ADJ
ejpam-3347	89	4	space	space	NOUN
ejpam-3347	89	5	,	,	PUNCT
ejpam-3347	89	6	any	any	DET
ejpam-3347	89	7	orthogonal	orthogonal	ADJ
ejpam-3347	89	8	family	family	NOUN
ejpam-3347	89	9	can	can	AUX
ejpam-3347	89	10	be	be	AUX
ejpam-3347	89	11	completed	complete	VERB
ejpam-3347	89	12	in	in	ADP
ejpam-3347	89	13	an	an	DET
ejpam-3347	89	14	orthogonal	orthogonal	ADJ
ejpam-3347	89	15	basis	basis	NOUN
ejpam-3347	89	16	.	.	PUNCT
ejpam-3347	90	1	let	let	VERB
ejpam-3347	90	2	an	an	DET
ejpam-3347	90	3	orthogonal	orthogonal	ADJ
ejpam-3347	90	4	base	base	NOUN
ejpam-3347	90	5	of	of	ADP
ejpam-3347	90	6	a	a	DET
ejpam-3347	90	7	euclidean	euclidean	ADJ
ejpam-3347	90	8	vector	vector	NOUN
ejpam-3347	90	9	space	space	NOUN
ejpam-3347	90	10	(	(	PUNCT
ejpam-3347	90	11	e	e	NOUN
ejpam-3347	90	12	,	,	PUNCT
ejpam-3347	90	13	〈	〈	PROPN
ejpam-3347	90	14	,	,	PUNCT
ejpam-3347	90	15	〉	〉	PROPN
ejpam-3347	90	16	)	)	PUNCT
ejpam-3347	90	17	and	and	CCONJ
ejpam-3347	90	18	u	u	PRON
ejpam-3347	90	19	an	an	DET
ejpam-3347	90	20	endomorphism	endomorphism	NOUN
ejpam-3347	90	21	from	from	ADP
ejpam-3347	90	22	e	e	NOUN
ejpam-3347	90	23	:	:	PUNCT
ejpam-3347	90	24	3	3	X
ejpam-3347	90	25	.	.	X
ejpam-3347	90	26	main	main	ADJ
ejpam-3347	90	27	results	result	NOUN
ejpam-3347	90	28	let	let	VERB
ejpam-3347	90	29	’s	’s	NOUN
ejpam-3347	90	30	consider	consider	VERB
ejpam-3347	90	31	a	a	DET
ejpam-3347	90	32	linear	linear	ADJ
ejpam-3347	90	33	portfolio	portfolio	NOUN
ejpam-3347	90	34	of	of	ADP
ejpam-3347	90	35	consisting	consist	VERB
ejpam-3347	90	36	of	of	ADP
ejpam-3347	90	37	n	n	CCONJ
ejpam-3347	90	38	different	different	ADJ
ejpam-3347	90	39	financial	financial	ADJ
ejpam-3347	90	40	instruments	instrument	NOUN
ejpam-3347	90	41	(	(	PUNCT
ejpam-3347	90	42	risks	risk	NOUN
ejpam-3347	90	43	,	,	PUNCT
ejpam-3347	90	44	actions	action	NOUN
ejpam-3347	90	45	)	)	PUNCT
ejpam-3347	90	46	x	x	X
ejpam-3347	91	1	=	=	PUNCT
ejpam-3347	92	1	(	(	PUNCT
ejpam-3347	92	2	x1	x1	PROPN
ejpam-3347	92	3	,	,	PUNCT
ejpam-3347	92	4	...	...	PUNCT
ejpam-3347	92	5	,	,	PUNCT
ejpam-3347	92	6	xn	xn	PROPN
ejpam-3347	92	7	)	)	PUNCT
ejpam-3347	93	1	and	and	CCONJ
ejpam-3347	93	2	let	let	VERB
ejpam-3347	93	3	pt	pt	X
ejpam-3347	93	4	=	=	SYM
ejpam-3347	93	5	(	(	PUNCT
ejpam-3347	93	6	p1,t	p1,t	PROPN
ejpam-3347	93	7	,	,	PUNCT
ejpam-3347	93	8	p2,t	p2,t	PROPN
ejpam-3347	93	9	,	,	PUNCT
ejpam-3347	93	10	...	...	PUNCT
ejpam-3347	93	11	,	,	PUNCT
ejpam-3347	93	12	pn	pn	PROPN
ejpam-3347	93	13	,	,	PUNCT
ejpam-3347	93	14	t	t	PROPN
ejpam-3347	93	15	)	)	PUNCT
ejpam-3347	93	16	at	at	ADP
ejpam-3347	93	17	a	a	DET
ejpam-3347	93	18	given	give	VERB
ejpam-3347	93	19	date	date	NOUN
ejpam-3347	93	20	measured	measure	VERB
ejpam-3347	93	21	at	at	ADP
ejpam-3347	93	22	given	give	VERB
ejpam-3347	93	23	time	time	NOUN
ejpam-3347	93	24	t.	t.	NOUN
ejpam-3347	93	25	further	far	ADV
ejpam-3347	93	26	,	,	PUNCT
ejpam-3347	93	27	let	let	VERB
ejpam-3347	93	28	p0	p0	NOUN
ejpam-3347	93	29	=	=	SYM
ejpam-3347	93	30	(	(	PUNCT
ejpam-3347	93	31	p0,1	p0,1	PROPN
ejpam-3347	93	32	,	,	PUNCT
ejpam-3347	93	33	...	...	PUNCT
ejpam-3347	93	34	,	,	PUNCT
ejpam-3347	93	35	p0,n	p0,n	PROPN
ejpam-3347	93	36	)	)	PUNCT
ejpam-3347	93	37	the	the	DET
ejpam-3347	93	38	initial	initial	ADJ
ejpam-3347	93	39	value	value	NOUN
ejpam-3347	93	40	of	of	ADP
ejpam-3347	93	41	the	the	DET
ejpam-3347	93	42	portfolio	portfolio	NOUN
ejpam-3347	93	43	is	be	AUX
ejpam-3347	93	44	given	give	VERB
ejpam-3347	93	45	by	by	ADP
ejpam-3347	93	46	v0	v0	NOUN
ejpam-3347	93	47	=	=	PUNCT
ejpam-3347	93	48	[	[	PUNCT
ejpam-3347	93	49	i=	i=	PROPN
ejpam-3347	93	50	1]n	1]n	NUM
ejpam-3347	93	51	∑	∑	PUNCT
ejpam-3347	93	52	xip0,i	xip0,i	PROPN
ejpam-3347	93	53	for	for	ADP
ejpam-3347	93	54	a	a	DET
ejpam-3347	93	55	realization	realization	NOUN
ejpam-3347	93	56	x	x	PUNCT
ejpam-3347	93	57	=	=	SYM
ejpam-3347	93	58	(	(	PUNCT
ejpam-3347	93	59	x1	x1	PROPN
ejpam-3347	93	60	,	,	PUNCT
ejpam-3347	93	61	...	...	PUNCT
ejpam-3347	93	62	,	,	PUNCT
ejpam-3347	93	63	xn	xn	PROPN
ejpam-3347	93	64	)	)	PUNCT
ejpam-3347	93	65	of	of	ADP
ejpam-3347	93	66	x.	x.	PROPN
ejpam-3347	93	67	pt	pt	PROPN
ejpam-3347	94	1	=	=	SYM
ejpam-3347	94	2	(	(	PUNCT
ejpam-3347	94	3	p1,t	p1,t	PROPN
ejpam-3347	94	4	,	,	PUNCT
ejpam-3347	94	5	...	...	PUNCT
ejpam-3347	94	6	,	,	PUNCT
ejpam-3347	94	7	pn	pn	PROPN
ejpam-3347	94	8	,	,	PUNCT
ejpam-3347	94	9	t	t	PROPN
ejpam-3347	94	10	)	)	PUNCT
ejpam-3347	94	11	=	=	PUNCT
ejpam-3347	95	1	[	[	PUNCT
ejpam-3347	95	2	i=1]n	i=1]n	NOUN
ejpam-3347	95	3	∑	∑	ADP
ejpam-3347	95	4	〈	〈	PROPN
ejpam-3347	95	5	pi	pi	NOUN
ejpam-3347	95	6	,	,	PUNCT
ejpam-3347	95	7	t	t	PROPN
ejpam-3347	95	8	,	,	PUNCT
ejpam-3347	95	9	ei	ei	PROPN
ejpam-3347	95	10	〉	〉	PROPN
ejpam-3347	95	11	ei	ei	NOUN
ejpam-3347	95	12	,	,	PUNCT
ejpam-3347	95	13	and	and	CCONJ
ejpam-3347	95	14	‖pt‖	‖pt‖	PROPN
ejpam-3347	95	15	=	=	PUNCT
ejpam-3347	95	16	√	√	NUM
ejpam-3347	95	17	[	[	PUNCT
ejpam-3347	95	18	i=1]n	i=1]n	NOUN
ejpam-3347	95	19	∑	∑	PUNCT
ejpam-3347	95	20	p2	p2	PROPN
ejpam-3347	95	21	i	i	PROPN
ejpam-3347	95	22	,	,	PUNCT
ejpam-3347	95	23	t	t	PROPN
ejpam-3347	95	24	=	=	SYM
ejpam-3347	95	25	√	√	PROPN
ejpam-3347	95	26	[	[	PUNCT
ejpam-3347	95	27	i=1]n	i=1]n	NOUN
ejpam-3347	95	28	∑	∑	ADP
ejpam-3347	95	29	〈	〈	PROPN
ejpam-3347	95	30	pt	pt	NOUN
ejpam-3347	95	31	,	,	PUNCT
ejpam-3347	95	32	ei〉2	ei〉2	PROPN
ejpam-3347	95	33	.	.	PUNCT
ejpam-3347	96	1	consider	consider	VERB
ejpam-3347	96	2	pt	pt	NOUN
ejpam-3347	96	3	=	=	SYM
ejpam-3347	96	4	(	(	PUNCT
ejpam-3347	96	5	p1,te	p1,te	PROPN
ejpam-3347	96	6	zt,1	zt,1	PROPN
ejpam-3347	96	7	,	,	PUNCT
ejpam-3347	96	8	...	...	PUNCT
ejpam-3347	96	9	,	,	PUNCT
ejpam-3347	96	10	pn	pn	PROPN
ejpam-3347	96	11	,	,	PUNCT
ejpam-3347	96	12	te	te	PROPN
ejpam-3347	96	13	zn,1	zn,1	PROPN
ejpam-3347	96	14	)	)	PUNCT
ejpam-3347	97	1	=	=	PUNCT
ejpam-3347	97	2	[	[	PUNCT
ejpam-3347	97	3	i=1]n	i=1]n	NOUN
ejpam-3347	97	4	∑	∑	ADP
ejpam-3347	97	5	〈	〈	PROPN
ejpam-3347	97	6	pi	pi	NOUN
ejpam-3347	97	7	,	,	PUNCT
ejpam-3347	97	8	tezt	tezt	ADJ
ejpam-3347	97	9	,	,	PUNCT
ejpam-3347	97	10	i	i	PRON
ejpam-3347	97	11	,	,	PUNCT
ejpam-3347	97	12	ei	ei	PROPN
ejpam-3347	97	13	〉	〉	PROPN
ejpam-3347	97	14	ei	ei	NOUN
ejpam-3347	97	15	,	,	PUNCT
ejpam-3347	97	16	and	and	CCONJ
ejpam-3347	97	17	‖pt‖	‖pt‖	PROPN
ejpam-3347	97	18	=	=	PUNCT
ejpam-3347	97	19	√	√	NUM
ejpam-3347	97	20	[	[	PUNCT
ejpam-3347	97	21	i=1]n	i=1]n	NOUN
ejpam-3347	97	22	∑	∑	PUNCT
ejpam-3347	97	23	p2	p2	PROPN
ejpam-3347	98	1	i	i	PRON
ejpam-3347	98	2	,	,	PUNCT
ejpam-3347	98	3	te	te	PROPN
ejpam-3347	98	4	2zt	2zt	NOUN
ejpam-3347	98	5	,	,	PUNCT
ejpam-3347	99	1	i	i	PRON
ejpam-3347	99	2	=	=	PUNCT
ejpam-3347	99	3	√	√	PROPN
ejpam-3347	99	4	[	[	PUNCT
ejpam-3347	99	5	i=1]n	i=1]n	NOUN
ejpam-3347	99	6	∑	∑	ADP
ejpam-3347	99	7	〈	〈	PROPN
ejpam-3347	99	8	pt	pt	NOUN
ejpam-3347	99	9	,	,	PUNCT
ejpam-3347	99	10	ei〉2	ei〉2	PROPN
ejpam-3347	99	11	.	.	PUNCT
ejpam-3347	100	1	the	the	DET
ejpam-3347	100	2	concept	concept	NOUN
ejpam-3347	100	3	of	of	ADP
ejpam-3347	100	4	scalar	scalar	ADJ
ejpam-3347	100	5	product	product	NOUN
ejpam-3347	100	6	that	that	PRON
ejpam-3347	100	7	allowed	allow	VERB
ejpam-3347	100	8	us	we	PRON
ejpam-3347	100	9	to	to	PART
ejpam-3347	100	10	highlight	highlight	VERB
ejpam-3347	100	11	a	a	DET
ejpam-3347	100	12	link	link	NOUN
ejpam-3347	100	13	between	between	ADP
ejpam-3347	100	14	the	the	DET
ejpam-3347	100	15	conditional	conditional	ADJ
ejpam-3347	100	16	copula	copula	NOUN
ejpam-3347	100	17	and	and	CCONJ
ejpam-3347	100	18	the	the	DET
ejpam-3347	100	19	notion	notion	NOUN
ejpam-3347	100	20	of	of	ADP
ejpam-3347	100	21	norms	norm	NOUN
ejpam-3347	100	22	in	in	ADP
ejpam-3347	100	23	the	the	DET
ejpam-3347	100	24	metric	metric	ADJ
ejpam-3347	100	25	spaces	space	NOUN
ejpam-3347	100	26	.	.	PUNCT
ejpam-3347	101	1	let	let	AUX
ejpam-3347	101	2	assume	assume	VERB
ejpam-3347	101	3	that	that	SCONJ
ejpam-3347	101	4	we	we	PRON
ejpam-3347	101	5	are	be	AUX
ejpam-3347	101	6	in	in	ADP
ejpam-3347	101	7	an	an	DET
ejpam-3347	101	8	euclidean	euclidean	ADJ
ejpam-3347	101	9	space	space	NOUN
ejpam-3347	101	10	and	and	CCONJ
ejpam-3347	101	11	that	that	SCONJ
ejpam-3347	101	12	all	all	DET
ejpam-3347	101	13	necessary	necessary	ADJ
ejpam-3347	101	14	conditions	condition	NOUN
ejpam-3347	101	15	are	be	AUX
ejpam-3347	101	16	fulfilled	fulfil	VERB
ejpam-3347	101	17	.	.	PUNCT
ejpam-3347	102	1	we	we	PRON
ejpam-3347	102	2	use	use	VERB
ejpam-3347	102	3	the	the	DET
ejpam-3347	102	4	characteristic	characteristic	ADJ
ejpam-3347	102	5	elements	element	NOUN
ejpam-3347	102	6	of	of	ADP
ejpam-3347	102	7	metric	metric	ADJ
ejpam-3347	102	8	spaces	space	NOUN
ejpam-3347	102	9	(	(	PUNCT
ejpam-3347	102	10	euclidean	euclidean	ADJ
ejpam-3347	102	11	space	space	NOUN
ejpam-3347	102	12	)	)	PUNCT
ejpam-3347	102	13	,	,	PUNCT
ejpam-3347	102	14	to	to	PART
ejpam-3347	102	15	establish	establish	VERB
ejpam-3347	102	16	with	with	ADP
ejpam-3347	102	17	the	the	DET
ejpam-3347	102	18	notion	notion	NOUN
ejpam-3347	102	19	of	of	ADP
ejpam-3347	102	20	scalar	scalar	ADJ
ejpam-3347	102	21	product	product	NOUN
ejpam-3347	102	22	or	or	CCONJ
ejpam-3347	102	23	norm	norm	VERB
ejpam-3347	102	24	a	a	DET
ejpam-3347	102	25	relation	relation	NOUN
ejpam-3347	102	26	between	between	ADP
ejpam-3347	102	27	the	the	DET
ejpam-3347	102	28	var	var	NOUN
ejpam-3347	102	29	and	and	CCONJ
ejpam-3347	102	30	the	the	DET
ejpam-3347	102	31	conditional	conditional	ADJ
ejpam-3347	102	32	time	time	NOUN
ejpam-3347	102	33	-	-	PUNCT
ejpam-3347	102	34	dependent	dependent	ADJ
ejpam-3347	102	35	copula	copula	NOUN
ejpam-3347	102	36	.	.	PUNCT
ejpam-3347	103	1	v.	v.	PROPN
ejpam-3347	103	2	y.	y.	PROPN
ejpam-3347	103	3	b.	b.	PROPN
ejpam-3347	104	1	loyara	loyara	PROPN
ejpam-3347	104	2	,	,	PUNCT
ejpam-3347	104	3	d.	d.	PROPN
ejpam-3347	104	4	barro	barro	PROPN
ejpam-3347	104	5	/	/	SYM
ejpam-3347	104	6	eur	eur	PROPN
ejpam-3347	104	7	.	.	PUNCT
ejpam-3347	105	1	j.	j.	PROPN
ejpam-3347	105	2	pure	pure	PROPN
ejpam-3347	105	3	appl	appl	PROPN
ejpam-3347	105	4	.	.	PROPN
ejpam-3347	105	5	math	math	PROPN
ejpam-3347	105	6	,	,	PUNCT
ejpam-3347	105	7	12	12	NUM
ejpam-3347	105	8	(	(	PUNCT
ejpam-3347	105	9	1	1	NUM
ejpam-3347	105	10	)	)	PUNCT
ejpam-3347	105	11	(	(	PUNCT
ejpam-3347	105	12	2019	2019	NUM
ejpam-3347	105	13	)	)	PUNCT
ejpam-3347	105	14	,	,	PUNCT
ejpam-3347	105	15	194	194	NUM
ejpam-3347	105	16	-	-	SYM
ejpam-3347	105	17	207	207	NUM
ejpam-3347	105	18	198	198	NUM
ejpam-3347	105	19	3.1	3.1	NUM
ejpam-3347	105	20	.	.	PUNCT
ejpam-3347	105	21	scalar	scalar	ADJ
ejpam-3347	105	22	product	product	NOUN
ejpam-3347	105	23	and	and	CCONJ
ejpam-3347	105	24	copulas	copula	NOUN
ejpam-3347	105	25	applications	application	NOUN
ejpam-3347	105	26	on	on	ADP
ejpam-3347	105	27	the	the	DET
ejpam-3347	105	28	var	var	NOUN
ejpam-3347	105	29	the	the	DET
ejpam-3347	105	30	following	follow	VERB
ejpam-3347	105	31	sub	sub	ADJ
ejpam-3347	105	32	-	-	ADJ
ejpam-3347	105	33	section	section	NOUN
ejpam-3347	105	34	proposal	proposal	NOUN
ejpam-3347	105	35	was	be	AUX
ejpam-3347	105	36	inspired	inspire	VERB
ejpam-3347	105	37	by	by	ADP
ejpam-3347	105	38	the	the	DET
ejpam-3347	105	39	gram	gram	NOUN
ejpam-3347	105	40	-	-	PUNCT
ejpam-3347	105	41	schmidt	schmidt	NOUN
ejpam-3347	105	42	process	process	NOUN
ejpam-3347	105	43	.	.	PUNCT
ejpam-3347	106	1	we	we	PRON
ejpam-3347	106	2	think	think	VERB
ejpam-3347	106	3	it	it	PRON
ejpam-3347	106	4	is	be	AUX
ejpam-3347	106	5	necessary	necessary	ADJ
ejpam-3347	106	6	to	to	PART
ejpam-3347	106	7	depend	depend	VERB
ejpam-3347	106	8	the	the	DET
ejpam-3347	106	9	proposition	proposition	NOUN
ejpam-3347	106	10	2	2	NUM
ejpam-3347	106	11	afterwards	afterwards	ADV
ejpam-3347	106	12	.	.	PUNCT
ejpam-3347	107	1	proposition	proposition	NOUN
ejpam-3347	107	2	2	2	NUM
ejpam-3347	107	3	.	.	PUNCT
ejpam-3347	108	1	let	let	VERB
ejpam-3347	108	2	e	e	PRON
ejpam-3347	108	3	be	be	AUX
ejpam-3347	108	4	a	a	DET
ejpam-3347	108	5	euclidean	euclidean	ADJ
ejpam-3347	108	6	space	space	NOUN
ejpam-3347	108	7	and	and	CCONJ
ejpam-3347	108	8	(	(	PUNCT
ejpam-3347	108	9	e1	e1	PROPN
ejpam-3347	108	10	,	,	PUNCT
ejpam-3347	108	11	...	...	PUNCT
ejpam-3347	108	12	,	,	PUNCT
ejpam-3347	108	13	en	en	X
ejpam-3347	108	14	)	)	PUNCT
ejpam-3347	108	15	be	be	AUX
ejpam-3347	108	16	a	a	DET
ejpam-3347	108	17	base	base	NOUN
ejpam-3347	108	18	of	of	ADP
ejpam-3347	108	19	e	e	NOUN
ejpam-3347	108	20	in	in	ADP
ejpam-3347	108	21	which	which	PRON
ejpam-3347	108	22	.	.	PUNCT
ejpam-3347	109	1	then	then	ADV
ejpam-3347	109	2	,	,	PUNCT
ejpam-3347	109	3	there	there	PRON
ejpam-3347	109	4	is	be	VERB
ejpam-3347	109	5	a	a	DET
ejpam-3347	109	6	only	only	ADJ
ejpam-3347	109	7	base	base	NOUN
ejpam-3347	109	8	ξ	ξ	PROPN
ejpam-3347	109	9	=	=	SYM
ejpam-3347	109	10	(	(	PUNCT
ejpam-3347	109	11	ξ1	ξ1	PROPN
ejpam-3347	109	12	,	,	PUNCT
ejpam-3347	109	13	...	...	PUNCT
ejpam-3347	109	14	,	,	PUNCT
ejpam-3347	109	15	ξn	ξn	NOUN
ejpam-3347	109	16	)	)	PUNCT
ejpam-3347	109	17	such	such	ADJ
ejpam-3347	109	18	that	that	SCONJ
ejpam-3347	109	19	;	;	PUNCT
ejpam-3347	109	20	if	if	SCONJ
ejpam-3347	109	21	v	v	NUM
ejpam-3347	109	22	aru	aru	NOUN
ejpam-3347	109	23	(	(	PUNCT
ejpam-3347	109	24	x	x	NOUN
ejpam-3347	109	25	)	)	PUNCT
ejpam-3347	109	26	=	=	SYM
ejpam-3347	109	27	(	(	PUNCT
ejpam-3347	109	28	v	v	NUM
ejpam-3347	109	29	aru1	aru1	NOUN
ejpam-3347	109	30	(	(	PUNCT
ejpam-3347	109	31	x1	x1	PROPN
ejpam-3347	109	32	)	)	PUNCT
ejpam-3347	109	33	,	,	PUNCT
ejpam-3347	109	34	...	...	PUNCT
ejpam-3347	109	35	,	,	PUNCT
ejpam-3347	109	36	v	v	ADP
ejpam-3347	109	37	arun	arun	NOUN
ejpam-3347	109	38	(	(	PUNCT
ejpam-3347	109	39	xn	xn	NOUN
ejpam-3347	109	40	)	)	PUNCT
ejpam-3347	109	41	)	)	PUNCT
ejpam-3347	110	1	=	=	PUNCT
ejpam-3347	110	2	[	[	PUNCT
ejpam-3347	110	3	i=1]n	i=1]n	NOUN
ejpam-3347	110	4	∑	∑	ADP
ejpam-3347	110	5	〈	〈	PROPN
ejpam-3347	110	6	v	v	ADJ
ejpam-3347	110	7	arui	arui	NOUN
ejpam-3347	110	8	,	,	PUNCT
ejpam-3347	110	9	ei	ei	PROPN
ejpam-3347	110	10	〉	〉	NOUN
ejpam-3347	110	11	ei	ei	X
ejpam-3347	110	12	then	then	ADV
ejpam-3347	110	13	〈	〈	PROPN
ejpam-3347	110	14	v	v	ADJ
ejpam-3347	110	15	aru	aru	NOUN
ejpam-3347	110	16	(	(	PUNCT
ejpam-3347	110	17	x	x	NOUN
ejpam-3347	110	18	)	)	PUNCT
ejpam-3347	110	19	,	,	PUNCT
ejpam-3347	110	20	ξ〉−	ξ〉−	PROPN
ejpam-3347	110	21	[	[	PUNCT
ejpam-3347	110	22	i=2]n	i=2]n	NOUN
ejpam-3347	110	23	∑v	∑v	ADJ
ejpam-3347	110	24	aruiϑi	aruiϑi	VERB
ejpam-3347	110	25	‖ϑi‖	‖ϑi‖	NOUN
ejpam-3347	110	26	=	=	SYM
ejpam-3347	110	27	v	v	NUM
ejpam-3347	110	28	aru1	aru1	PROPN
ejpam-3347	110	29	e1	e1	VERB
ejpam-3347	110	30	‖e1‖	‖e1‖	X
ejpam-3347	110	31	(	(	PUNCT
ejpam-3347	110	32	12	12	NUM
ejpam-3347	110	33	)	)	PUNCT
ejpam-3347	110	34	with	with	ADP
ejpam-3347	110	35	ξ1	ξ1	NOUN
ejpam-3347	110	36	=	=	SYM
ejpam-3347	110	37	e1	e1	PROPN
ejpam-3347	110	38	‖e1‖	‖e1‖	NOUN
ejpam-3347	110	39	and	and	CCONJ
ejpam-3347	110	40	∀i	∀i	NOUN
ejpam-3347	110	41	∈	∈	NOUN
ejpam-3347	110	42	{	{	PUNCT
ejpam-3347	110	43	1	1	NUM
ejpam-3347	110	44	,	,	PUNCT
ejpam-3347	110	45	...	...	PUNCT
ejpam-3347	110	46	,	,	PUNCT
ejpam-3347	110	47	n−	n−	NOUN
ejpam-3347	110	48	1	1	NUM
ejpam-3347	110	49	}	}	PUNCT
ejpam-3347	110	50	,	,	PUNCT
ejpam-3347	110	51	and	and	CCONJ
ejpam-3347	110	52	ξi+1	ξi+1	X
ejpam-3347	110	53	=	=	SYM
ejpam-3347	110	54	ϑi+1	ϑi+1	PRON
ejpam-3347	110	55	‖ϑi+1‖	‖ϑi+1‖	PROPN
ejpam-3347	110	56	with	with	ADP
ejpam-3347	110	57	ϑi+1	ϑi+1	PROPN
ejpam-3347	110	58	=	=	SYM
ejpam-3347	110	59	ei+1−	ei+1−	PROPN
ejpam-3347	110	60	[	[	PUNCT
ejpam-3347	110	61	k=1]i	k=1]i	X
ejpam-3347	110	62	∑	∑	ADP
ejpam-3347	110	63	〈	〈	PROPN
ejpam-3347	110	64	ei+1	ei+1	PART
ejpam-3347	110	65	,	,	PUNCT
ejpam-3347	110	66	ξk	ξk	ADP
ejpam-3347	110	67	〉	〉	PROPN
ejpam-3347	110	68	ξk	ξk	NOUN
ejpam-3347	110	69	.	.	PUNCT
ejpam-3347	111	1	proof	proof	NOUN
ejpam-3347	111	2	.	.	PUNCT
ejpam-3347	112	1	by	by	ADP
ejpam-3347	112	2	assumption	assumption	NOUN
ejpam-3347	112	3	e	e	NOUN
ejpam-3347	112	4	is	be	AUX
ejpam-3347	112	5	a	a	DET
ejpam-3347	112	6	euclidean	euclidean	ADJ
ejpam-3347	112	7	space	space	NOUN
ejpam-3347	112	8	and	and	CCONJ
ejpam-3347	112	9	let	let	AUX
ejpam-3347	112	10	(	(	PUNCT
ejpam-3347	112	11	e1	e1	NOUN
ejpam-3347	112	12	,	,	PUNCT
ejpam-3347	112	13	e2	e2	PROPN
ejpam-3347	112	14	,	,	PUNCT
ejpam-3347	112	15	...	...	PUNCT
ejpam-3347	112	16	,	,	PUNCT
ejpam-3347	112	17	en	en	X
ejpam-3347	112	18	)	)	PUNCT
ejpam-3347	112	19	be	be	AUX
ejpam-3347	112	20	a	a	DET
ejpam-3347	112	21	base	base	NOUN
ejpam-3347	112	22	of	of	ADP
ejpam-3347	112	23	e	e	NOUN
ejpam-3347	113	1	such	such	ADJ
ejpam-3347	113	2	that	that	PRON
ejpam-3347	113	3	v	v	NOUN
ejpam-3347	113	4	aru	aru	NOUN
ejpam-3347	113	5	(	(	PUNCT
ejpam-3347	113	6	x	x	NOUN
ejpam-3347	113	7	)	)	PUNCT
ejpam-3347	113	8	=	=	SYM
ejpam-3347	113	9	(	(	PUNCT
ejpam-3347	113	10	v	v	NUM
ejpam-3347	113	11	aru1	aru1	NOUN
ejpam-3347	113	12	(	(	PUNCT
ejpam-3347	113	13	x1	x1	PROPN
ejpam-3347	113	14	)	)	PUNCT
ejpam-3347	113	15	,	,	PUNCT
ejpam-3347	113	16	...	...	PUNCT
ejpam-3347	113	17	,	,	PUNCT
ejpam-3347	113	18	v	v	ADP
ejpam-3347	113	19	arun	arun	NOUN
ejpam-3347	113	20	(	(	PUNCT
ejpam-3347	113	21	xn	xn	NOUN
ejpam-3347	113	22	)	)	PUNCT
ejpam-3347	113	23	)	)	PUNCT
ejpam-3347	114	1	=	=	PUNCT
ejpam-3347	114	2	[	[	PUNCT
ejpam-3347	114	3	i=1]n	i=1]n	NOUN
ejpam-3347	114	4	∑	∑	ADP
ejpam-3347	114	5	〈	〈	PROPN
ejpam-3347	114	6	v	v	ADJ
ejpam-3347	114	7	arui	arui	NOUN
ejpam-3347	114	8	,	,	PUNCT
ejpam-3347	114	9	ei	ei	PROPN
ejpam-3347	114	10	〉	〉	PROPN
ejpam-3347	114	11	ei	ei	NOUN
ejpam-3347	114	12	.	.	PUNCT
ejpam-3347	115	1	so	so	ADV
ejpam-3347	115	2	,	,	PUNCT
ejpam-3347	115	3	it	it	PRON
ejpam-3347	115	4	follows	follow	VERB
ejpam-3347	115	5	that	that	SCONJ
ejpam-3347	115	6	,	,	PUNCT
ejpam-3347	116	1	‖v	‖v	ADJ
ejpam-3347	116	2	aru	aru	NOUN
ejpam-3347	116	3	(	(	PUNCT
ejpam-3347	116	4	x)‖	x)‖	NOUN
ejpam-3347	116	5	=	=	PUNCT
ejpam-3347	116	6	√	√	NUM
ejpam-3347	116	7	[	[	PUNCT
ejpam-3347	116	8	i=1]n	i=1]n	NOUN
ejpam-3347	116	9	∑	∑	X
ejpam-3347	116	10	v	v	ADP
ejpam-3347	116	11	ar2	ar2	PROPN
ejpam-3347	116	12	ui	ui	PROPN
ejpam-3347	116	13	=	=	PUNCT
ejpam-3347	116	14	√	√	PROPN
ejpam-3347	116	15	[	[	PUNCT
ejpam-3347	116	16	i=1]n	i=1]n	NOUN
ejpam-3347	116	17	∑	∑	ADP
ejpam-3347	116	18	〈	〈	PROPN
ejpam-3347	116	19	v	v	NUM
ejpam-3347	116	20	aru	aru	NOUN
ejpam-3347	116	21	,	,	PUNCT
ejpam-3347	116	22	ei〉2	ei〉2	VERB
ejpam-3347	116	23	the	the	DET
ejpam-3347	116	24	orthogonalization	orthogonalization	NOUN
ejpam-3347	116	25	process	process	NOUN
ejpam-3347	116	26	of	of	ADP
ejpam-3347	116	27	gram	gram	NOUN
ejpam-3347	116	28	-	-	PUNCT
ejpam-3347	116	29	schimdt	schimdt	NOUN
ejpam-3347	116	30	(	(	PUNCT
ejpam-3347	116	31	1875	1875	NUM
ejpam-3347	116	32	)	)	PUNCT
ejpam-3347	116	33	allows	allow	VERB
ejpam-3347	116	34	us	we	PRON
ejpam-3347	116	35	to	to	PART
ejpam-3347	116	36	say	say	VERB
ejpam-3347	116	37	that	that	SCONJ
ejpam-3347	116	38	there	there	PRON
ejpam-3347	116	39	is	be	VERB
ejpam-3347	116	40	only	only	ADV
ejpam-3347	116	41	one	one	NUM
ejpam-3347	116	42	base	base	NOUN
ejpam-3347	116	43	(	(	PUNCT
ejpam-3347	116	44	ξ1	ξ1	NOUN
ejpam-3347	116	45	,	,	PUNCT
ejpam-3347	116	46	...	...	PUNCT
ejpam-3347	116	47	,	,	PUNCT
ejpam-3347	116	48	ξn	ξn	PROPN
ejpam-3347	116	49	)	)	PUNCT
ejpam-3347	116	50	as	as	ADP
ejpam-3347	116	51	ξ1	ξ1	NOUN
ejpam-3347	116	52	=	=	PUNCT
ejpam-3347	116	53	e1	e1	PROPN
ejpam-3347	116	54	‖e1‖	‖e1‖	NOUN
ejpam-3347	116	55	and	and	CCONJ
ejpam-3347	116	56	∀i	∀i	NOUN
ejpam-3347	116	57	∈	∈	NOUN
ejpam-3347	116	58	{	{	PUNCT
ejpam-3347	116	59	1	1	NUM
ejpam-3347	116	60	,	,	PUNCT
ejpam-3347	116	61	...	...	PUNCT
ejpam-3347	116	62	,	,	PUNCT
ejpam-3347	116	63	n−	n−	NOUN
ejpam-3347	116	64	1	1	NUM
ejpam-3347	116	65	}	}	PUNCT
ejpam-3347	116	66	,	,	PUNCT
ejpam-3347	116	67	ξi+1	ξi+1	X
ejpam-3347	116	68	=	=	SYM
ejpam-3347	116	69	ϑi+1	ϑi+1	DET
ejpam-3347	116	70	‖ϑi+1‖	‖ϑi+1‖	PROPN
ejpam-3347	116	71	withϑi+1	withϑi+1	NOUN
ejpam-3347	116	72	=	=	SYM
ejpam-3347	116	73	ei+1−	ei+1−	PROPN
ejpam-3347	116	74	[	[	PUNCT
ejpam-3347	116	75	k=1]i	k=1]i	X
ejpam-3347	116	76	∑	∑	ADP
ejpam-3347	116	77	〈	〈	PROPN
ejpam-3347	116	78	ei+1	ei+1	PART
ejpam-3347	116	79	,	,	PUNCT
ejpam-3347	116	80	ξk	ξk	ADP
ejpam-3347	116	81	〉	〉	NOUN
ejpam-3347	116	82	ξk	ξk	NOUN
ejpam-3347	116	83	.	.	PUNCT
ejpam-3347	117	1	(	(	PUNCT
ejpam-3347	117	2	13	13	NUM
ejpam-3347	117	3	)	)	PUNCT
ejpam-3347	117	4	futhermore	futhermore	NOUN
ejpam-3347	117	5	,	,	PUNCT
ejpam-3347	117	6	it	it	PRON
ejpam-3347	117	7	comes	come	VERB
ejpam-3347	117	8	that	that	SCONJ
ejpam-3347	117	9	:	:	PUNCT
ejpam-3347	117	10	〈	〈	PROPN
ejpam-3347	117	11	v	v	ADJ
ejpam-3347	117	12	aru	aru	NOUN
ejpam-3347	117	13	(	(	PUNCT
ejpam-3347	117	14	x	x	NOUN
ejpam-3347	117	15	)	)	PUNCT
ejpam-3347	117	16	,	,	PUNCT
ejpam-3347	117	17	ξ	ξ	X
ejpam-3347	117	18	〉	〉	NUM
ejpam-3347	117	19	=	=	SYM
ejpam-3347	117	20	[	[	PUNCT
ejpam-3347	117	21	i=1]n	i=1]n	NOUN
ejpam-3347	117	22	∑	∑	NOUN
ejpam-3347	117	23	v	v	NOUN
ejpam-3347	117	24	aruiξi	aruiξi	ADJ
ejpam-3347	117	25	〈	〈	PROPN
ejpam-3347	117	26	v	v	ADJ
ejpam-3347	117	27	aru	aru	NOUN
ejpam-3347	117	28	(	(	PUNCT
ejpam-3347	117	29	x	x	NOUN
ejpam-3347	117	30	)	)	PUNCT
ejpam-3347	117	31	,	,	PUNCT
ejpam-3347	117	32	ξ〉−	ξ〉−	PROPN
ejpam-3347	117	33	[	[	PUNCT
ejpam-3347	117	34	i=2]n	i=2]n	NOUN
ejpam-3347	117	35	∑v	∑v	ADJ
ejpam-3347	117	36	aruiϑi	aruiϑi	VERB
ejpam-3347	117	37	‖ϑi‖	‖ϑi‖	NOUN
ejpam-3347	117	38	=	=	SYM
ejpam-3347	117	39	v	v	NUM
ejpam-3347	117	40	aru1	aru1	PROPN
ejpam-3347	117	41	e1	e1	NOUN
ejpam-3347	117	42	‖e1‖	‖e1‖	NOUN
ejpam-3347	117	43	let	let	VERB
ejpam-3347	117	44	’s	’s	NOUN
ejpam-3347	117	45	consider	consider	VERB
ejpam-3347	117	46	a	a	DET
ejpam-3347	117	47	linear	linear	ADJ
ejpam-3347	117	48	portfolio	portfolio	NOUN
ejpam-3347	117	49	of	of	ADP
ejpam-3347	117	50	consisting	consist	VERB
ejpam-3347	117	51	of	of	ADP
ejpam-3347	117	52	n	n	CCONJ
ejpam-3347	117	53	different	different	ADJ
ejpam-3347	117	54	financial	financial	ADJ
ejpam-3347	117	55	instruments	instrument	NOUN
ejpam-3347	117	56	(	(	PUNCT
ejpam-3347	117	57	risks	risk	NOUN
ejpam-3347	117	58	,	,	PUNCT
ejpam-3347	117	59	actions	action	NOUN
ejpam-3347	117	60	)	)	PUNCT
ejpam-3347	117	61	x	x	X
ejpam-3347	118	1	=	=	PUNCT
ejpam-3347	118	2	(	(	PUNCT
ejpam-3347	118	3	x1	x1	PROPN
ejpam-3347	118	4	,	,	PUNCT
ejpam-3347	118	5	...	...	PUNCT
ejpam-3347	118	6	,	,	PUNCT
ejpam-3347	118	7	xn	xn	PROPN
ejpam-3347	118	8	)	)	PUNCT
ejpam-3347	119	1	and	and	CCONJ
ejpam-3347	119	2	let	let	VERB
ejpam-3347	119	3	pt	pt	X
ejpam-3347	119	4	=	=	SYM
ejpam-3347	119	5	(	(	PUNCT
ejpam-3347	119	6	p1,t	p1,t	PROPN
ejpam-3347	119	7	,	,	PUNCT
ejpam-3347	119	8	p2,t	p2,t	PROPN
ejpam-3347	119	9	,	,	PUNCT
ejpam-3347	119	10	...	...	PUNCT
ejpam-3347	119	11	,	,	PUNCT
ejpam-3347	119	12	pn	pn	PROPN
ejpam-3347	119	13	,	,	PUNCT
ejpam-3347	119	14	t	t	PROPN
ejpam-3347	119	15	)	)	PUNCT
ejpam-3347	119	16	at	at	ADP
ejpam-3347	119	17	a	a	DET
ejpam-3347	119	18	given	give	VERB
ejpam-3347	119	19	date	date	NOUN
ejpam-3347	119	20	measured	measure	VERB
ejpam-3347	119	21	at	at	ADP
ejpam-3347	119	22	given	give	VERB
ejpam-3347	119	23	time	time	NOUN
ejpam-3347	119	24	t.	t.	NOUN
ejpam-3347	119	25	further	far	ADV
ejpam-3347	119	26	,	,	PUNCT
ejpam-3347	119	27	let	let	VERB
ejpam-3347	119	28	p0	p0	NOUN
ejpam-3347	119	29	=	=	SYM
ejpam-3347	119	30	(	(	PUNCT
ejpam-3347	119	31	p0,1	p0,1	PROPN
ejpam-3347	119	32	,	,	PUNCT
ejpam-3347	119	33	...	...	PUNCT
ejpam-3347	119	34	,	,	PUNCT
ejpam-3347	119	35	p0,n	p0,n	PROPN
ejpam-3347	119	36	)	)	PUNCT
ejpam-3347	119	37	the	the	DET
ejpam-3347	119	38	initial	initial	ADJ
ejpam-3347	119	39	value	value	NOUN
ejpam-3347	119	40	of	of	ADP
ejpam-3347	119	41	the	the	DET
ejpam-3347	119	42	portfolio	portfolio	NOUN
ejpam-3347	119	43	is	be	AUX
ejpam-3347	119	44	given	give	VERB
ejpam-3347	119	45	by	by	ADP
ejpam-3347	119	46	v0	v0	NOUN
ejpam-3347	119	47	=	=	PUNCT
ejpam-3347	119	48	[	[	PUNCT
ejpam-3347	119	49	i=	i=	PROPN
ejpam-3347	119	50	1]n	1]n	NUM
ejpam-3347	119	51	∑	∑	PROPN
ejpam-3347	119	52	xip0,i	xip0,i	PROPN
ejpam-3347	119	53	.	.	PUNCT
ejpam-3347	120	1	v.	v.	PROPN
ejpam-3347	120	2	y.	y.	PROPN
ejpam-3347	120	3	b.	b.	PROPN
ejpam-3347	121	1	loyara	loyara	PROPN
ejpam-3347	121	2	,	,	PUNCT
ejpam-3347	121	3	d.	d.	PROPN
ejpam-3347	121	4	barro	barro	PROPN
ejpam-3347	121	5	/	/	SYM
ejpam-3347	121	6	eur	eur	PROPN
ejpam-3347	121	7	.	.	PUNCT
ejpam-3347	122	1	j.	j.	PROPN
ejpam-3347	122	2	pure	pure	PROPN
ejpam-3347	122	3	appl	appl	PROPN
ejpam-3347	122	4	.	.	PROPN
ejpam-3347	122	5	math	math	PROPN
ejpam-3347	122	6	,	,	PUNCT
ejpam-3347	122	7	12	12	NUM
ejpam-3347	122	8	(	(	PUNCT
ejpam-3347	122	9	1	1	NUM
ejpam-3347	122	10	)	)	PUNCT
ejpam-3347	122	11	(	(	PUNCT
ejpam-3347	122	12	2019	2019	NUM
ejpam-3347	122	13	)	)	PUNCT
ejpam-3347	122	14	,	,	PUNCT
ejpam-3347	122	15	194	194	NUM
ejpam-3347	122	16	-	-	SYM
ejpam-3347	122	17	207	207	NUM
ejpam-3347	122	18	199	199	NUM
ejpam-3347	122	19	theorem	theorem	NOUN
ejpam-3347	122	20	1	1	NUM
ejpam-3347	122	21	.	.	X
ejpam-3347	123	1	for	for	ADP
ejpam-3347	123	2	a	a	DET
ejpam-3347	123	3	realization	realization	NOUN
ejpam-3347	123	4	x	x	PUNCT
ejpam-3347	123	5	=	=	SYM
ejpam-3347	123	6	(	(	PUNCT
ejpam-3347	123	7	x1	x1	PROPN
ejpam-3347	123	8	,	,	PUNCT
ejpam-3347	123	9	...	...	PUNCT
ejpam-3347	123	10	,	,	PUNCT
ejpam-3347	123	11	xn	xn	PROPN
ejpam-3347	123	12	)	)	PUNCT
ejpam-3347	123	13	of	of	ADP
ejpam-3347	123	14	x	x	PRON
ejpam-3347	123	15	,	,	PUNCT
ejpam-3347	123	16	at	at	ADP
ejpam-3347	123	17	the	the	DET
ejpam-3347	123	18	next	next	ADJ
ejpam-3347	123	19	date	date	NOUN
ejpam-3347	123	20	t	t	X
ejpam-3347	123	21	the	the	DET
ejpam-3347	123	22	uncertain	uncertain	ADJ
ejpam-3347	123	23	profit	profit	NOUN
ejpam-3347	123	24	and	and	CCONJ
ejpam-3347	123	25	loss	loss	NOUN
ejpam-3347	123	26	function	function	NOUN
ejpam-3347	123	27	of	of	ADP
ejpam-3347	123	28	the	the	DET
ejpam-3347	123	29	portfolio	portfolio	NOUN
ejpam-3347	123	30	is	be	AUX
ejpam-3347	123	31	given	give	VERB
ejpam-3347	123	32	by	by	ADP
ejpam-3347	123	33	ft	ft	X
ejpam-3347	123	34	(	(	PUNCT
ejpam-3347	123	35	x1	x1	PROPN
ejpam-3347	123	36	,	,	PUNCT
ejpam-3347	123	37	...	...	PUNCT
ejpam-3347	123	38	,	,	PUNCT
ejpam-3347	123	39	xn	xn	PROPN
ejpam-3347	123	40	)	)	PUNCT
ejpam-3347	124	1	=	=	PRON
ejpam-3347	124	2	[	[	PUNCT
ejpam-3347	124	3	i=1]n	i=1]n	NOUN
ejpam-3347	124	4	∑	∑	PROPN
ejpam-3347	124	5	xi	xi	X
ejpam-3347	124	6	(	(	PUNCT
ejpam-3347	124	7	p0,i	p0,i	PROPN
ejpam-3347	124	8	−	−	PROPN
ejpam-3347	124	9	pt	pt	PROPN
ejpam-3347	124	10	,	,	PUNCT
ejpam-3347	124	11	i	i	NOUN
ejpam-3347	124	12	)	)	PUNCT
ejpam-3347	124	13	=	=	PUNCT
ejpam-3347	125	1	[	[	PUNCT
ejpam-3347	125	2	i=1]n	i=1]n	NOUN
ejpam-3347	125	3	∑	∑	SYM
ejpam-3347	125	4	xipt	xipt	PROPN
ejpam-3347	125	5	,	,	PUNCT
ejpam-3347	125	6	i	i	PRON
ejpam-3347	125	7	(	(	PUNCT
ejpam-3347	125	8	ezt	ezt	PROPN
ejpam-3347	125	9	,	,	PUNCT
ejpam-3347	125	10	i	i	PRON
ejpam-3347	125	11	−	−	PROPN
ejpam-3347	125	12	1	1	NUM
ejpam-3347	125	13	)	)	PUNCT
ejpam-3347	125	14	;	;	PUNCT
ejpam-3347	125	15	then	then	ADV
ejpam-3347	125	16	ct	ct	PRON
ejpam-3347	125	17	(	(	PUNCT
ejpam-3347	125	18	u1	u1	PROPN
ejpam-3347	125	19	,	,	PUNCT
ejpam-3347	125	20	...	...	PUNCT
ejpam-3347	125	21	,	,	PUNCT
ejpam-3347	125	22	un	un	PROPN
ejpam-3347	125	23	)	)	PUNCT
ejpam-3347	125	24	=	=	SYM
ejpam-3347	125	25	‖v	‖v	ADJ
ejpam-3347	125	26	aru	aru	NOUN
ejpam-3347	125	27	(	(	PUNCT
ejpam-3347	125	28	x)‖	x)‖	PROPN
ejpam-3347	125	29	‖pt	‖pt	PROPN
ejpam-3347	125	30	−	−	PROPN
ejpam-3347	125	31	pt‖	pt‖	PROPN
ejpam-3347	125	32	.	.	PUNCT
ejpam-3347	126	1	(	(	PUNCT
ejpam-3347	126	2	14	14	NUM
ejpam-3347	126	3	)	)	PUNCT
ejpam-3347	126	4	furthermore	furthermore	ADV
ejpam-3347	126	5	,	,	PUNCT
ejpam-3347	126	6	ct	ct	PROPN
ejpam-3347	126	7	(	(	PUNCT
ejpam-3347	126	8	u1	u1	PROPN
ejpam-3347	126	9	,	,	PUNCT
ejpam-3347	126	10	...	...	PUNCT
ejpam-3347	126	11	,	,	PUNCT
ejpam-3347	126	12	un	un	PROPN
ejpam-3347	126	13	)	)	PUNCT
ejpam-3347	126	14	=	=	SYM
ejpam-3347	126	15	1	1	NUM
ejpam-3347	126	16	4	4	NUM
ejpam-3347	126	17	(	(	PUNCT
ejpam-3347	126	18	‖v	‖v	ADJ
ejpam-3347	126	19	aru	aru	NOUN
ejpam-3347	126	20	(	(	PUNCT
ejpam-3347	126	21	x	x	X
ejpam-3347	126	22	)	)	PUNCT
ejpam-3347	127	1	+	+	NUM
ejpam-3347	127	2	pt	pt	INTJ
ejpam-3347	127	3	−	−	PRON
ejpam-3347	127	4	pt‖2	pt‖2	NOUN
ejpam-3347	127	5	+	+	CCONJ
ejpam-3347	127	6	‖v	‖v	ADJ
ejpam-3347	127	7	aru	aru	NOUN
ejpam-3347	127	8	(	(	PUNCT
ejpam-3347	127	9	x)−	x)−	PROPN
ejpam-3347	127	10	(	(	PUNCT
ejpam-3347	127	11	pt	pt	INTJ
ejpam-3347	127	12	−	−	PROPN
ejpam-3347	127	13	pt)‖2	pt)‖2	NOUN
ejpam-3347	127	14	)	)	PUNCT
ejpam-3347	127	15	(	(	PUNCT
ejpam-3347	127	16	15	15	NUM
ejpam-3347	127	17	)	)	PUNCT
ejpam-3347	127	18	and	and	CCONJ
ejpam-3347	127	19	where	where	SCONJ
ejpam-3347	127	20	pt	pt	X
ejpam-3347	127	21	=	=	SYM
ejpam-3347	127	22	(	(	PUNCT
ejpam-3347	127	23	p1,te	p1,te	PROPN
ejpam-3347	127	24	zt,1	zt,1	PROPN
ejpam-3347	127	25	,	,	PUNCT
ejpam-3347	127	26	...	...	PUNCT
ejpam-3347	127	27	,	,	PUNCT
ejpam-3347	127	28	pn	pn	PROPN
ejpam-3347	127	29	,	,	PUNCT
ejpam-3347	127	30	te	te	PROPN
ejpam-3347	127	31	zn,1	zn,1	PROPN
ejpam-3347	127	32	)	)	PUNCT
ejpam-3347	127	33	,	,	PUNCT
ejpam-3347	127	34	v	v	X
ejpam-3347	127	35	aru	aru	NOUN
ejpam-3347	127	36	(	(	PUNCT
ejpam-3347	127	37	x	x	NOUN
ejpam-3347	127	38	)	)	PUNCT
ejpam-3347	127	39	=	=	SYM
ejpam-3347	127	40	(	(	PUNCT
ejpam-3347	127	41	v	v	NUM
ejpam-3347	127	42	aru1	aru1	NOUN
ejpam-3347	127	43	(	(	PUNCT
ejpam-3347	127	44	x1	x1	PROPN
ejpam-3347	127	45	)	)	PUNCT
ejpam-3347	127	46	,	,	PUNCT
ejpam-3347	127	47	...	...	PUNCT
ejpam-3347	127	48	,	,	PUNCT
ejpam-3347	127	49	v	v	ADP
ejpam-3347	127	50	arun	arun	NOUN
ejpam-3347	127	51	(	(	PUNCT
ejpam-3347	127	52	xn	xn	PROPN
ejpam-3347	127	53	)	)	PUNCT
ejpam-3347	127	54	)	)	PUNCT
ejpam-3347	127	55	.	.	PUNCT
ejpam-3347	127	56	is	be	AUX
ejpam-3347	127	57	a	a	DET
ejpam-3347	127	58	value	value	NOUN
ejpam-3347	127	59	at	at	ADP
ejpam-3347	127	60	risk	risk	NOUN
ejpam-3347	127	61	of	of	ADP
ejpam-3347	127	62	the	the	DET
ejpam-3347	127	63	x	x	X
ejpam-3347	127	64	and	and	CCONJ
ejpam-3347	127	65	‖·‖	‖·‖	NUM
ejpam-3347	127	66	euclidean	euclidean	ADJ
ejpam-3347	127	67	norm	norm	NOUN
ejpam-3347	127	68	and	and	CCONJ
ejpam-3347	127	69	noted	note	VERB
ejpam-3347	127	70	.	.	PUNCT
ejpam-3347	128	1	proof	proof	NOUN
ejpam-3347	128	2	.	.	PUNCT
ejpam-3347	129	1	consider	consider	VERB
ejpam-3347	129	2	the	the	DET
ejpam-3347	129	3	following	follow	VERB
ejpam-3347	129	4	relation	relation	NOUN
ejpam-3347	129	5	ct	ct	PROPN
ejpam-3347	129	6	(	(	PUNCT
ejpam-3347	129	7	u1	u1	PROPN
ejpam-3347	129	8	,	,	PUNCT
ejpam-3347	129	9	...	...	PUNCT
ejpam-3347	129	10	,	,	PUNCT
ejpam-3347	129	11	un	un	PROPN
ejpam-3347	129	12	)	)	PUNCT
ejpam-3347	129	13	=	=	SYM
ejpam-3347	129	14	fwt	fwt	PROPN
ejpam-3347	129	15	(	(	PUNCT
ejpam-3347	129	16	f	f	PROPN
ejpam-3347	129	17	(	(	PUNCT
ejpam-3347	129	18	−1	−1	NOUN
ejpam-3347	129	19	)	)	PUNCT
ejpam-3347	129	20	1,wt	1,wt	NUM
ejpam-3347	129	21	(	(	PUNCT
ejpam-3347	129	22	u1	u1	NOUN
ejpam-3347	129	23	)	)	PUNCT
ejpam-3347	129	24	,	,	PUNCT
ejpam-3347	129	25	...	...	PUNCT
ejpam-3347	129	26	,	,	PUNCT
ejpam-3347	129	27	f	f	X
ejpam-3347	129	28	(	(	PUNCT
ejpam-3347	129	29	−1	−1	NOUN
ejpam-3347	129	30	)	)	PUNCT
ejpam-3347	129	31	n	n	CCONJ
ejpam-3347	129	32	,	,	PUNCT
ejpam-3347	129	33	wt	wt	PROPN
ejpam-3347	129	34	(	(	PUNCT
ejpam-3347	129	35	un	un	PROPN
ejpam-3347	129	36	)	)	PUNCT
ejpam-3347	129	37	)	)	PUNCT
ejpam-3347	129	38	.	.	PUNCT
ejpam-3347	130	1	ff	ff	INTJ
ejpam-3347	130	2	we	we	PRON
ejpam-3347	130	3	consider	consider	VERB
ejpam-3347	130	4	relation	relation	NOUN
ejpam-3347	130	5	(	(	PUNCT
ejpam-3347	130	6	7	7	X
ejpam-3347	130	7	)	)	PUNCT
ejpam-3347	130	8	we	we	PRON
ejpam-3347	130	9	obtain	obtain	VERB
ejpam-3347	130	10	,	,	PUNCT
ejpam-3347	130	11	ct	ct	PROPN
ejpam-3347	130	12	(	(	PUNCT
ejpam-3347	130	13	u1	u1	PROPN
ejpam-3347	130	14	,	,	PUNCT
ejpam-3347	130	15	...	...	PUNCT
ejpam-3347	130	16	,	,	PUNCT
ejpam-3347	130	17	un	un	PROPN
ejpam-3347	130	18	)	)	PUNCT
ejpam-3347	130	19	=	=	PUNCT
ejpam-3347	131	1	[	[	PUNCT
ejpam-3347	131	2	i=1]n	i=1]n	NOUN
ejpam-3347	131	3	∑	∑	NOUN
ejpam-3347	131	4	v	v	ADP
ejpam-3347	131	5	arui	arui	NOUN
ejpam-3347	131	6	(	(	PUNCT
ejpam-3347	131	7	xi	xi	NOUN
ejpam-3347	131	8	)	)	PUNCT
ejpam-3347	131	9	(	(	PUNCT
ejpam-3347	131	10	pt	pt	INTJ
ejpam-3347	131	11	,	,	PUNCT
ejpam-3347	131	12	ie	ie	X
ejpam-3347	131	13	zt	zt	PROPN
ejpam-3347	131	14	,	,	PUNCT
ejpam-3347	131	15	i	i	PRON
ejpam-3347	131	16	−	−	PROPN
ejpam-3347	131	17	pt	pt	PROPN
ejpam-3347	131	18	,	,	PUNCT
ejpam-3347	131	19	i	i	NOUN
ejpam-3347	131	20	)	)	PUNCT
ejpam-3347	131	21	.	.	PUNCT
ejpam-3347	132	1	consider	consider	VERB
ejpam-3347	132	2	pt	pt	NOUN
ejpam-3347	132	3	=	=	SYM
ejpam-3347	132	4	(	(	PUNCT
ejpam-3347	132	5	p1,te	p1,te	PROPN
ejpam-3347	132	6	zt,1	zt,1	PROPN
ejpam-3347	132	7	,	,	PUNCT
ejpam-3347	132	8	...	...	PUNCT
ejpam-3347	132	9	,	,	PUNCT
ejpam-3347	132	10	pn	pn	PROPN
ejpam-3347	132	11	,	,	PUNCT
ejpam-3347	132	12	te	te	PROPN
ejpam-3347	132	13	zn,1	zn,1	PROPN
ejpam-3347	132	14	)	)	PUNCT
ejpam-3347	132	15	and	and	CCONJ
ejpam-3347	132	16	v	v	ADP
ejpam-3347	132	17	aru	aru	NOUN
ejpam-3347	132	18	(	(	PUNCT
ejpam-3347	132	19	x	x	NOUN
ejpam-3347	132	20	)	)	PUNCT
ejpam-3347	133	1	=	=	SYM
ejpam-3347	133	2	(	(	PUNCT
ejpam-3347	133	3	v	v	NUM
ejpam-3347	133	4	aru1	aru1	NOUN
ejpam-3347	133	5	(	(	PUNCT
ejpam-3347	133	6	x1	x1	PROPN
ejpam-3347	133	7	)	)	PUNCT
ejpam-3347	133	8	,	,	PUNCT
ejpam-3347	133	9	...	...	PUNCT
ejpam-3347	133	10	,	,	PUNCT
ejpam-3347	133	11	v	v	ADP
ejpam-3347	133	12	arun	arun	NOUN
ejpam-3347	133	13	(	(	PUNCT
ejpam-3347	133	14	x	x	NOUN
ejpam-3347	133	15	)	)	PUNCT
ejpam-3347	133	16	)	)	PUNCT
ejpam-3347	133	17	.	.	PUNCT
ejpam-3347	134	1	then	then	ADV
ejpam-3347	134	2	,	,	PUNCT
ejpam-3347	134	3	ct	ct	PROPN
ejpam-3347	134	4	(	(	PUNCT
ejpam-3347	134	5	u1	u1	PROPN
ejpam-3347	134	6	,	,	PUNCT
ejpam-3347	134	7	...	...	PUNCT
ejpam-3347	134	8	,	,	PUNCT
ejpam-3347	134	9	un	un	PROPN
ejpam-3347	134	10	)	)	PUNCT
ejpam-3347	134	11	=	=	PUNCT
ejpam-3347	135	1	〈	〈	PROPN
ejpam-3347	135	2	v	v	ADJ
ejpam-3347	135	3	aru	aru	NOUN
ejpam-3347	135	4	(	(	PUNCT
ejpam-3347	135	5	x	x	NOUN
ejpam-3347	135	6	)	)	PUNCT
ejpam-3347	135	7	,	,	PUNCT
ejpam-3347	135	8	pt	pt	INTJ
ejpam-3347	135	9	−	−	PROPN
ejpam-3347	135	10	pt	pt	PROPN
ejpam-3347	135	11	〉	〉	PROPN
ejpam-3347	135	12	value	value	NOUN
ejpam-3347	135	13	at	at	ADP
ejpam-3347	135	14	risk	risk	NOUN
ejpam-3347	135	15	is	be	AUX
ejpam-3347	135	16	intrinsically	intrinsically	ADV
ejpam-3347	135	17	linked	link	VERB
ejpam-3347	135	18	to	to	ADP
ejpam-3347	135	19	the	the	DET
ejpam-3347	135	20	portfolio	portfolio	NOUN
ejpam-3347	135	21	and	and	CCONJ
ejpam-3347	135	22	therefore	therefore	ADV
ejpam-3347	135	23	to	to	ADP
ejpam-3347	135	24	the	the	DET
ejpam-3347	135	25	initial	initial	ADJ
ejpam-3347	135	26	amount	amount	NOUN
ejpam-3347	135	27	and	and	CCONJ
ejpam-3347	135	28	the	the	DET
ejpam-3347	135	29	amount	amount	NOUN
ejpam-3347	135	30	at	at	ADP
ejpam-3347	135	31	a	a	DET
ejpam-3347	135	32	given	give	VERB
ejpam-3347	135	33	time	time	NOUN
ejpam-3347	135	34	t.	t.	NOUN
ejpam-3347	135	35	we	we	PRON
ejpam-3347	135	36	will	will	AUX
ejpam-3347	135	37	suppose	suppose	VERB
ejpam-3347	135	38	linked	link	VERB
ejpam-3347	135	39	vector	vector	NOUN
ejpam-3347	135	40	v	v	ADP
ejpam-3347	135	41	aru	aru	NOUN
ejpam-3347	135	42	(	(	PUNCT
ejpam-3347	135	43	x	x	NOUN
ejpam-3347	135	44	)	)	PUNCT
ejpam-3347	135	45	and	and	CCONJ
ejpam-3347	135	46	vector	vector	NOUN
ejpam-3347	135	47	pt	pt	INTJ
ejpam-3347	135	48	−	−	PROPN
ejpam-3347	135	49	pt	pt	PROPN
ejpam-3347	135	50	.	.	PUNCT
ejpam-3347	136	1	the	the	DET
ejpam-3347	136	2	relation	relation	NOUN
ejpam-3347	136	3	10	10	NUM
ejpam-3347	136	4	we	we	PRON
ejpam-3347	136	5	give	give	VERB
ejpam-3347	136	6	|〈v	|〈v	ADP
ejpam-3347	136	7	aru	aru	NOUN
ejpam-3347	136	8	(	(	PUNCT
ejpam-3347	136	9	x	x	NOUN
ejpam-3347	136	10	)	)	PUNCT
ejpam-3347	136	11	,	,	PUNCT
ejpam-3347	136	12	pt	pt	INTJ
ejpam-3347	136	13	−	−	PROPN
ejpam-3347	136	14	pt〉|	pt〉|	NOUN
ejpam-3347	136	15	=	=	SYM
ejpam-3347	136	16	‖v	‖v	NOUN
ejpam-3347	136	17	aru	aru	NOUN
ejpam-3347	136	18	(	(	PUNCT
ejpam-3347	136	19	x)‖	x)‖	PROPN
ejpam-3347	136	20	‖pt	‖pt	PROPN
ejpam-3347	136	21	−	−	PROPN
ejpam-3347	136	22	pt‖	pt‖	PROPN
ejpam-3347	136	23	.	.	PUNCT
ejpam-3347	137	1	then	then	ADV
ejpam-3347	137	2	,	,	PUNCT
ejpam-3347	137	3	ct	ct	PROPN
ejpam-3347	137	4	(	(	PUNCT
ejpam-3347	137	5	u1	u1	PROPN
ejpam-3347	137	6	,	,	PUNCT
ejpam-3347	137	7	...	...	PUNCT
ejpam-3347	137	8	,	,	PUNCT
ejpam-3347	137	9	un	un	PROPN
ejpam-3347	137	10	)	)	PUNCT
ejpam-3347	137	11	=	=	SYM
ejpam-3347	137	12	‖v	‖v	ADJ
ejpam-3347	137	13	aru	aru	NOUN
ejpam-3347	137	14	(	(	PUNCT
ejpam-3347	137	15	x)‖	x)‖	PROPN
ejpam-3347	137	16	‖pt	‖pt	PROPN
ejpam-3347	137	17	−	−	PROPN
ejpam-3347	137	18	pt‖	pt‖	NOUN
ejpam-3347	137	19	and	and	CCONJ
ejpam-3347	137	20	equality	equality	NOUN
ejpam-3347	137	21	(	(	PUNCT
ejpam-3347	137	22	11	11	NUM
ejpam-3347	137	23	)	)	PUNCT
ejpam-3347	137	24	given	give	VERB
ejpam-3347	137	25	ct	ct	PROPN
ejpam-3347	137	26	(	(	PUNCT
ejpam-3347	137	27	u1	u1	PROPN
ejpam-3347	137	28	,	,	PUNCT
ejpam-3347	137	29	...	...	PUNCT
ejpam-3347	137	30	,	,	PUNCT
ejpam-3347	137	31	un	un	PROPN
ejpam-3347	137	32	)	)	PUNCT
ejpam-3347	137	33	=	=	SYM
ejpam-3347	137	34	1	1	NUM
ejpam-3347	137	35	4	4	NUM
ejpam-3347	137	36	(	(	PUNCT
ejpam-3347	137	37	‖v	‖v	ADJ
ejpam-3347	137	38	aru	aru	NOUN
ejpam-3347	137	39	(	(	PUNCT
ejpam-3347	137	40	x	x	X
ejpam-3347	137	41	)	)	PUNCT
ejpam-3347	137	42	+	+	NUM
ejpam-3347	137	43	pt	pt	INTJ
ejpam-3347	137	44	−	−	PRON
ejpam-3347	137	45	pt‖2	pt‖2	NOUN
ejpam-3347	137	46	+	+	CCONJ
ejpam-3347	137	47	‖v	‖v	ADJ
ejpam-3347	137	48	aru	aru	NOUN
ejpam-3347	137	49	(	(	PUNCT
ejpam-3347	137	50	x)−	x)−	PROPN
ejpam-3347	137	51	(	(	PUNCT
ejpam-3347	137	52	pt	pt	INTJ
ejpam-3347	137	53	−	−	PROPN
ejpam-3347	137	54	pt)‖2	pt)‖2	NOUN
ejpam-3347	137	55	)	)	PUNCT
ejpam-3347	137	56	the	the	DET
ejpam-3347	137	57	following	follow	VERB
ejpam-3347	137	58	result	result	NOUN
ejpam-3347	137	59	allows	allow	VERB
ejpam-3347	137	60	us	we	PRON
ejpam-3347	137	61	to	to	PART
ejpam-3347	137	62	obtain	obtain	VERB
ejpam-3347	137	63	;	;	PUNCT
ejpam-3347	137	64	v.	v.	PROPN
ejpam-3347	137	65	y.	y.	PROPN
ejpam-3347	137	66	b.	b.	PROPN
ejpam-3347	138	1	loyara	loyara	PROPN
ejpam-3347	138	2	,	,	PUNCT
ejpam-3347	138	3	d.	d.	PROPN
ejpam-3347	138	4	barro	barro	PROPN
ejpam-3347	138	5	/	/	SYM
ejpam-3347	138	6	eur	eur	PROPN
ejpam-3347	138	7	.	.	PUNCT
ejpam-3347	139	1	j.	j.	PROPN
ejpam-3347	139	2	pure	pure	PROPN
ejpam-3347	139	3	appl	appl	PROPN
ejpam-3347	139	4	.	.	PROPN
ejpam-3347	139	5	math	math	PROPN
ejpam-3347	139	6	,	,	PUNCT
ejpam-3347	139	7	12	12	NUM
ejpam-3347	139	8	(	(	PUNCT
ejpam-3347	139	9	1	1	NUM
ejpam-3347	139	10	)	)	PUNCT
ejpam-3347	139	11	(	(	PUNCT
ejpam-3347	139	12	2019	2019	NUM
ejpam-3347	139	13	)	)	PUNCT
ejpam-3347	139	14	,	,	PUNCT
ejpam-3347	139	15	194	194	NUM
ejpam-3347	139	16	-	-	SYM
ejpam-3347	139	17	207	207	NUM
ejpam-3347	139	18	200	200	NUM
ejpam-3347	139	19	proposition	proposition	NOUN
ejpam-3347	139	20	3	3	NUM
ejpam-3347	139	21	.	.	PUNCT
ejpam-3347	140	1	let	let	VERB
ejpam-3347	140	2	pt	pt	X
ejpam-3347	140	3	=	=	SYM
ejpam-3347	140	4	(	(	PUNCT
ejpam-3347	140	5	p1,t	p1,t	PROPN
ejpam-3347	140	6	,	,	PUNCT
ejpam-3347	140	7	p2,t	p2,t	PROPN
ejpam-3347	140	8	,	,	PUNCT
ejpam-3347	140	9	...	...	PUNCT
ejpam-3347	140	10	,	,	PUNCT
ejpam-3347	140	11	pn	pn	PROPN
ejpam-3347	140	12	,	,	PUNCT
ejpam-3347	140	13	t	t	PROPN
ejpam-3347	140	14	)	)	PUNCT
ejpam-3347	140	15	at	at	ADP
ejpam-3347	140	16	a	a	DET
ejpam-3347	140	17	given	give	VERB
ejpam-3347	140	18	date	date	NOUN
ejpam-3347	140	19	measured	measure	VERB
ejpam-3347	140	20	at	at	ADP
ejpam-3347	140	21	given	give	VERB
ejpam-3347	140	22	time	time	NOUN
ejpam-3347	140	23	t.	t.	PROPN
ejpam-3347	140	24	and	and	CCONJ
ejpam-3347	140	25	suppose	suppose	VERB
ejpam-3347	140	26	these	these	DET
ejpam-3347	140	27	risks	risk	NOUN
ejpam-3347	140	28	represent	represent	VERB
ejpam-3347	140	29	potential	potential	ADJ
ejpam-3347	140	30	losses	loss	NOUN
ejpam-3347	140	31	in	in	ADP
ejpam-3347	140	32	dependent	dependent	ADJ
ejpam-3347	140	33	lines	line	NOUN
ejpam-3347	140	34	of	of	ADP
ejpam-3347	140	35	business	business	NOUN
ejpam-3347	140	36	for	for	ADP
ejpam-3347	140	37	example	example	NOUN
ejpam-3347	140	38	an	an	DET
ejpam-3347	140	39	insurance	insurance	NOUN
ejpam-3347	140	40	company	company	NOUN
ejpam-3347	140	41	.	.	PUNCT
ejpam-3347	141	1	then	then	ADV
ejpam-3347	141	2	c	c	X
ejpam-3347	141	3	(	(	PUNCT
ejpam-3347	141	4	u1	u1	PROPN
ejpam-3347	141	5	,	,	PUNCT
ejpam-3347	141	6	...	...	PUNCT
ejpam-3347	141	7	,	,	PUNCT
ejpam-3347	141	8	un	un	PROPN
ejpam-3347	141	9	/	/	SYM
ejpam-3347	141	10	wt	wt	NOUN
ejpam-3347	141	11	)	)	PUNCT
ejpam-3347	142	1	=	=	SYM
ejpam-3347	142	2	f−1	f−1	PROPN
ejpam-3347	142	3	w	w	ADP
ejpam-3347	142	4	(	(	PUNCT
ejpam-3347	142	5	wt	wt	NOUN
ejpam-3347	142	6	)	)	PUNCT
ejpam-3347	142	7	〈	〈	PROPN
ejpam-3347	142	8	∂	∂	NUM
ejpam-3347	142	9	∂wt	∂wt	PROPN
ejpam-3347	142	10	(	(	PUNCT
ejpam-3347	142	11	v	v	NUM
ejpam-3347	142	12	aru	aru	NOUN
ejpam-3347	142	13	(	(	PUNCT
ejpam-3347	142	14	x	x	NOUN
ejpam-3347	142	15	/	/	SYM
ejpam-3347	142	16	wt	wt	NOUN
ejpam-3347	142	17	)	)	PUNCT
ejpam-3347	142	18	)	)	PUNCT
ejpam-3347	142	19	,	,	PUNCT
ejpam-3347	142	20	(	(	PUNCT
ejpam-3347	142	21	pt	pt	INTJ
ejpam-3347	142	22	−	−	PROPN
ejpam-3347	142	23	pt	pt	PROPN
ejpam-3347	142	24	)	)	PUNCT
ejpam-3347	142	25	〉	〉	NOUN
ejpam-3347	142	26	(	(	PUNCT
ejpam-3347	142	27	16	16	NUM
ejpam-3347	142	28	)	)	PUNCT
ejpam-3347	142	29	and	and	CCONJ
ejpam-3347	142	30	where	where	SCONJ
ejpam-3347	142	31	pt	pt	X
ejpam-3347	142	32	=	=	SYM
ejpam-3347	142	33	(	(	PUNCT
ejpam-3347	142	34	p1,te	p1,te	PROPN
ejpam-3347	142	35	zt,1	zt,1	PROPN
ejpam-3347	142	36	,	,	PUNCT
ejpam-3347	142	37	...	...	PUNCT
ejpam-3347	142	38	,	,	PUNCT
ejpam-3347	142	39	pn	pn	PROPN
ejpam-3347	142	40	,	,	PUNCT
ejpam-3347	142	41	te	te	PROPN
ejpam-3347	142	42	zn,1	zn,1	PROPN
ejpam-3347	142	43	)	)	PUNCT
ejpam-3347	142	44	,	,	PUNCT
ejpam-3347	142	45	v	v	X
ejpam-3347	142	46	aru	aru	NOUN
ejpam-3347	142	47	(	(	PUNCT
ejpam-3347	142	48	x	x	NOUN
ejpam-3347	142	49	/	/	SYM
ejpam-3347	142	50	wt	wt	NOUN
ejpam-3347	142	51	)	)	PUNCT
ejpam-3347	142	52	is	be	AUX
ejpam-3347	142	53	a	a	DET
ejpam-3347	142	54	value	value	NOUN
ejpam-3347	142	55	at	at	ADP
ejpam-3347	142	56	risk	risk	NOUN
ejpam-3347	142	57	of	of	ADP
ejpam-3347	142	58	the	the	DET
ejpam-3347	142	59	x	x	PUNCT
ejpam-3347	142	60	such	such	ADJ
ejpam-3347	142	61	that	that	DET
ejpam-3347	142	62	wt	wt	NOUN
ejpam-3347	142	63	and	and	CCONJ
ejpam-3347	142	64	‖‖	‖‖	ADV
ejpam-3347	142	65	euclidean	euclidean	ADJ
ejpam-3347	142	66	norm	norm	NOUN
ejpam-3347	142	67	and	and	CCONJ
ejpam-3347	142	68	noted	note	VERB
ejpam-3347	142	69	.	.	PUNCT
ejpam-3347	143	1	proof	proof	NOUN
ejpam-3347	143	2	.	.	PUNCT
ejpam-3347	144	1	let	let	VERB
ejpam-3347	144	2	fwt	fwt	PROPN
ejpam-3347	144	3	be	be	AUX
ejpam-3347	144	4	any	any	DET
ejpam-3347	144	5	conditional	conditional	ADJ
ejpam-3347	144	6	time	time	NOUN
ejpam-3347	144	7	-	-	PUNCT
ejpam-3347	144	8	varying	vary	VERB
ejpam-3347	144	9	conditional	conditional	ADJ
ejpam-3347	144	10	distribution	distribution	NOUN
ejpam-3347	144	11	with	with	ADP
ejpam-3347	144	12	marginal	marginal	ADJ
ejpam-3347	144	13	{	{	PUNCT
ejpam-3347	144	14	fi	fi	NOUN
ejpam-3347	144	15	,	,	PUNCT
ejpam-3347	144	16	wt	wt	INTJ
ejpam-3347	144	17	;	;	PUNCT
ejpam-3347	144	18	1	1	NUM
ejpam-3347	144	19	≤	≤	NUM
ejpam-3347	144	20	i	i	PRON
ejpam-3347	144	21	≤	≤	NOUN
ejpam-3347	144	22	n	n	CCONJ
ejpam-3347	144	23	}	}	PUNCT
ejpam-3347	144	24	.	.	PUNCT
ejpam-3347	145	1	then	then	ADV
ejpam-3347	145	2	there	there	PRON
ejpam-3347	145	3	exists	exist	VERB
ejpam-3347	145	4	a	a	DET
ejpam-3347	145	5	only	only	ADJ
ejpam-3347	145	6	copula	copula	NOUN
ejpam-3347	145	7	c	c	NOUN
ejpam-3347	145	8	:	:	PUNCT
ejpam-3347	146	1	[	[	X
ejpam-3347	146	2	0	0	NUM
ejpam-3347	146	3	,	,	PUNCT
ejpam-3347	146	4	1]n	1]n	NOUN
ejpam-3347	146	5	−→	−→	ADJ
ejpam-3347	146	6	[	[	X
ejpam-3347	146	7	0	0	NUM
ejpam-3347	146	8	,	,	PUNCT
ejpam-3347	146	9	1	1	NUM
ejpam-3347	146	10	]	]	PUNCT
ejpam-3347	146	11	such	such	ADJ
ejpam-3347	146	12	as	as	ADP
ejpam-3347	146	13	c	c	PROPN
ejpam-3347	146	14	(	(	PUNCT
ejpam-3347	146	15	u1	u1	PROPN
ejpam-3347	146	16	,	,	PUNCT
ejpam-3347	146	17	...	...	PUNCT
ejpam-3347	146	18	,	,	PUNCT
ejpam-3347	146	19	un	un	PROPN
ejpam-3347	146	20	/	/	SYM
ejpam-3347	146	21	wt	wt	NOUN
ejpam-3347	146	22	)	)	PUNCT
ejpam-3347	146	23	=	=	NOUN
ejpam-3347	146	24	fwt	fwt	PROPN
ejpam-3347	146	25	(	(	PUNCT
ejpam-3347	146	26	f	f	PROPN
ejpam-3347	146	27	(	(	PUNCT
ejpam-3347	146	28	−1	−1	NOUN
ejpam-3347	146	29	)	)	PUNCT
ejpam-3347	146	30	1,wt	1,wt	NUM
ejpam-3347	146	31	(	(	PUNCT
ejpam-3347	146	32	u1	u1	PROPN
ejpam-3347	146	33	/	/	SYM
ejpam-3347	146	34	w	w	PROPN
ejpam-3347	146	35	)	)	PUNCT
ejpam-3347	146	36	,	,	PUNCT
ejpam-3347	146	37	...	...	PUNCT
ejpam-3347	146	38	,	,	PUNCT
ejpam-3347	146	39	f	f	X
ejpam-3347	146	40	(	(	PUNCT
ejpam-3347	146	41	−1	−1	NOUN
ejpam-3347	146	42	)	)	PUNCT
ejpam-3347	146	43	n	n	CCONJ
ejpam-3347	146	44	,	,	PUNCT
ejpam-3347	146	45	wt	wt	PROPN
ejpam-3347	146	46	(	(	PUNCT
ejpam-3347	146	47	un	un	PROPN
ejpam-3347	146	48	/	/	SYM
ejpam-3347	146	49	w	w	NOUN
ejpam-3347	146	50	)	)	PUNCT
ejpam-3347	146	51	)	)	PUNCT
ejpam-3347	146	52	(	(	PUNCT
ejpam-3347	146	53	17	17	NUM
ejpam-3347	146	54	)	)	PUNCT
ejpam-3347	146	55	where	where	SCONJ
ejpam-3347	146	56	f	f	PROPN
ejpam-3347	146	57	(	(	PUNCT
ejpam-3347	146	58	−1	−1	NOUN
ejpam-3347	146	59	)	)	PUNCT
ejpam-3347	146	60	i	i	PRON
ejpam-3347	146	61	,	,	PUNCT
ejpam-3347	146	62	wt	wt	PROPN
ejpam-3347	146	63	(	(	PUNCT
ejpam-3347	146	64	ui	ui	PROPN
ejpam-3347	146	65	/	/	SYM
ejpam-3347	146	66	w	w	NOUN
ejpam-3347	146	67	)	)	PUNCT
ejpam-3347	146	68	=	=	SYM
ejpam-3347	146	69	inf	inf	NOUN
ejpam-3347	146	70	{	{	PUNCT
ejpam-3347	146	71	x	x	NOUN
ejpam-3347	146	72	:	:	PUNCT
ejpam-3347	146	73	fi	fi	NOUN
ejpam-3347	146	74	,	,	PUNCT
ejpam-3347	146	75	wt	wt	INTJ
ejpam-3347	146	76	(	(	PUNCT
ejpam-3347	146	77	x	x	SYM
ejpam-3347	146	78	/	/	SYM
ejpam-3347	146	79	w	w	NOUN
ejpam-3347	146	80	)	)	PUNCT
ejpam-3347	146	81	≥	≥	NOUN
ejpam-3347	146	82	ui	ui	NOUN
ejpam-3347	146	83	}	}	PUNCT
ejpam-3347	146	84	for	for	ADP
ejpam-3347	146	85	each	each	DET
ejpam-3347	146	86	ui	ui	NOUN
ejpam-3347	146	87	and	and	CCONJ
ejpam-3347	146	88	wt	wt	PROPN
ejpam-3347	146	89	∈	∈	PROPN
ejpam-3347	146	90	wt	wt	PROPN
ejpam-3347	146	91	.	.	PUNCT
ejpam-3347	147	1	then	then	ADV
ejpam-3347	147	2	,	,	PUNCT
ejpam-3347	147	3	it	it	PRON
ejpam-3347	147	4	follows	follow	VERB
ejpam-3347	147	5	that	that	PRON
ejpam-3347	147	6	:	:	PUNCT
ejpam-3347	148	1	c	c	X
ejpam-3347	148	2	(	(	PUNCT
ejpam-3347	148	3	u1	u1	PROPN
ejpam-3347	148	4	,	,	PUNCT
ejpam-3347	148	5	...	...	PUNCT
ejpam-3347	148	6	,	,	PUNCT
ejpam-3347	148	7	un	un	PROPN
ejpam-3347	148	8	/	/	SYM
ejpam-3347	148	9	wt	wt	NOUN
ejpam-3347	148	10	)	)	PUNCT
ejpam-3347	148	11	=	=	PRON
ejpam-3347	148	12	∂fwt	∂fwt	NUM
ejpam-3347	148	13	(	(	PUNCT
ejpam-3347	148	14	f	f	X
ejpam-3347	148	15	(	(	PUNCT
ejpam-3347	148	16	−1	−1	NOUN
ejpam-3347	148	17	)	)	PUNCT
ejpam-3347	148	18	1,wt	1,wt	NUM
ejpam-3347	148	19	(	(	PUNCT
ejpam-3347	148	20	u1	u1	NOUN
ejpam-3347	148	21	/	/	SYM
ejpam-3347	148	22	wt	wt	NOUN
ejpam-3347	148	23	)	)	PUNCT
ejpam-3347	148	24	,	,	PUNCT
ejpam-3347	148	25	...	...	PUNCT
ejpam-3347	148	26	,	,	PUNCT
ejpam-3347	148	27	f	f	X
ejpam-3347	148	28	(	(	PUNCT
ejpam-3347	148	29	−1	−1	NOUN
ejpam-3347	148	30	)	)	PUNCT
ejpam-3347	148	31	n−1,wt	n−1,wt	NOUN
ejpam-3347	148	32	(	(	PUNCT
ejpam-3347	148	33	un−/wt	un−/wt	PROPN
ejpam-3347	148	34	)	)	PUNCT
ejpam-3347	148	35	,	,	PUNCT
ejpam-3347	148	36	wt	wt	INTJ
ejpam-3347	148	37	)	)	PUNCT
ejpam-3347	148	38	∂wt	∂wt	PROPN
ejpam-3347	148	39	.	.	PUNCT
ejpam-3347	149	1	by	by	ADP
ejpam-3347	149	2	considering	consider	VERB
ejpam-3347	149	3	the	the	DET
ejpam-3347	149	4	equality	equality	NOUN
ejpam-3347	149	5	(	(	PUNCT
ejpam-3347	149	6	7	7	NUM
ejpam-3347	149	7	)	)	PUNCT
ejpam-3347	149	8	int	int	NOUN
ejpam-3347	149	9	the	the	DET
ejpam-3347	149	10	following	follow	VERB
ejpam-3347	149	11	relation	relation	NOUN
ejpam-3347	149	12	c	c	PROPN
ejpam-3347	149	13	(	(	PUNCT
ejpam-3347	149	14	u1	u1	PROPN
ejpam-3347	149	15	,	,	PUNCT
ejpam-3347	149	16	...	...	PUNCT
ejpam-3347	149	17	,	,	PUNCT
ejpam-3347	149	18	un	un	PROPN
ejpam-3347	149	19	/	/	SYM
ejpam-3347	149	20	wt	wt	NOUN
ejpam-3347	149	21	)	)	PUNCT
ejpam-3347	149	22	=	=	NOUN
ejpam-3347	149	23	fwt	fwt	PROPN
ejpam-3347	149	24	(	(	PUNCT
ejpam-3347	149	25	f	f	PROPN
ejpam-3347	149	26	(	(	PUNCT
ejpam-3347	149	27	−1	−1	NOUN
ejpam-3347	149	28	)	)	PUNCT
ejpam-3347	149	29	1,wt	1,wt	NUM
ejpam-3347	149	30	(	(	PUNCT
ejpam-3347	149	31	u1	u1	NOUN
ejpam-3347	149	32	/	/	SYM
ejpam-3347	149	33	wt	wt	NOUN
ejpam-3347	149	34	)	)	PUNCT
ejpam-3347	149	35	,	,	PUNCT
ejpam-3347	149	36	...	...	PUNCT
ejpam-3347	149	37	,	,	PUNCT
ejpam-3347	149	38	f	f	X
ejpam-3347	149	39	(	(	PUNCT
ejpam-3347	149	40	−1	−1	NOUN
ejpam-3347	149	41	)	)	PUNCT
ejpam-3347	149	42	n	n	CCONJ
ejpam-3347	149	43	,	,	PUNCT
ejpam-3347	149	44	wt	wt	PROPN
ejpam-3347	149	45	(	(	PUNCT
ejpam-3347	149	46	un	un	PROPN
ejpam-3347	149	47	/	/	SYM
ejpam-3347	149	48	wt	wt	NOUN
ejpam-3347	149	49	)	)	PUNCT
ejpam-3347	149	50	/wt	/wt	PUNCT
ejpam-3347	149	51	)	)	PUNCT
ejpam-3347	149	52	are	be	AUX
ejpam-3347	149	53	obtains	obtain	NOUN
ejpam-3347	149	54	:	:	PUNCT
ejpam-3347	150	1	c	c	X
ejpam-3347	150	2	(	(	PUNCT
ejpam-3347	150	3	u1	u1	PROPN
ejpam-3347	150	4	,	,	PUNCT
ejpam-3347	150	5	...	...	PUNCT
ejpam-3347	150	6	,	,	PUNCT
ejpam-3347	150	7	un	un	PROPN
ejpam-3347	150	8	/	/	SYM
ejpam-3347	150	9	wt	wt	NOUN
ejpam-3347	150	10	)	)	PUNCT
ejpam-3347	150	11	=	=	PUNCT
ejpam-3347	151	1	=	=	SYM
ejpam-3347	151	2	f−1	f−1	PROPN
ejpam-3347	151	3	w	w	ADP
ejpam-3347	151	4	(	(	PUNCT
ejpam-3347	151	5	wt)×	wt)×	X
ejpam-3347	151	6	[	[	PUNCT
ejpam-3347	151	7	[	[	PUNCT
ejpam-3347	151	8	i=1]n	i=1]n	NOUN
ejpam-3347	151	9	∑∂(v	∑∂(v	X
ejpam-3347	151	10	arui	arui	NOUN
ejpam-3347	151	11	(	(	PUNCT
ejpam-3347	151	12	xi	xi	NOUN
ejpam-3347	151	13	/	/	SYM
ejpam-3347	151	14	wt	wt	NOUN
ejpam-3347	151	15	)	)	PUNCT
ejpam-3347	151	16	)	)	PUNCT
ejpam-3347	152	1	∂wt	∂wt	PROPN
ejpam-3347	152	2	pi	pi	PROPN
ejpam-3347	152	3	,	,	PUNCT
ejpam-3347	152	4	te	te	PROPN
ejpam-3347	152	5	zt	zt	PROPN
ejpam-3347	152	6	,	,	PUNCT
ejpam-3347	152	7	i	i	PRON
ejpam-3347	152	8	−	−	X
ejpam-3347	152	9	[	[	PUNCT
ejpam-3347	152	10	i=1]n	i=1]n	NOUN
ejpam-3347	152	11	∑∂(v	∑∂(v	X
ejpam-3347	152	12	arui	arui	NOUN
ejpam-3347	152	13	(	(	PUNCT
ejpam-3347	152	14	xi	xi	NOUN
ejpam-3347	152	15	/	/	SYM
ejpam-3347	152	16	wt	wt	NOUN
ejpam-3347	152	17	)	)	PUNCT
ejpam-3347	152	18	)	)	PUNCT
ejpam-3347	153	1	∂wt	∂wt	PROPN
ejpam-3347	153	2	pi	pi	PROPN
ejpam-3347	153	3	,	,	PUNCT
ejpam-3347	153	4	t	t	PROPN
ejpam-3347	153	5	]	]	PUNCT
ejpam-3347	153	6	consider	consider	VERB
ejpam-3347	153	7	pt	pt	X
ejpam-3347	153	8	=	=	SYM
ejpam-3347	153	9	(	(	PUNCT
ejpam-3347	153	10	p1,te	p1,te	PROPN
ejpam-3347	153	11	zt,1	zt,1	PROPN
ejpam-3347	153	12	,	,	PUNCT
ejpam-3347	153	13	...	...	PUNCT
ejpam-3347	153	14	,	,	PUNCT
ejpam-3347	153	15	pn	pn	PROPN
ejpam-3347	153	16	,	,	PUNCT
ejpam-3347	153	17	te	te	PROPN
ejpam-3347	153	18	zn,1	zn,1	PROPN
ejpam-3347	153	19	)	)	PUNCT
ejpam-3347	153	20	,	,	PUNCT
ejpam-3347	153	21	we	we	PRON
ejpam-3347	153	22	have	have	VERB
ejpam-3347	153	23	:	:	PUNCT
ejpam-3347	154	1	c	c	X
ejpam-3347	154	2	(	(	PUNCT
ejpam-3347	154	3	u1	u1	PROPN
ejpam-3347	154	4	,	,	PUNCT
ejpam-3347	154	5	...	...	PUNCT
ejpam-3347	154	6	,	,	PUNCT
ejpam-3347	154	7	un	un	PROPN
ejpam-3347	154	8	/	/	SYM
ejpam-3347	154	9	wt	wt	NOUN
ejpam-3347	154	10	)	)	PUNCT
ejpam-3347	155	1	=	=	SYM
ejpam-3347	155	2	f−1	f−1	PROPN
ejpam-3347	155	3	w	w	ADP
ejpam-3347	155	4	(	(	PUNCT
ejpam-3347	155	5	wt)×	wt)×	NOUN
ejpam-3347	155	6	〈	〈	PROPN
ejpam-3347	155	7	∂	∂	NUM
ejpam-3347	155	8	∂wt	∂wt	PROPN
ejpam-3347	155	9	v	v	PROPN
ejpam-3347	155	10	aru	aru	NOUN
ejpam-3347	155	11	(	(	PUNCT
ejpam-3347	155	12	x	x	NOUN
ejpam-3347	155	13	/	/	SYM
ejpam-3347	155	14	wt	wt	NOUN
ejpam-3347	155	15	)	)	PUNCT
ejpam-3347	155	16	,	,	PUNCT
ejpam-3347	155	17	pt	pt	X
ejpam-3347	155	18	〉	〉	NOUN
ejpam-3347	155	19	−f−1	−f−1	NUM
ejpam-3347	155	20	w	w	NOUN
ejpam-3347	155	21	(	(	PUNCT
ejpam-3347	155	22	wt)×	wt)×	NOUN
ejpam-3347	155	23	〈	〈	PROPN
ejpam-3347	155	24	∂	∂	NUM
ejpam-3347	155	25	∂wt	∂wt	PROPN
ejpam-3347	155	26	v	v	PROPN
ejpam-3347	155	27	aru	aru	NOUN
ejpam-3347	155	28	(	(	PUNCT
ejpam-3347	155	29	x	x	NOUN
ejpam-3347	155	30	/	/	SYM
ejpam-3347	155	31	wt	wt	NOUN
ejpam-3347	155	32	)	)	PUNCT
ejpam-3347	155	33	,	,	PUNCT
ejpam-3347	155	34	pt	pt	X
ejpam-3347	155	35	〉	〉	NOUN
ejpam-3347	155	36	c	c	PROPN
ejpam-3347	155	37	(	(	PUNCT
ejpam-3347	155	38	u1	u1	PROPN
ejpam-3347	155	39	,	,	PUNCT
ejpam-3347	155	40	...	...	PUNCT
ejpam-3347	155	41	,	,	PUNCT
ejpam-3347	155	42	un	un	PROPN
ejpam-3347	155	43	/	/	SYM
ejpam-3347	155	44	wt	wt	NOUN
ejpam-3347	155	45	)	)	PUNCT
ejpam-3347	155	46	=	=	SYM
ejpam-3347	155	47	〈	〈	NOUN
ejpam-3347	155	48	∂	∂	NOUN
ejpam-3347	155	49	∂wt	∂wt	PROPN
ejpam-3347	155	50	v	v	PROPN
ejpam-3347	155	51	aru	aru	NOUN
ejpam-3347	155	52	(	(	PUNCT
ejpam-3347	155	53	x	x	NOUN
ejpam-3347	155	54	/	/	SYM
ejpam-3347	155	55	wt	wt	NOUN
ejpam-3347	155	56	)	)	PUNCT
ejpam-3347	155	57	,	,	PUNCT
ejpam-3347	155	58	f	f	PROPN
ejpam-3347	155	59	−1	−1	NOUN
ejpam-3347	155	60	w	w	PROPN
ejpam-3347	155	61	(	(	PUNCT
ejpam-3347	155	62	wt	wt	NOUN
ejpam-3347	155	63	)	)	PUNCT
ejpam-3347	155	64	(	(	PUNCT
ejpam-3347	155	65	pt	pt	INTJ
ejpam-3347	155	66	−	−	PROPN
ejpam-3347	155	67	pt	pt	NOUN
ejpam-3347	155	68	)	)	PUNCT
ejpam-3347	155	69	〉	〉	NOUN
ejpam-3347	155	70	if	if	SCONJ
ejpam-3347	155	71	f−1	f−1	PROPN
ejpam-3347	155	72	w	w	PROPN
ejpam-3347	155	73	∈	∈	PROPN
ejpam-3347	155	74	c1	c1	NOUN
ejpam-3347	155	75	we	we	PRON
ejpam-3347	155	76	can	can	AUX
ejpam-3347	155	77	write	write	VERB
ejpam-3347	155	78	,	,	PUNCT
ejpam-3347	155	79	then	then	ADV
ejpam-3347	155	80	c	c	PROPN
ejpam-3347	155	81	(	(	PUNCT
ejpam-3347	155	82	u1	u1	PROPN
ejpam-3347	155	83	,	,	PUNCT
ejpam-3347	155	84	...	...	PUNCT
ejpam-3347	155	85	,	,	PUNCT
ejpam-3347	155	86	un	un	PROPN
ejpam-3347	155	87	/	/	SYM
ejpam-3347	155	88	wt	wt	NOUN
ejpam-3347	155	89	)	)	PUNCT
ejpam-3347	155	90	=	=	SYM
ejpam-3347	155	91	f−1	f−1	PROPN
ejpam-3347	155	92	w	w	ADP
ejpam-3347	155	93	(	(	PUNCT
ejpam-3347	155	94	wt	wt	NOUN
ejpam-3347	155	95	)	)	PUNCT
ejpam-3347	155	96	〈	〈	PROPN
ejpam-3347	155	97	∂	∂	NUM
ejpam-3347	155	98	∂wt	∂wt	PROPN
ejpam-3347	155	99	(	(	PUNCT
ejpam-3347	155	100	v	v	NUM
ejpam-3347	155	101	aru	aru	NOUN
ejpam-3347	155	102	(	(	PUNCT
ejpam-3347	155	103	x	x	NOUN
ejpam-3347	155	104	/	/	SYM
ejpam-3347	155	105	wt	wt	NOUN
ejpam-3347	155	106	)	)	PUNCT
ejpam-3347	155	107	)	)	PUNCT
ejpam-3347	155	108	,	,	PUNCT
ejpam-3347	155	109	(	(	PUNCT
ejpam-3347	155	110	pt	pt	INTJ
ejpam-3347	155	111	−	−	PROPN
ejpam-3347	155	112	pt	pt	NOUN
ejpam-3347	155	113	)	)	PUNCT
ejpam-3347	155	114	〉	〉	NOUN
ejpam-3347	155	115	v.	v.	ADP
ejpam-3347	155	116	y.	y.	PROPN
ejpam-3347	155	117	b.	b.	PROPN
ejpam-3347	156	1	loyara	loyara	PROPN
ejpam-3347	156	2	,	,	PUNCT
ejpam-3347	156	3	d.	d.	PROPN
ejpam-3347	156	4	barro	barro	PROPN
ejpam-3347	156	5	/	/	SYM
ejpam-3347	156	6	eur	eur	PROPN
ejpam-3347	156	7	.	.	PUNCT
ejpam-3347	157	1	j.	j.	PROPN
ejpam-3347	157	2	pure	pure	PROPN
ejpam-3347	157	3	appl	appl	PROPN
ejpam-3347	157	4	.	.	PROPN
ejpam-3347	157	5	math	math	PROPN
ejpam-3347	157	6	,	,	PUNCT
ejpam-3347	157	7	12	12	NUM
ejpam-3347	157	8	(	(	PUNCT
ejpam-3347	157	9	1	1	NUM
ejpam-3347	157	10	)	)	PUNCT
ejpam-3347	157	11	(	(	PUNCT
ejpam-3347	157	12	2019	2019	NUM
ejpam-3347	157	13	)	)	PUNCT
ejpam-3347	157	14	,	,	PUNCT
ejpam-3347	157	15	194	194	NUM
ejpam-3347	157	16	-	-	SYM
ejpam-3347	157	17	207	207	NUM
ejpam-3347	157	18	201	201	NUM
ejpam-3347	157	19	proposition	proposition	NOUN
ejpam-3347	157	20	4	4	NUM
ejpam-3347	157	21	.	.	PUNCT
ejpam-3347	158	1	let	let	VERB
ejpam-3347	158	2	these	these	DET
ejpam-3347	158	3	risks	risk	NOUN
ejpam-3347	158	4	represent	represent	VERB
ejpam-3347	158	5	potential	potential	ADJ
ejpam-3347	158	6	losses	loss	NOUN
ejpam-3347	158	7	in	in	ADP
ejpam-3347	158	8	dependent	dependent	ADJ
ejpam-3347	158	9	lines	line	NOUN
ejpam-3347	158	10	of	of	ADP
ejpam-3347	158	11	business	business	NOUN
ejpam-3347	158	12	for	for	ADP
ejpam-3347	158	13	an	an	DET
ejpam-3347	158	14	insurance	insurance	NOUN
ejpam-3347	158	15	company	company	NOUN
ejpam-3347	158	16	for	for	ADP
ejpam-3347	158	17	example	example	NOUN
ejpam-3347	158	18	.	.	PUNCT
ejpam-3347	159	1	in	in	ADP
ejpam-3347	159	2	the	the	DET
ejpam-3347	159	3	following	following	NOUN
ejpam-3347	159	4	we	we	PRON
ejpam-3347	159	5	consider	consider	VERB
ejpam-3347	159	6	ourselves	ourselves	PRON
ejpam-3347	159	7	in	in	ADP
ejpam-3347	159	8	finite	finite	ADJ
ejpam-3347	159	9	dimension	dimension	NOUN
ejpam-3347	159	10	and	and	CCONJ
ejpam-3347	159	11	(	(	PUNCT
ejpam-3347	159	12	e	e	NOUN
ejpam-3347	159	13	,	,	PUNCT
ejpam-3347	159	14	〈	〈	PROPN
ejpam-3347	159	15	,	,	PUNCT
ejpam-3347	159	16	〉	〉	PROPN
ejpam-3347	159	17	)	)	PUNCT
ejpam-3347	159	18	is	be	AUX
ejpam-3347	159	19	euclidean	euclidean	ADJ
ejpam-3347	159	20	space	space	NOUN
ejpam-3347	159	21	.	.	PUNCT
ejpam-3347	160	1	further	far	ADV
ejpam-3347	160	2	,	,	PUNCT
ejpam-3347	160	3	the	the	DET
ejpam-3347	160	4	conditional	conditional	ADJ
ejpam-3347	160	5	copula	copula	NOUN
ejpam-3347	160	6	of	of	ADP
ejpam-3347	160	7	is	be	AUX
ejpam-3347	160	8	given	give	VERB
ejpam-3347	160	9	by	by	ADP
ejpam-3347	160	10	c	c	PROPN
ejpam-3347	160	11	(	(	PUNCT
ejpam-3347	160	12	u1	u1	PROPN
ejpam-3347	160	13	,	,	PUNCT
ejpam-3347	160	14	...	...	PUNCT
ejpam-3347	160	15	,	,	PUNCT
ejpam-3347	160	16	un	un	PROPN
ejpam-3347	160	17	/	/	SYM
ejpam-3347	160	18	wt	wt	NOUN
ejpam-3347	160	19	)	)	PUNCT
ejpam-3347	160	20	=	=	NOUN
ejpam-3347	161	1	∣∣f−1	∣∣f−1	PROPN
ejpam-3347	161	2	w	w	ADP
ejpam-3347	161	3	(	(	PUNCT
ejpam-3347	161	4	wt	wt	NOUN
ejpam-3347	161	5	)	)	PUNCT
ejpam-3347	161	6	∣∣	∣∣	X
ejpam-3347	161	7	∥∥∥∥	∥∥∥∥	SYM
ejpam-3347	161	8	∂	∂	NUM
ejpam-3347	161	9	∂wt	∂wt	PROPN
ejpam-3347	161	10	(	(	PUNCT
ejpam-3347	161	11	v	v	NUM
ejpam-3347	161	12	aru	aru	NOUN
ejpam-3347	161	13	(	(	PUNCT
ejpam-3347	161	14	x	x	NOUN
ejpam-3347	161	15	/	/	SYM
ejpam-3347	161	16	wt	wt	NOUN
ejpam-3347	161	17	)	)	PUNCT
ejpam-3347	161	18	)	)	PUNCT
ejpam-3347	161	19	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3347	162	1	‖pt	‖pt	NUM
ejpam-3347	162	2	−	−	PROPN
ejpam-3347	162	3	pt‖	pt‖	PROPN
ejpam-3347	162	4	(	(	PUNCT
ejpam-3347	162	5	18	18	NUM
ejpam-3347	162	6	)	)	PUNCT
ejpam-3347	162	7	furthermore	furthermore	ADV
ejpam-3347	162	8	c	c	NOUN
ejpam-3347	162	9	(	(	PUNCT
ejpam-3347	162	10	u1	u1	PROPN
ejpam-3347	162	11	,	,	PUNCT
ejpam-3347	162	12	...	...	PUNCT
ejpam-3347	162	13	,	,	PUNCT
ejpam-3347	162	14	un	un	PROPN
ejpam-3347	162	15	/	/	SYM
ejpam-3347	162	16	wt	wt	NOUN
ejpam-3347	162	17	)	)	PUNCT
ejpam-3347	162	18	=	=	SYM
ejpam-3347	162	19	1	1	NUM
ejpam-3347	162	20	4f	4f	NUM
ejpam-3347	162	21	−1	−1	NOUN
ejpam-3347	162	22	w	w	NOUN
ejpam-3347	162	23	(	(	PUNCT
ejpam-3347	162	24	wt	wt	NOUN
ejpam-3347	162	25	)	)	PUNCT
ejpam-3347	162	26	(	(	PUNCT
ejpam-3347	162	27	∥∥∥	∥∥∥	NUM
ejpam-3347	162	28	∂	∂	NUM
ejpam-3347	162	29	∂wt	∂wt	PROPN
ejpam-3347	162	30	(	(	PUNCT
ejpam-3347	162	31	v	v	NUM
ejpam-3347	162	32	aru	aru	NOUN
ejpam-3347	162	33	(	(	PUNCT
ejpam-3347	162	34	x	x	NOUN
ejpam-3347	162	35	/	/	SYM
ejpam-3347	162	36	wt	wt	NOUN
ejpam-3347	162	37	)	)	PUNCT
ejpam-3347	162	38	)	)	PUNCT
ejpam-3347	163	1	+	+	CCONJ
ejpam-3347	163	2	(	(	PUNCT
ejpam-3347	163	3	pt	pt	INTJ
ejpam-3347	163	4	−	−	PROPN
ejpam-3347	163	5	pt	pt	PROPN
ejpam-3347	163	6	)	)	PUNCT
ejpam-3347	163	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	164	1	+	+	NOUN
ejpam-3347	164	2	∥∥∥	∥∥∥	NUM
ejpam-3347	164	3	∂	∂	NUM
ejpam-3347	164	4	∂wt	∂wt	PROPN
ejpam-3347	164	5	(	(	PUNCT
ejpam-3347	164	6	v	v	NUM
ejpam-3347	164	7	aru	aru	NOUN
ejpam-3347	164	8	(	(	PUNCT
ejpam-3347	164	9	x	x	NOUN
ejpam-3347	164	10	/	/	SYM
ejpam-3347	164	11	wt))−	wt))−	NOUN
ejpam-3347	164	12	(	(	PUNCT
ejpam-3347	164	13	pt	pt	INTJ
ejpam-3347	164	14	−	−	PROPN
ejpam-3347	164	15	pt	pt	PROPN
ejpam-3347	164	16	)	)	PUNCT
ejpam-3347	164	17	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	164	18	)	)	PUNCT
ejpam-3347	164	19	.	.	PUNCT
ejpam-3347	165	1	(	(	PUNCT
ejpam-3347	165	2	19	19	NUM
ejpam-3347	165	3	)	)	PUNCT
ejpam-3347	165	4	proof	proof	NOUN
ejpam-3347	165	5	.	.	PUNCT
ejpam-3347	166	1	for	for	ADP
ejpam-3347	166	2	this	this	DET
ejpam-3347	166	3	proof	proof	NOUN
ejpam-3347	166	4	,	,	PUNCT
ejpam-3347	166	5	consider	consider	VERB
ejpam-3347	166	6	the	the	DET
ejpam-3347	166	7	following	follow	VERB
ejpam-3347	166	8	relation	relation	NOUN
ejpam-3347	166	9	:	:	PUNCT
ejpam-3347	167	1	c	c	X
ejpam-3347	167	2	(	(	PUNCT
ejpam-3347	167	3	u1	u1	PROPN
ejpam-3347	167	4	,	,	PUNCT
ejpam-3347	167	5	...	...	PUNCT
ejpam-3347	167	6	,	,	PUNCT
ejpam-3347	167	7	un	un	PROPN
ejpam-3347	167	8	/	/	SYM
ejpam-3347	167	9	wt	wt	NOUN
ejpam-3347	167	10	)	)	PUNCT
ejpam-3347	168	1	=	=	SYM
ejpam-3347	168	2	f−1	f−1	PROPN
ejpam-3347	168	3	w	w	ADP
ejpam-3347	168	4	(	(	PUNCT
ejpam-3347	168	5	wt	wt	NOUN
ejpam-3347	168	6	)	)	PUNCT
ejpam-3347	168	7	〈	〈	PROPN
ejpam-3347	168	8	∂	∂	NUM
ejpam-3347	168	9	∂wt	∂wt	PROPN
ejpam-3347	168	10	(	(	PUNCT
ejpam-3347	168	11	v	v	NUM
ejpam-3347	168	12	aru	aru	NOUN
ejpam-3347	168	13	(	(	PUNCT
ejpam-3347	168	14	x	x	NOUN
ejpam-3347	168	15	/	/	SYM
ejpam-3347	168	16	wt	wt	NOUN
ejpam-3347	168	17	)	)	PUNCT
ejpam-3347	168	18	)	)	PUNCT
ejpam-3347	168	19	,	,	PUNCT
ejpam-3347	168	20	pt	pt	INTJ
ejpam-3347	168	21	−	−	PROPN
ejpam-3347	168	22	pt	pt	NOUN
ejpam-3347	168	23	〉	〉	NOUN
ejpam-3347	168	24	;	;	PUNCT
ejpam-3347	168	25	moreover	moreover	ADV
ejpam-3347	168	26	considering	consider	VERB
ejpam-3347	168	27	equality	equality	NOUN
ejpam-3347	168	28	(	(	PUNCT
ejpam-3347	168	29	10	10	NUM
ejpam-3347	168	30	)	)	PUNCT
ejpam-3347	168	31	it	it	PRON
ejpam-3347	168	32	came	come	VERB
ejpam-3347	168	33	that;∣∣∣∣f−1	that;∣∣∣∣f−1	NOUN
ejpam-3347	168	34	w	w	PROPN
ejpam-3347	168	35	(	(	PUNCT
ejpam-3347	168	36	wt	wt	NOUN
ejpam-3347	168	37	)	)	PUNCT
ejpam-3347	168	38	〈	〈	PROPN
ejpam-3347	168	39	∂	∂	NUM
ejpam-3347	168	40	∂wt	∂wt	PROPN
ejpam-3347	168	41	(	(	PUNCT
ejpam-3347	168	42	v	v	NUM
ejpam-3347	168	43	aru	aru	NOUN
ejpam-3347	168	44	(	(	PUNCT
ejpam-3347	168	45	x	x	NOUN
ejpam-3347	168	46	/	/	SYM
ejpam-3347	168	47	wt	wt	NOUN
ejpam-3347	168	48	)	)	PUNCT
ejpam-3347	168	49	)	)	PUNCT
ejpam-3347	168	50	,	,	PUNCT
ejpam-3347	168	51	pt	pt	INTJ
ejpam-3347	168	52	−	−	NOUN
ejpam-3347	168	53	pt	pt	NOUN
ejpam-3347	168	54	〉	〉	NOUN
ejpam-3347	168	55	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3347	168	56	=	=	PUNCT
ejpam-3347	168	57	∣∣f−1	∣∣f−1	ADJ
ejpam-3347	168	58	w	w	X
ejpam-3347	168	59	(	(	PUNCT
ejpam-3347	168	60	wt	wt	NOUN
ejpam-3347	168	61	)	)	PUNCT
ejpam-3347	168	62	∣∣	∣∣	X
ejpam-3347	168	63	∥∥∥∥	∥∥∥∥	SYM
ejpam-3347	168	64	∂	∂	NUM
ejpam-3347	168	65	∂wt	∂wt	PROPN
ejpam-3347	168	66	(	(	PUNCT
ejpam-3347	168	67	v	v	NUM
ejpam-3347	168	68	aru	aru	NOUN
ejpam-3347	168	69	(	(	PUNCT
ejpam-3347	168	70	x	x	NOUN
ejpam-3347	168	71	/	/	SYM
ejpam-3347	168	72	wt	wt	NOUN
ejpam-3347	168	73	)	)	PUNCT
ejpam-3347	168	74	)	)	PUNCT
ejpam-3347	168	75	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3347	169	1	‖pt	‖pt	NUM
ejpam-3347	169	2	−	−	PROPN
ejpam-3347	169	3	pt‖	pt‖	NOUN
ejpam-3347	169	4	so	so	SCONJ
ejpam-3347	169	5	c	c	PROPN
ejpam-3347	169	6	(	(	PUNCT
ejpam-3347	169	7	u1	u1	PROPN
ejpam-3347	169	8	,	,	PUNCT
ejpam-3347	169	9	...	...	PUNCT
ejpam-3347	169	10	,	,	PUNCT
ejpam-3347	169	11	un	un	PROPN
ejpam-3347	169	12	/	/	SYM
ejpam-3347	169	13	wt	wt	NOUN
ejpam-3347	169	14	)	)	PUNCT
ejpam-3347	169	15	=	=	NOUN
ejpam-3347	169	16	∣∣f−1	∣∣f−1	PROPN
ejpam-3347	169	17	w	w	ADP
ejpam-3347	169	18	(	(	PUNCT
ejpam-3347	169	19	wt	wt	NOUN
ejpam-3347	169	20	)	)	PUNCT
ejpam-3347	169	21	∣∣	∣∣	X
ejpam-3347	169	22	∥∥∥∥	∥∥∥∥	SYM
ejpam-3347	169	23	∂	∂	NUM
ejpam-3347	169	24	∂wt	∂wt	PROPN
ejpam-3347	169	25	(	(	PUNCT
ejpam-3347	169	26	v	v	NUM
ejpam-3347	169	27	aru	aru	NOUN
ejpam-3347	169	28	(	(	PUNCT
ejpam-3347	169	29	x	x	NOUN
ejpam-3347	169	30	/	/	SYM
ejpam-3347	169	31	wt	wt	NOUN
ejpam-3347	169	32	)	)	PUNCT
ejpam-3347	169	33	)	)	PUNCT
ejpam-3347	169	34	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3347	170	1	‖pt	‖pt	NUM
ejpam-3347	170	2	−	−	PROPN
ejpam-3347	170	3	pt‖	pt‖	NOUN
ejpam-3347	170	4	and	and	CCONJ
ejpam-3347	170	5	if	if	SCONJ
ejpam-3347	170	6	we	we	PRON
ejpam-3347	170	7	take	take	VERB
ejpam-3347	170	8	it	it	PRON
ejpam-3347	170	9	the	the	DET
ejpam-3347	170	10	relation	relation	NOUN
ejpam-3347	170	11	(	(	PUNCT
ejpam-3347	170	12	11	11	NUM
ejpam-3347	170	13	)	)	PUNCT
ejpam-3347	170	14	〈	〈	PROPN
ejpam-3347	170	15	v	v	ADJ
ejpam-3347	170	16	aru	aru	NOUN
ejpam-3347	170	17	(	(	PUNCT
ejpam-3347	170	18	x	x	NOUN
ejpam-3347	170	19	/	/	SYM
ejpam-3347	170	20	wt	wt	NOUN
ejpam-3347	170	21	)	)	PUNCT
ejpam-3347	170	22	,	,	PUNCT
ejpam-3347	170	23	pt	pt	INTJ
ejpam-3347	170	24	−	−	NUM
ejpam-3347	170	25	pt	pt	PROPN
ejpam-3347	170	26	〉	〉	NOUN
ejpam-3347	170	27	=	=	SYM
ejpam-3347	170	28	1	1	NUM
ejpam-3347	170	29	4	4	NUM
ejpam-3347	170	30	(	(	PUNCT
ejpam-3347	170	31	∥∥∥	∥∥∥	NUM
ejpam-3347	170	32	∂	∂	NUM
ejpam-3347	171	1	∂wt	∂wt	PROPN
ejpam-3347	171	2	(	(	PUNCT
ejpam-3347	171	3	v	v	NUM
ejpam-3347	171	4	aru	aru	NOUN
ejpam-3347	171	5	(	(	PUNCT
ejpam-3347	171	6	x	x	NOUN
ejpam-3347	171	7	/	/	SYM
ejpam-3347	171	8	wt	wt	NOUN
ejpam-3347	171	9	)	)	PUNCT
ejpam-3347	171	10	)	)	PUNCT
ejpam-3347	172	1	+	+	CCONJ
ejpam-3347	172	2	(	(	PUNCT
ejpam-3347	172	3	pt	pt	INTJ
ejpam-3347	172	4	−	−	PROPN
ejpam-3347	172	5	pt	pt	PROPN
ejpam-3347	172	6	)	)	PUNCT
ejpam-3347	172	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	173	1	+	+	NOUN
ejpam-3347	173	2	∥∥∥	∥∥∥	NUM
ejpam-3347	173	3	∂	∂	NUM
ejpam-3347	173	4	∂wt	∂wt	PROPN
ejpam-3347	173	5	(	(	PUNCT
ejpam-3347	173	6	v	v	NUM
ejpam-3347	173	7	aru	aru	NOUN
ejpam-3347	173	8	(	(	PUNCT
ejpam-3347	173	9	x	x	NOUN
ejpam-3347	173	10	/	/	SYM
ejpam-3347	173	11	wt))−	wt))−	NOUN
ejpam-3347	173	12	(	(	PUNCT
ejpam-3347	173	13	pt	pt	INTJ
ejpam-3347	173	14	−	−	PROPN
ejpam-3347	173	15	pt	pt	PROPN
ejpam-3347	173	16	)	)	PUNCT
ejpam-3347	173	17	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	173	18	)	)	PUNCT
ejpam-3347	173	19	.	.	PUNCT
ejpam-3347	174	1	then	then	ADV
ejpam-3347	174	2	,	,	PUNCT
ejpam-3347	174	3	it	it	PRON
ejpam-3347	174	4	follows	follow	VERB
ejpam-3347	174	5	that	that	SCONJ
ejpam-3347	174	6	:	:	PUNCT
ejpam-3347	174	7	f−1	f−1	PROPN
ejpam-3347	174	8	w	w	PROPN
ejpam-3347	174	9	(	(	PUNCT
ejpam-3347	174	10	wt	wt	NOUN
ejpam-3347	174	11	)	)	PUNCT
ejpam-3347	174	12	〈	〈	PROPN
ejpam-3347	174	13	∂	∂	NUM
ejpam-3347	174	14	∂wt	∂wt	PROPN
ejpam-3347	174	15	(	(	PUNCT
ejpam-3347	174	16	v	v	NUM
ejpam-3347	174	17	aru	aru	NOUN
ejpam-3347	174	18	(	(	PUNCT
ejpam-3347	174	19	x	x	NOUN
ejpam-3347	174	20	/	/	SYM
ejpam-3347	174	21	wt	wt	NOUN
ejpam-3347	174	22	)	)	PUNCT
ejpam-3347	174	23	)	)	PUNCT
ejpam-3347	174	24	,	,	PUNCT
ejpam-3347	174	25	pt	pt	INTJ
ejpam-3347	174	26	−	−	NOUN
ejpam-3347	174	27	pt	pt	NOUN
ejpam-3347	174	28	〉	〉	NOUN
ejpam-3347	174	29	=	=	SYM
ejpam-3347	174	30	1	1	NUM
ejpam-3347	174	31	4	4	NUM
ejpam-3347	174	32	∂	∂	NUM
ejpam-3347	174	33	∂wt	∂wt	PROPN
ejpam-3347	174	34	(	(	PUNCT
ejpam-3347	174	35	f−1	f−1	PROPN
ejpam-3347	174	36	w	w	PROPN
ejpam-3347	174	37	(	(	PUNCT
ejpam-3347	174	38	wt	wt	NOUN
ejpam-3347	174	39	)	)	PUNCT
ejpam-3347	174	40	)	)	PUNCT
ejpam-3347	174	41	(	(	PUNCT
ejpam-3347	174	42	∥∥∥	∥∥∥	NUM
ejpam-3347	174	43	∂	∂	NUM
ejpam-3347	174	44	∂wt	∂wt	PROPN
ejpam-3347	174	45	(	(	PUNCT
ejpam-3347	174	46	v	v	NUM
ejpam-3347	174	47	aru	aru	NOUN
ejpam-3347	174	48	(	(	PUNCT
ejpam-3347	174	49	x	x	NOUN
ejpam-3347	174	50	/	/	SYM
ejpam-3347	174	51	wt	wt	NOUN
ejpam-3347	174	52	)	)	PUNCT
ejpam-3347	174	53	)	)	PUNCT
ejpam-3347	175	1	+	+	CCONJ
ejpam-3347	175	2	(	(	PUNCT
ejpam-3347	175	3	pt	pt	INTJ
ejpam-3347	175	4	−	−	PROPN
ejpam-3347	175	5	pt	pt	PROPN
ejpam-3347	175	6	)	)	PUNCT
ejpam-3347	175	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	176	1	+	+	NOUN
ejpam-3347	176	2	∥∥∥	∥∥∥	NUM
ejpam-3347	176	3	∂	∂	NUM
ejpam-3347	176	4	∂wt	∂wt	PROPN
ejpam-3347	176	5	(	(	PUNCT
ejpam-3347	176	6	v	v	NUM
ejpam-3347	176	7	aru	aru	NOUN
ejpam-3347	176	8	(	(	PUNCT
ejpam-3347	176	9	x	x	NOUN
ejpam-3347	176	10	/	/	SYM
ejpam-3347	176	11	wt))−	wt))−	NOUN
ejpam-3347	176	12	(	(	PUNCT
ejpam-3347	176	13	pt	pt	INTJ
ejpam-3347	176	14	−	−	PROPN
ejpam-3347	176	15	pt	pt	PROPN
ejpam-3347	176	16	)	)	PUNCT
ejpam-3347	176	17	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	176	18	)	)	PUNCT
ejpam-3347	176	19	hence	hence	ADV
ejpam-3347	176	20	the	the	DET
ejpam-3347	176	21	result	result	NOUN
ejpam-3347	176	22	:	:	PUNCT
ejpam-3347	176	23	v.	v.	PROPN
ejpam-3347	176	24	y.	y.	PROPN
ejpam-3347	176	25	b.	b.	PROPN
ejpam-3347	177	1	loyara	loyara	PROPN
ejpam-3347	177	2	,	,	PUNCT
ejpam-3347	177	3	d.	d.	PROPN
ejpam-3347	177	4	barro	barro	PROPN
ejpam-3347	177	5	/	/	SYM
ejpam-3347	177	6	eur	eur	PROPN
ejpam-3347	177	7	.	.	PUNCT
ejpam-3347	178	1	j.	j.	PROPN
ejpam-3347	178	2	pure	pure	PROPN
ejpam-3347	178	3	appl	appl	PROPN
ejpam-3347	178	4	.	.	PROPN
ejpam-3347	178	5	math	math	PROPN
ejpam-3347	178	6	,	,	PUNCT
ejpam-3347	178	7	12	12	NUM
ejpam-3347	178	8	(	(	PUNCT
ejpam-3347	178	9	1	1	NUM
ejpam-3347	178	10	)	)	PUNCT
ejpam-3347	178	11	(	(	PUNCT
ejpam-3347	178	12	2019	2019	NUM
ejpam-3347	178	13	)	)	PUNCT
ejpam-3347	178	14	,	,	PUNCT
ejpam-3347	178	15	194	194	NUM
ejpam-3347	178	16	-	-	SYM
ejpam-3347	178	17	207	207	NUM
ejpam-3347	178	18	202	202	NUM
ejpam-3347	178	19	c	c	NOUN
ejpam-3347	178	20	(	(	PUNCT
ejpam-3347	178	21	u1	u1	PROPN
ejpam-3347	178	22	,	,	PUNCT
ejpam-3347	178	23	...	...	PUNCT
ejpam-3347	178	24	,	,	PUNCT
ejpam-3347	178	25	un	un	PROPN
ejpam-3347	178	26	/	/	SYM
ejpam-3347	178	27	wt	wt	NOUN
ejpam-3347	178	28	)	)	PUNCT
ejpam-3347	178	29	=	=	SYM
ejpam-3347	178	30	1	1	NUM
ejpam-3347	178	31	4f	4f	NUM
ejpam-3347	178	32	−1	−1	NOUN
ejpam-3347	178	33	w	w	NOUN
ejpam-3347	178	34	(	(	PUNCT
ejpam-3347	178	35	wt	wt	NOUN
ejpam-3347	178	36	)	)	PUNCT
ejpam-3347	178	37	(	(	PUNCT
ejpam-3347	178	38	∥∥∥	∥∥∥	NUM
ejpam-3347	178	39	∂	∂	NUM
ejpam-3347	178	40	∂wt	∂wt	PROPN
ejpam-3347	178	41	(	(	PUNCT
ejpam-3347	178	42	v	v	NUM
ejpam-3347	178	43	aru	aru	NOUN
ejpam-3347	178	44	(	(	PUNCT
ejpam-3347	178	45	x	x	NOUN
ejpam-3347	178	46	/	/	SYM
ejpam-3347	178	47	wt	wt	NOUN
ejpam-3347	178	48	)	)	PUNCT
ejpam-3347	178	49	)	)	PUNCT
ejpam-3347	179	1	+	+	CCONJ
ejpam-3347	179	2	(	(	PUNCT
ejpam-3347	179	3	pt	pt	INTJ
ejpam-3347	179	4	−	−	PROPN
ejpam-3347	179	5	pt	pt	PROPN
ejpam-3347	179	6	)	)	PUNCT
ejpam-3347	179	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	180	1	+	+	NOUN
ejpam-3347	180	2	∥∥∥	∥∥∥	NUM
ejpam-3347	180	3	∂	∂	NUM
ejpam-3347	180	4	∂wt	∂wt	PROPN
ejpam-3347	180	5	(	(	PUNCT
ejpam-3347	180	6	v	v	NUM
ejpam-3347	180	7	aru	aru	NOUN
ejpam-3347	180	8	(	(	PUNCT
ejpam-3347	180	9	x	x	NOUN
ejpam-3347	180	10	/	/	SYM
ejpam-3347	180	11	wt))−	wt))−	NOUN
ejpam-3347	180	12	(	(	PUNCT
ejpam-3347	180	13	pt	pt	INTJ
ejpam-3347	180	14	−	−	PROPN
ejpam-3347	180	15	pt	pt	PROPN
ejpam-3347	180	16	)	)	PUNCT
ejpam-3347	180	17	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	180	18	)	)	PUNCT
ejpam-3347	180	19	.	.	PUNCT
ejpam-3347	181	1	3.2	3.2	NUM
ejpam-3347	181	2	.	.	PUNCT
ejpam-3347	182	1	the	the	DET
ejpam-3347	182	2	cvar	cvar	NOUN
ejpam-3347	182	3	in	in	ADP
ejpam-3347	182	4	an	an	DET
ejpam-3347	182	5	euclidean	euclidean	ADJ
ejpam-3347	182	6	space	space	NOUN
ejpam-3347	182	7	the	the	DET
ejpam-3347	182	8	tail	tail	NOUN
ejpam-3347	182	9	-	-	PUNCT
ejpam-3347	182	10	var	var	NOUN
ejpam-3347	182	11	(	(	PUNCT
ejpam-3347	182	12	tvar	tvar	NOUN
ejpam-3347	182	13	)	)	PUNCT
ejpam-3347	182	14	is	be	AUX
ejpam-3347	182	15	derivative	derivative	ADJ
ejpam-3347	182	16	coherent	coherent	ADJ
ejpam-3347	182	17	risk	risk	NOUN
ejpam-3347	182	18	measure	measure	NOUN
ejpam-3347	182	19	of	of	ADP
ejpam-3347	182	20	the	the	DET
ejpam-3347	182	21	var	var	NOUN
ejpam-3347	182	22	.	.	PUNCT
ejpam-3347	183	1	for	for	ADP
ejpam-3347	183	2	a	a	DET
ejpam-3347	183	3	given	give	VERB
ejpam-3347	183	4	confidence	confidence	NOUN
ejpam-3347	183	5	level	level	NOUN
ejpam-3347	183	6	α	α	X
ejpam-3347	183	7	∈	∈	NOUN
ejpam-3347	183	8	]	]	X
ejpam-3347	183	9	0	0	NUM
ejpam-3347	183	10	,	,	PUNCT
ejpam-3347	183	11	1	1	NUM
ejpam-3347	183	12	[	[	X
ejpam-3347	183	13	,	,	PUNCT
ejpam-3347	183	14	it	it	PRON
ejpam-3347	183	15	follows	follow	VERB
ejpam-3347	183	16	that	that	SCONJ
ejpam-3347	183	17	tv	tv	NOUN
ejpam-3347	183	18	arα	arα	NOUN
ejpam-3347	183	19	(	(	PUNCT
ejpam-3347	183	20	x	x	NOUN
ejpam-3347	183	21	)	)	PUNCT
ejpam-3347	183	22	=	=	SYM
ejpam-3347	184	1	1	1	NUM
ejpam-3347	184	2	1−	1−	NUM
ejpam-3347	184	3	α	α	NUM
ejpam-3347	184	4	∫	∫	PROPN
ejpam-3347	184	5	1	1	NUM
ejpam-3347	184	6	α	α	PROPN
ejpam-3347	184	7	v	v	NOUN
ejpam-3347	184	8	arξ	arξ	NOUN
ejpam-3347	184	9	(	(	PUNCT
ejpam-3347	184	10	x	x	NOUN
ejpam-3347	184	11	)	)	PUNCT
ejpam-3347	184	12	dξ	dξ	PROPN
ejpam-3347	185	1	=	=	NOUN
ejpam-3347	185	2	1	1	NUM
ejpam-3347	185	3	1−	1−	NUM
ejpam-3347	185	4	α	α	NOUN
ejpam-3347	185	5	[	[	PUNCT
ejpam-3347	185	6	e	e	X
ejpam-3347	186	1	[	[	X
ejpam-3347	186	2	x]−	x]−	PROPN
ejpam-3347	186	3	∫	∫	PROPN
ejpam-3347	186	4	α	α	NOUN
ejpam-3347	186	5	0	0	NUM
ejpam-3347	186	6	v	v	NUM
ejpam-3347	186	7	arξ	arξ	NOUN
ejpam-3347	186	8	(	(	PUNCT
ejpam-3347	186	9	x	x	X
ejpam-3347	186	10	)	)	PUNCT
ejpam-3347	186	11	dξ	dξ	X
ejpam-3347	186	12	]	]	PUNCT
ejpam-3347	186	13	(	(	PUNCT
ejpam-3347	186	14	20	20	NUM
ejpam-3347	186	15	)	)	PUNCT
ejpam-3347	186	16	the	the	DET
ejpam-3347	186	17	xtvar	xtvar	PROPN
ejpam-3347	186	18	is	be	AUX
ejpam-3347	186	19	the	the	DET
ejpam-3347	186	20	average	average	ADJ
ejpam-3347	186	21	amount	amount	NOUN
ejpam-3347	186	22	of	of	ADP
ejpam-3347	186	23	ruins	ruin	NOUN
ejpam-3347	186	24	beyond	beyond	ADP
ejpam-3347	186	25	the	the	DET
ejpam-3347	186	26	var	var	NOUN
ejpam-3347	186	27	;	;	PUNCT
ejpam-3347	186	28	xtv	xtv	PROPN
ejpam-3347	186	29	arα	arα	PROPN
ejpam-3347	186	30	(	(	PUNCT
ejpam-3347	186	31	x	x	NOUN
ejpam-3347	186	32	)	)	PUNCT
ejpam-3347	186	33	=	=	SYM
ejpam-3347	186	34	tv	tv	NOUN
ejpam-3347	186	35	arα	arα	NOUN
ejpam-3347	186	36	(	(	PUNCT
ejpam-3347	186	37	x)−	x)−	PROPN
ejpam-3347	186	38	v	v	NUM
ejpam-3347	186	39	arα	arα	NOUN
ejpam-3347	186	40	(	(	PUNCT
ejpam-3347	186	41	x	x	X
ejpam-3347	186	42	)	)	PUNCT
ejpam-3347	186	43	(	(	PUNCT
ejpam-3347	186	44	21	21	NUM
ejpam-3347	186	45	)	)	PUNCT
ejpam-3347	186	46	the	the	DET
ejpam-3347	186	47	relation	relation	NOUN
ejpam-3347	186	48	21	21	NUM
ejpam-3347	186	49	we	we	PRON
ejpam-3347	186	50	get	get	VERB
ejpam-3347	186	51	the	the	DET
ejpam-3347	186	52	following	follow	VERB
ejpam-3347	186	53	proposition	proposition	NOUN
ejpam-3347	186	54	.	.	PUNCT
ejpam-3347	187	1	proposition	proposition	NOUN
ejpam-3347	187	2	5	5	NUM
ejpam-3347	187	3	.	.	PUNCT
ejpam-3347	188	1	the	the	DET
ejpam-3347	188	2	tail	tail	NOUN
ejpam-3347	188	3	-	-	PUNCT
ejpam-3347	188	4	var	var	NOUN
ejpam-3347	188	5	(	(	PUNCT
ejpam-3347	188	6	tvar	tvar	NOUN
ejpam-3347	188	7	)	)	PUNCT
ejpam-3347	188	8	is	be	AUX
ejpam-3347	188	9	derivative	derivative	ADJ
ejpam-3347	188	10	coherent	coherent	ADJ
ejpam-3347	188	11	risk	risk	NOUN
ejpam-3347	188	12	measure	measure	NOUN
ejpam-3347	188	13	of	of	ADP
ejpam-3347	188	14	the	the	DET
ejpam-3347	188	15	var	var	NOUN
ejpam-3347	188	16	.	.	PUNCT
ejpam-3347	189	1	for	for	ADP
ejpam-3347	189	2	a	a	DET
ejpam-3347	189	3	given	give	VERB
ejpam-3347	189	4	confidence	confidence	NOUN
ejpam-3347	189	5	level	level	NOUN
ejpam-3347	189	6	α	α	X
ejpam-3347	189	7	∈	∈	NOUN
ejpam-3347	189	8	]	]	X
ejpam-3347	189	9	0	0	NUM
ejpam-3347	189	10	,	,	PUNCT
ejpam-3347	189	11	1	1	NUM
ejpam-3347	189	12	[	[	X
ejpam-3347	189	13	,	,	PUNCT
ejpam-3347	189	14	it	it	PRON
ejpam-3347	189	15	follows	follow	VERB
ejpam-3347	189	16	that	that	SCONJ
ejpam-3347	190	1	c	c	PROPN
ejpam-3347	190	2	(	(	PUNCT
ejpam-3347	190	3	u1	u1	PROPN
ejpam-3347	190	4	,	,	PUNCT
ejpam-3347	190	5	...	...	PUNCT
ejpam-3347	190	6	,	,	PUNCT
ejpam-3347	190	7	un	un	PROPN
ejpam-3347	190	8	/	/	SYM
ejpam-3347	190	9	wt	wt	NOUN
ejpam-3347	190	10	)	)	PUNCT
ejpam-3347	190	11	=	=	SYM
ejpam-3347	190	12	f−1	f−1	PROPN
ejpam-3347	190	13	w	w	ADP
ejpam-3347	190	14	(	(	PUNCT
ejpam-3347	190	15	wt	wt	NOUN
ejpam-3347	190	16	)	)	PUNCT
ejpam-3347	190	17	〈	〈	PROPN
ejpam-3347	190	18	∂	∂	NUM
ejpam-3347	190	19	∂wt	∂wt	PROPN
ejpam-3347	190	20	(	(	PUNCT
ejpam-3347	190	21	tv	tv	NOUN
ejpam-3347	190	22	aru	aru	NOUN
ejpam-3347	190	23	(	(	PUNCT
ejpam-3347	190	24	x	x	NOUN
ejpam-3347	190	25	/	/	SYM
ejpam-3347	190	26	wt	wt	NOUN
ejpam-3347	190	27	)	)	PUNCT
ejpam-3347	190	28	)	)	PUNCT
ejpam-3347	190	29	,	,	PUNCT
ejpam-3347	190	30	(	(	PUNCT
ejpam-3347	190	31	pt	pt	INTJ
ejpam-3347	190	32	−	−	PROPN
ejpam-3347	190	33	pt	pt	NOUN
ejpam-3347	190	34	)	)	PUNCT
ejpam-3347	190	35	〉	〉	NOUN
ejpam-3347	190	36	−	−	NOUN
ejpam-3347	190	37	f−1	f−1	PROPN
ejpam-3347	190	38	w	w	PROPN
ejpam-3347	190	39	(	(	PUNCT
ejpam-3347	190	40	wt	wt	NOUN
ejpam-3347	190	41	)	)	PUNCT
ejpam-3347	190	42	〈	〈	PROPN
ejpam-3347	190	43	∂	∂	NUM
ejpam-3347	190	44	∂wt	∂wt	PROPN
ejpam-3347	190	45	(	(	PUNCT
ejpam-3347	190	46	xtv	xtv	PROPN
ejpam-3347	190	47	aru	aru	PROPN
ejpam-3347	190	48	(	(	PUNCT
ejpam-3347	190	49	x	x	NOUN
ejpam-3347	190	50	/	/	SYM
ejpam-3347	190	51	wt	wt	NOUN
ejpam-3347	190	52	)	)	PUNCT
ejpam-3347	190	53	)	)	PUNCT
ejpam-3347	190	54	,	,	PUNCT
ejpam-3347	190	55	(	(	PUNCT
ejpam-3347	190	56	pt	pt	INTJ
ejpam-3347	190	57	−	−	PROPN
ejpam-3347	190	58	pt	pt	PROPN
ejpam-3347	190	59	)	)	PUNCT
ejpam-3347	190	60	〉	〉	NOUN
ejpam-3347	190	61	(	(	PUNCT
ejpam-3347	190	62	22	22	NUM
ejpam-3347	190	63	)	)	PUNCT
ejpam-3347	190	64	furthermore	furthermore	ADV
ejpam-3347	190	65	c	c	NOUN
ejpam-3347	190	66	(	(	PUNCT
ejpam-3347	190	67	u1	u1	PROPN
ejpam-3347	190	68	,	,	PUNCT
ejpam-3347	190	69	...	...	PUNCT
ejpam-3347	190	70	,	,	PUNCT
ejpam-3347	190	71	un	un	PROPN
ejpam-3347	190	72	/	/	SYM
ejpam-3347	190	73	wt	wt	NOUN
ejpam-3347	190	74	)	)	PUNCT
ejpam-3347	190	75	=	=	SYM
ejpam-3347	191	1	f−1	f−1	PROPN
ejpam-3347	191	2	w	w	PROPN
ejpam-3347	191	3	(	(	PUNCT
ejpam-3347	191	4	wt	wt	NOUN
ejpam-3347	191	5	)	)	PUNCT
ejpam-3347	191	6	1	1	NUM
ejpam-3347	191	7	2	2	NUM
ejpam-3347	191	8	(	(	PUNCT
ejpam-3347	191	9	∥∥∥∥	∥∥∥∥	NUM
ejpam-3347	191	10	∂	∂	NUM
ejpam-3347	192	1	∂wt	∂wt	PROPN
ejpam-3347	192	2	(	(	PUNCT
ejpam-3347	192	3	tv	tv	NOUN
ejpam-3347	192	4	aru	aru	NOUN
ejpam-3347	192	5	(	(	PUNCT
ejpam-3347	192	6	x	x	NOUN
ejpam-3347	192	7	/	/	SYM
ejpam-3347	192	8	wt	wt	NOUN
ejpam-3347	192	9	)	)	PUNCT
ejpam-3347	192	10	)	)	PUNCT
ejpam-3347	193	1	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3347	193	2	−	−	PROPN
ejpam-3347	193	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-3347	193	4	∂	∂	NUM
ejpam-3347	194	1	∂wt	∂wt	PROPN
ejpam-3347	194	2	(	(	PUNCT
ejpam-3347	194	3	xtv	xtv	PROPN
ejpam-3347	194	4	aru	aru	PROPN
ejpam-3347	194	5	(	(	PUNCT
ejpam-3347	194	6	x	x	NOUN
ejpam-3347	194	7	/	/	SYM
ejpam-3347	194	8	wt	wt	NOUN
ejpam-3347	194	9	)	)	PUNCT
ejpam-3347	194	10	)	)	PUNCT
ejpam-3347	194	11	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3347	194	12	)	)	PUNCT
ejpam-3347	194	13	(	(	PUNCT
ejpam-3347	194	14	23	23	X
ejpam-3347	194	15	)	)	PUNCT
ejpam-3347	194	16	proof	proof	NOUN
ejpam-3347	194	17	.	.	PUNCT
ejpam-3347	195	1	for	for	ADP
ejpam-3347	195	2	relation	relation	NOUN
ejpam-3347	195	3	(	(	PUNCT
ejpam-3347	195	4	21	21	NUM
ejpam-3347	195	5	)	)	PUNCT
ejpam-3347	195	6	and	and	CCONJ
ejpam-3347	195	7	the	the	DET
ejpam-3347	195	8	proposition	proposition	NOUN
ejpam-3347	195	9	(	(	PUNCT
ejpam-3347	195	10	3	3	X
ejpam-3347	195	11	)	)	PUNCT
ejpam-3347	195	12	we	we	PRON
ejpam-3347	195	13	obtain	obtain	VERB
ejpam-3347	195	14	the	the	DET
ejpam-3347	195	15	following	follow	VERB
ejpam-3347	195	16	equality	equality	NOUN
ejpam-3347	195	17	:	:	PUNCT
ejpam-3347	196	1	c	c	NOUN
ejpam-3347	196	2	(	(	PUNCT
ejpam-3347	196	3	u1	u1	PROPN
ejpam-3347	196	4	,	,	PUNCT
ejpam-3347	196	5	...	...	PUNCT
ejpam-3347	196	6	,	,	PUNCT
ejpam-3347	196	7	un	un	PROPN
ejpam-3347	196	8	/	/	SYM
ejpam-3347	196	9	wt	wt	NOUN
ejpam-3347	196	10	)	)	PUNCT
ejpam-3347	196	11	=	=	SYM
ejpam-3347	197	1	f−1	f−1	PROPN
ejpam-3347	197	2	w	w	PROPN
ejpam-3347	197	3	(	(	PUNCT
ejpam-3347	197	4	wt	wt	NOUN
ejpam-3347	197	5	)	)	PUNCT
ejpam-3347	198	1	[	[	X
ejpam-3347	198	2	〈	〈	NOUN
ejpam-3347	198	3	∂	∂	NUM
ejpam-3347	198	4	∂wt	∂wt	PROPN
ejpam-3347	198	5	(	(	PUNCT
ejpam-3347	198	6	tv	tv	NOUN
ejpam-3347	198	7	aru	aru	NOUN
ejpam-3347	198	8	(	(	PUNCT
ejpam-3347	198	9	x	x	NOUN
ejpam-3347	198	10	/	/	SYM
ejpam-3347	198	11	wt	wt	NOUN
ejpam-3347	198	12	)	)	PUNCT
ejpam-3347	198	13	)	)	PUNCT
ejpam-3347	198	14	,	,	PUNCT
ejpam-3347	198	15	(	(	PUNCT
ejpam-3347	198	16	pt	pt	INTJ
ejpam-3347	198	17	−	−	PROPN
ejpam-3347	198	18	pt	pt	NOUN
ejpam-3347	198	19	)	)	PUNCT
ejpam-3347	198	20	〉	〉	NOUN
ejpam-3347	198	21	−	−	NOUN
ejpam-3347	198	22	〈	〈	PROPN
ejpam-3347	198	23	∂	∂	NOUN
ejpam-3347	198	24	∂wt	∂wt	PROPN
ejpam-3347	198	25	(	(	PUNCT
ejpam-3347	198	26	xtv	xtv	PROPN
ejpam-3347	198	27	aru	aru	PROPN
ejpam-3347	198	28	(	(	PUNCT
ejpam-3347	198	29	x	x	NOUN
ejpam-3347	198	30	/	/	SYM
ejpam-3347	198	31	wt	wt	NOUN
ejpam-3347	198	32	)	)	PUNCT
ejpam-3347	198	33	)	)	PUNCT
ejpam-3347	198	34	,	,	PUNCT
ejpam-3347	198	35	(	(	PUNCT
ejpam-3347	198	36	pt	pt	INTJ
ejpam-3347	198	37	−	−	PROPN
ejpam-3347	198	38	pt	pt	NOUN
ejpam-3347	198	39	)	)	PUNCT
ejpam-3347	198	40	〉	〉	NOUN
ejpam-3347	198	41	]	]	PUNCT
ejpam-3347	198	42	v.	v.	PROPN
ejpam-3347	198	43	y.	y.	PROPN
ejpam-3347	198	44	b.	b.	PROPN
ejpam-3347	199	1	loyara	loyara	PROPN
ejpam-3347	199	2	,	,	PUNCT
ejpam-3347	199	3	d.	d.	PROPN
ejpam-3347	199	4	barro	barro	PROPN
ejpam-3347	199	5	/	/	SYM
ejpam-3347	199	6	eur	eur	PROPN
ejpam-3347	199	7	.	.	PUNCT
ejpam-3347	200	1	j.	j.	PROPN
ejpam-3347	200	2	pure	pure	PROPN
ejpam-3347	200	3	appl	appl	PROPN
ejpam-3347	200	4	.	.	PROPN
ejpam-3347	200	5	math	math	PROPN
ejpam-3347	200	6	,	,	PUNCT
ejpam-3347	200	7	12	12	NUM
ejpam-3347	200	8	(	(	PUNCT
ejpam-3347	200	9	1	1	NUM
ejpam-3347	200	10	)	)	PUNCT
ejpam-3347	200	11	(	(	PUNCT
ejpam-3347	200	12	2019	2019	NUM
ejpam-3347	200	13	)	)	PUNCT
ejpam-3347	200	14	,	,	PUNCT
ejpam-3347	200	15	194	194	NUM
ejpam-3347	200	16	-	-	SYM
ejpam-3347	200	17	207	207	NUM
ejpam-3347	200	18	203	203	NUM
ejpam-3347	200	19	then	then	ADV
ejpam-3347	200	20	,	,	PUNCT
ejpam-3347	200	21	it	it	PRON
ejpam-3347	200	22	follows	follow	VERB
ejpam-3347	200	23	that	that	PRON
ejpam-3347	200	24	:	:	PUNCT
ejpam-3347	201	1	c	c	X
ejpam-3347	201	2	(	(	PUNCT
ejpam-3347	201	3	u1	u1	PROPN
ejpam-3347	201	4	,	,	PUNCT
ejpam-3347	201	5	...	...	PUNCT
ejpam-3347	201	6	,	,	PUNCT
ejpam-3347	201	7	un	un	PROPN
ejpam-3347	201	8	/	/	SYM
ejpam-3347	201	9	wt	wt	NOUN
ejpam-3347	201	10	)	)	PUNCT
ejpam-3347	201	11	=	=	SYM
ejpam-3347	202	1	f−1	f−1	PROPN
ejpam-3347	202	2	w	w	PROPN
ejpam-3347	202	3	(	(	PUNCT
ejpam-3347	202	4	wt	wt	NOUN
ejpam-3347	202	5	)	)	PUNCT
ejpam-3347	202	6	1	1	NUM
ejpam-3347	202	7	4	4	NUM
ejpam-3347	202	8	[	[	X
ejpam-3347	202	9	∥∥∥	∥∥∥	NUM
ejpam-3347	202	10	∂	∂	NUM
ejpam-3347	202	11	∂wt	∂wt	PROPN
ejpam-3347	202	12	(	(	PUNCT
ejpam-3347	202	13	tv	tv	NOUN
ejpam-3347	202	14	aru	aru	NOUN
ejpam-3347	202	15	(	(	PUNCT
ejpam-3347	202	16	x	x	NOUN
ejpam-3347	202	17	/	/	SYM
ejpam-3347	202	18	wt	wt	NOUN
ejpam-3347	202	19	)	)	PUNCT
ejpam-3347	202	20	)	)	PUNCT
ejpam-3347	203	1	+	+	CCONJ
ejpam-3347	203	2	(	(	PUNCT
ejpam-3347	203	3	pt	pt	INTJ
ejpam-3347	203	4	−	−	PROPN
ejpam-3347	203	5	pt	pt	PROPN
ejpam-3347	203	6	)	)	PUNCT
ejpam-3347	203	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	203	8	−	−	PROPN
ejpam-3347	203	9	∥∥∥	∥∥∥	PROPN
ejpam-3347	203	10	∂	∂	NUM
ejpam-3347	203	11	∂wt	∂wt	PROPN
ejpam-3347	203	12	(	(	PUNCT
ejpam-3347	203	13	xtv	xtv	PROPN
ejpam-3347	203	14	aru	aru	PROPN
ejpam-3347	203	15	(	(	PUNCT
ejpam-3347	203	16	x	x	NOUN
ejpam-3347	203	17	/	/	SYM
ejpam-3347	203	18	wt	wt	NOUN
ejpam-3347	203	19	)	)	PUNCT
ejpam-3347	203	20	)	)	PUNCT
ejpam-3347	204	1	+	+	CCONJ
ejpam-3347	204	2	(	(	PUNCT
ejpam-3347	204	3	pt	pt	INTJ
ejpam-3347	204	4	−	−	PROPN
ejpam-3347	204	5	pt	pt	PROPN
ejpam-3347	204	6	)	)	PUNCT
ejpam-3347	204	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	204	8	]	]	PUNCT
ejpam-3347	205	1	=	=	PUNCT
ejpam-3347	205	2	f−1	f−1	PROPN
ejpam-3347	205	3	w	w	PROPN
ejpam-3347	205	4	(	(	PUNCT
ejpam-3347	205	5	wt	wt	NOUN
ejpam-3347	205	6	)	)	PUNCT
ejpam-3347	205	7	1	1	NUM
ejpam-3347	205	8	4	4	NUM
ejpam-3347	205	9	[	[	SYM
ejpam-3347	205	10	2	2	NUM
ejpam-3347	205	11	(	(	PUNCT
ejpam-3347	205	12	∥∥∥	∥∥∥	NOUN
ejpam-3347	205	13	∂	∂	NUM
ejpam-3347	205	14	∂wt	∂wt	PROPN
ejpam-3347	205	15	(	(	PUNCT
ejpam-3347	205	16	tv	tv	NOUN
ejpam-3347	205	17	aru	aru	NOUN
ejpam-3347	205	18	(	(	PUNCT
ejpam-3347	205	19	x	x	NOUN
ejpam-3347	205	20	/	/	SYM
ejpam-3347	205	21	wt	wt	NOUN
ejpam-3347	205	22	)	)	PUNCT
ejpam-3347	205	23	)	)	PUNCT
ejpam-3347	205	24	∥∥∥2	∥∥∥2	NOUN
ejpam-3347	206	1	+	+	PUNCT
ejpam-3347	206	2	‖pt	‖pt	PROPN
ejpam-3347	206	3	−	−	PROPN
ejpam-3347	206	4	pt‖2	pt‖2	NOUN
ejpam-3347	206	5	)	)	PUNCT
ejpam-3347	206	6	−	−	PROPN
ejpam-3347	206	7	2	2	NUM
ejpam-3347	206	8	(	(	PUNCT
ejpam-3347	206	9	‖xtv	‖xtv	PROPN
ejpam-3347	206	10	aru	aru	X
ejpam-3347	206	11	(	(	PUNCT
ejpam-3347	206	12	x	x	NOUN
ejpam-3347	206	13	/	/	SYM
ejpam-3347	206	14	wt)‖2	wt)‖2	ADP
ejpam-3347	206	15	+	+	CCONJ
ejpam-3347	206	16	‖(pt	‖(pt	NOUN
ejpam-3347	206	17	−	−	NOUN
ejpam-3347	206	18	pt)‖2	pt)‖2	NOUN
ejpam-3347	206	19	)	)	PUNCT
ejpam-3347	206	20	]	]	PUNCT
ejpam-3347	207	1	it	it	PRON
ejpam-3347	207	2	comes	come	VERB
ejpam-3347	207	3	that	that	PRON
ejpam-3347	207	4	:	:	PUNCT
ejpam-3347	208	1	c	c	X
ejpam-3347	208	2	(	(	PUNCT
ejpam-3347	208	3	u1	u1	PROPN
ejpam-3347	208	4	,	,	PUNCT
ejpam-3347	208	5	...	...	PUNCT
ejpam-3347	208	6	,	,	PUNCT
ejpam-3347	208	7	un	un	PROPN
ejpam-3347	208	8	/	/	SYM
ejpam-3347	208	9	wt	wt	NOUN
ejpam-3347	208	10	)	)	PUNCT
ejpam-3347	208	11	=	=	SYM
ejpam-3347	209	1	f−1	f−1	PROPN
ejpam-3347	209	2	w	w	PROPN
ejpam-3347	209	3	(	(	PUNCT
ejpam-3347	209	4	wt	wt	NOUN
ejpam-3347	209	5	)	)	PUNCT
ejpam-3347	209	6	1	1	NUM
ejpam-3347	209	7	2	2	NUM
ejpam-3347	209	8	(	(	PUNCT
ejpam-3347	209	9	∥∥∥∥	∥∥∥∥	NUM
ejpam-3347	209	10	∂	∂	NUM
ejpam-3347	210	1	∂wt	∂wt	PROPN
ejpam-3347	210	2	(	(	PUNCT
ejpam-3347	210	3	tv	tv	NOUN
ejpam-3347	210	4	aru	aru	NOUN
ejpam-3347	210	5	(	(	PUNCT
ejpam-3347	210	6	x	x	NOUN
ejpam-3347	210	7	/	/	SYM
ejpam-3347	210	8	wt	wt	NOUN
ejpam-3347	210	9	)	)	PUNCT
ejpam-3347	210	10	)	)	PUNCT
ejpam-3347	211	1	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3347	211	2	−	−	PROPN
ejpam-3347	211	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-3347	211	4	∂	∂	NUM
ejpam-3347	212	1	∂wt	∂wt	PROPN
ejpam-3347	212	2	(	(	PUNCT
ejpam-3347	212	3	xtv	xtv	PROPN
ejpam-3347	212	4	aru	aru	PROPN
ejpam-3347	212	5	(	(	PUNCT
ejpam-3347	212	6	x	x	NOUN
ejpam-3347	212	7	/	/	SYM
ejpam-3347	212	8	wt	wt	NOUN
ejpam-3347	212	9	)	)	PUNCT
ejpam-3347	212	10	)	)	PUNCT
ejpam-3347	212	11	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3347	212	12	)	)	PUNCT
ejpam-3347	212	13	.	.	PUNCT
ejpam-3347	213	1	3.3	3.3	NUM
ejpam-3347	213	2	.	.	PUNCT
ejpam-3347	214	1	performance	performance	NOUN
ejpam-3347	214	2	measures	measure	NOUN
ejpam-3347	214	3	and	and	CCONJ
ejpam-3347	214	4	the	the	DET
ejpam-3347	214	5	distribution	distribution	NOUN
ejpam-3347	214	6	of	of	ADP
ejpam-3347	214	7	l&p	l&p	PROPN
ejpam-3347	214	8	of	of	ADP
ejpam-3347	214	9	a	a	DET
ejpam-3347	214	10	portfolio	portfolio	NOUN
ejpam-3347	214	11	proposition	proposition	NOUN
ejpam-3347	214	12	6	6	NUM
ejpam-3347	214	13	.	.	PUNCT
ejpam-3347	215	1	let	let	VERB
ejpam-3347	215	2	w	w	NOUN
ejpam-3347	215	3	=	=	SYM
ejpam-3347	215	4	(	(	PUNCT
ejpam-3347	215	5	w1	w1	NOUN
ejpam-3347	215	6	,	,	PUNCT
ejpam-3347	215	7	...	...	PUNCT
ejpam-3347	215	8	,	,	PUNCT
ejpam-3347	215	9	wn)t	wn)t	PROPN
ejpam-3347	215	10	∈	∈	PROPN
ejpam-3347	215	11	rn	rn	PROPN
ejpam-3347	215	12	a	a	DET
ejpam-3347	215	13	portfolio	portfolio	NOUN
ejpam-3347	215	14	consisting	consist	VERB
ejpam-3347	215	15	of	of	ADP
ejpam-3347	215	16	n	n	DET
ejpam-3347	215	17	capital	capital	NOUN
ejpam-3347	215	18	(	(	PUNCT
ejpam-3347	215	19	the	the	DET
ejpam-3347	215	20	allocation	allocation	NOUN
ejpam-3347	215	21	of	of	ADP
ejpam-3347	215	22	capital	capital	NOUN
ejpam-3347	215	23	)	)	PUNCT
ejpam-3347	215	24	and	and	CCONJ
ejpam-3347	215	25	st	st	PROPN
ejpam-3347	215	26	=	=	SYM
ejpam-3347	215	27	(	(	PUNCT
ejpam-3347	215	28	s1,t	s1,t	PROPN
ejpam-3347	215	29	,	,	PUNCT
ejpam-3347	215	30	...	...	PUNCT
ejpam-3347	215	31	,	,	PUNCT
ejpam-3347	215	32	sn	sn	PROPN
ejpam-3347	215	33	,	,	PUNCT
ejpam-3347	215	34	t	t	PROPN
ejpam-3347	215	35	)	)	PUNCT
ejpam-3347	215	36	t	t	PROPN
ejpam-3347	215	37	the	the	DET
ejpam-3347	215	38	non	non	ADJ
ejpam-3347	215	39	-	-	ADJ
ejpam-3347	215	40	negative	negative	ADJ
ejpam-3347	215	41	random	random	ADJ
ejpam-3347	215	42	vector	vector	NOUN
ejpam-3347	215	43	representing	represent	VERB
ejpam-3347	215	44	the	the	DET
ejpam-3347	215	45	capital	capital	NOUN
ejpam-3347	215	46	at	at	ADP
ejpam-3347	215	47	the	the	DET
ejpam-3347	215	48	moment	moment	NOUN
ejpam-3347	216	1	t.	t.	NOUN
ejpam-3347	216	2	then	then	ADV
ejpam-3347	216	3	geometric	geometric	ADJ
ejpam-3347	216	4	yield	yield	NOUN
ejpam-3347	216	5	rt	rt	PROPN
ejpam-3347	216	6	=	=	PUNCT
ejpam-3347	216	7	log	log	PROPN
ejpam-3347	216	8	(	(	PUNCT
ejpam-3347	216	9	(	(	PUNCT
ejpam-3347	216	10	[	[	X
ejpam-3347	216	11	(	(	PUNCT
ejpam-3347	216	12	σ(st	σ(st	NOUN
ejpam-3347	216	13	)	)	PUNCT
ejpam-3347	216	14	)	)	PUNCT
ejpam-3347	216	15	2+(e(st	2+(e(st	NUM
ejpam-3347	216	16	)	)	PUNCT
ejpam-3347	216	17	)	)	PUNCT
ejpam-3347	216	18	2	2	NUM
ejpam-3347	216	19	]	]	SYM
ejpam-3347	216	20	)	)	PUNCT
ejpam-3347	216	21	1/2	1/2	NUM
ejpam-3347	216	22	(	(	PUNCT
ejpam-3347	216	23	[	[	X
ejpam-3347	216	24	(	(	PUNCT
ejpam-3347	216	25	σ(st−1))2+(e(st−1))2	σ(st−1))2+(e(st−1))2	NOUN
ejpam-3347	216	26	]	]	PUNCT
ejpam-3347	216	27	)	)	PUNCT
ejpam-3347	216	28	1/2	1/2	NUM
ejpam-3347	217	1	+	+	NUM
ejpam-3347	217	2	n×∆t	n×∆t	NOUN
ejpam-3347	217	3	(	(	PUNCT
ejpam-3347	217	4	[	[	X
ejpam-3347	217	5	(	(	PUNCT
ejpam-3347	217	6	σ(w))2+(e(w))2	σ(w))2+(e(w))2	PROPN
ejpam-3347	217	7	]	]	PUNCT
ejpam-3347	217	8	)	)	PUNCT
ejpam-3347	217	9	1/2×([(σ(st−1))2+(e(st−1))2	1/2×([(σ(st−1))2+(e(st−1))2	NUM
ejpam-3347	217	10	]	]	PUNCT
ejpam-3347	217	11	)	)	PUNCT
ejpam-3347	217	12	1/2	1/2	NUM
ejpam-3347	217	13	)	)	PUNCT
ejpam-3347	217	14	(	(	PUNCT
ejpam-3347	217	15	24	24	NUM
ejpam-3347	217	16	)	)	PUNCT
ejpam-3347	217	17	where	where	SCONJ
ejpam-3347	217	18	σ	σ	PROPN
ejpam-3347	217	19	(	(	PUNCT
ejpam-3347	217	20	·	·	PUNCT
ejpam-3347	217	21	)	)	PUNCT
ejpam-3347	217	22	is	be	AUX
ejpam-3347	217	23	a	a	DET
ejpam-3347	217	24	standard	standard	ADJ
ejpam-3347	217	25	deviation	deviation	NOUN
ejpam-3347	217	26	and	and	CCONJ
ejpam-3347	217	27	e	e	NOUN
ejpam-3347	217	28	(	(	PUNCT
ejpam-3347	217	29	·	·	PUNCT
ejpam-3347	217	30	)	)	PUNCT
ejpam-3347	217	31	is	be	AUX
ejpam-3347	217	32	a	a	DET
ejpam-3347	217	33	mean	mean	NOUN
ejpam-3347	217	34	and	and	CCONJ
ejpam-3347	217	35	with	with	ADP
ejpam-3347	217	36	∆t	∆t	PROPN
ejpam-3347	217	37	all	all	DET
ejpam-3347	217	38	the	the	DET
ejpam-3347	217	39	interim	interim	ADJ
ejpam-3347	217	40	payments	payment	NOUN
ejpam-3347	217	41	obtained	obtain	VERB
ejpam-3347	217	42	between	between	ADP
ejpam-3347	217	43	the	the	DET
ejpam-3347	217	44	dates	date	NOUN
ejpam-3347	217	45	t−	t−	PROPN
ejpam-3347	217	46	1	1	NUM
ejpam-3347	217	47	and	and	CCONJ
ejpam-3347	217	48	t.	t.	NOUN
ejpam-3347	217	49	the	the	DET
ejpam-3347	217	50	distribution	distribution	NOUN
ejpam-3347	217	51	of	of	ADP
ejpam-3347	217	52	(	(	PUNCT
ejpam-3347	217	53	pt+τ	pt+τ	NOUN
ejpam-3347	217	54	−	−	NOUN
ejpam-3347	217	55	pt	pt	NOUN
ejpam-3347	217	56	)	)	PUNCT
ejpam-3347	217	57	is	be	AUX
ejpam-3347	217	58	called	call	VERB
ejpam-3347	217	59	profit	profit	NOUN
ejpam-3347	217	60	distribution	distribution	NOUN
ejpam-3347	217	61	loss	loss	NOUN
ejpam-3347	217	62	that	that	PRON
ejpam-3347	217	63	expresses	express	VERB
ejpam-3347	217	64	the	the	DET
ejpam-3347	217	65	change	change	NOUN
ejpam-3347	217	66	in	in	ADP
ejpam-3347	217	67	the	the	DET
ejpam-3347	217	68	value	value	NOUN
ejpam-3347	217	69	of	of	ADP
ejpam-3347	217	70	the	the	DET
ejpam-3347	217	71	portfolio	portfolio	NOUN
ejpam-3347	217	72	.	.	PUNCT
ejpam-3347	218	1	proof	proof	NOUN
ejpam-3347	218	2	.	.	PUNCT
ejpam-3347	219	1	the	the	DET
ejpam-3347	219	2	pt	pt	PROPN
ejpam-3347	219	3	value	value	NOUN
ejpam-3347	219	4	of	of	ADP
ejpam-3347	219	5	the	the	DET
ejpam-3347	219	6	portfolio	portfolio	NOUN
ejpam-3347	219	7	is	be	AUX
ejpam-3347	219	8	given	give	VERB
ejpam-3347	219	9	by	by	ADP
ejpam-3347	219	10	:	:	PUNCT
ejpam-3347	219	11	pt	pt	PROPN
ejpam-3347	219	12	=	=	SYM
ejpam-3347	219	13	n∑	n∑	PROPN
ejpam-3347	219	14	j=1	j=1	PROPN
ejpam-3347	219	15	wjsj	wjsj	X
ejpam-3347	219	16	,	,	PUNCT
ejpam-3347	219	17	t.	t.	PROPN
ejpam-3347	219	18	(	(	PUNCT
ejpam-3347	219	19	25	25	NUM
ejpam-3347	219	20	)	)	PUNCT
ejpam-3347	219	21	v.	v.	ADP
ejpam-3347	219	22	y.	y.	PROPN
ejpam-3347	219	23	b.	b.	PROPN
ejpam-3347	220	1	loyara	loyara	PROPN
ejpam-3347	220	2	,	,	PUNCT
ejpam-3347	220	3	d.	d.	PROPN
ejpam-3347	220	4	barro	barro	PROPN
ejpam-3347	220	5	/	/	SYM
ejpam-3347	220	6	eur	eur	PROPN
ejpam-3347	220	7	.	.	PUNCT
ejpam-3347	221	1	j.	j.	PROPN
ejpam-3347	221	2	pure	pure	PROPN
ejpam-3347	221	3	appl	appl	PROPN
ejpam-3347	221	4	.	.	PROPN
ejpam-3347	221	5	math	math	PROPN
ejpam-3347	221	6	,	,	PUNCT
ejpam-3347	221	7	12	12	NUM
ejpam-3347	221	8	(	(	PUNCT
ejpam-3347	221	9	1	1	NUM
ejpam-3347	221	10	)	)	PUNCT
ejpam-3347	221	11	(	(	PUNCT
ejpam-3347	221	12	2019	2019	NUM
ejpam-3347	221	13	)	)	PUNCT
ejpam-3347	221	14	,	,	PUNCT
ejpam-3347	221	15	194	194	NUM
ejpam-3347	221	16	-	-	SYM
ejpam-3347	221	17	207	207	NUM
ejpam-3347	221	18	204	204	NUM
ejpam-3347	221	19	the	the	DET
ejpam-3347	221	20	profits	profit	NOUN
ejpam-3347	221	21	and	and	CCONJ
ejpam-3347	221	22	losses	loss	NOUN
ejpam-3347	221	23	associated	associate	VERB
ejpam-3347	221	24	with	with	ADP
ejpam-3347	221	25	holding	hold	VERB
ejpam-3347	221	26	the	the	DET
ejpam-3347	221	27	asset	asset	NOUN
ejpam-3347	221	28	are	be	AUX
ejpam-3347	221	29	then	then	ADV
ejpam-3347	221	30	defined	define	VERB
ejpam-3347	221	31	by	by	ADP
ejpam-3347	221	32	the	the	DET
ejpam-3347	221	33	difference	difference	NOUN
ejpam-3347	221	34	:	:	PUNCT
ejpam-3347	221	35	p&l	p&l	NOUN
ejpam-3347	221	36	=	=	SYM
ejpam-3347	221	37	pt	pt	PROPN
ejpam-3347	221	38	+	+	CCONJ
ejpam-3347	221	39	∆t	∆t	PROPN
ejpam-3347	221	40	−	−	NOUN
ejpam-3347	221	41	pt−1	pt−1	NOUN
ejpam-3347	221	42	=	=	SYM
ejpam-3347	221	43	n∑	n∑	PROPN
ejpam-3347	221	44	j=1	j=1	PROPN
ejpam-3347	221	45	wj	wj	X
ejpam-3347	221	46	(	(	PUNCT
ejpam-3347	221	47	sj	sj	PROPN
ejpam-3347	221	48	,	,	PUNCT
ejpam-3347	221	49	t	t	PROPN
ejpam-3347	221	50	−	−	PROPN
ejpam-3347	221	51	sj	sj	PROPN
ejpam-3347	221	52	,	,	PUNCT
ejpam-3347	221	53	t−1	t−1	PROPN
ejpam-3347	221	54	)	)	PUNCT
ejpam-3347	221	55	+	+	NUM
ejpam-3347	221	56	∆t	∆t	NOUN
ejpam-3347	221	57	.	.	PUNCT
ejpam-3347	222	1	(	(	PUNCT
ejpam-3347	222	2	26	26	NUM
ejpam-3347	222	3	)	)	PUNCT
ejpam-3347	222	4	the	the	DET
ejpam-3347	222	5	equality	equality	NOUN
ejpam-3347	222	6	26	26	NUM
ejpam-3347	222	7	becomes	become	VERB
ejpam-3347	222	8	using	use	VERB
ejpam-3347	222	9	the	the	DET
ejpam-3347	222	10	scalar	scalar	ADJ
ejpam-3347	222	11	product	product	NOUN
ejpam-3347	222	12	:	:	PUNCT
ejpam-3347	222	13	:	:	PUNCT
ejpam-3347	222	14	p&l	p&l	PROPN
ejpam-3347	222	15	=	=	PUNCT
ejpam-3347	222	16	〈	〈	PROPN
ejpam-3347	222	17	w	w	PROPN
ejpam-3347	222	18	,	,	PUNCT
ejpam-3347	222	19	st	st	PROPN
ejpam-3347	222	20	−	−	PROPN
ejpam-3347	222	21	st−1	st−1	PROPN
ejpam-3347	222	22	〉	〉	NOUN
ejpam-3347	222	23	=	=	SYM
ejpam-3347	223	1	‖w‖	‖w‖	PROPN
ejpam-3347	223	2	‖st	‖st	NUM
ejpam-3347	223	3	−	−	PROPN
ejpam-3347	223	4	st−1‖+	st−1‖+	NOUN
ejpam-3347	223	5	∆t	∆t	PROPN
ejpam-3347	223	6	(	(	PUNCT
ejpam-3347	223	7	27	27	NUM
ejpam-3347	223	8	)	)	PUNCT
ejpam-3347	223	9	indeed	indeed	ADV
ejpam-3347	223	10	on	on	ADP
ejpam-3347	223	11	the	the	DET
ejpam-3347	223	12	same	same	ADJ
ejpam-3347	223	13	types	type	NOUN
ejpam-3347	223	14	of	of	ADP
ejpam-3347	223	15	considerations	consideration	NOUN
ejpam-3347	223	16	of	of	ADP
ejpam-3347	223	17	the	the	DET
ejpam-3347	223	18	section	section	NOUN
ejpam-3347	223	19	3.1	3.1	NUM
ejpam-3347	223	20	(	(	PUNCT
ejpam-3347	223	21	w	w	PROPN
ejpam-3347	223	22	and	and	CCONJ
ejpam-3347	223	23	st	st	PROPN
ejpam-3347	223	24	are	be	AUX
ejpam-3347	223	25	linked	link	VERB
ejpam-3347	223	26	)	)	PUNCT
ejpam-3347	223	27	.	.	PUNCT
ejpam-3347	224	1	then	then	ADV
ejpam-3347	224	2	:	:	PUNCT
ejpam-3347	224	3	p&l	p&l	NOUN
ejpam-3347	224	4	=	=	PUNCT
ejpam-3347	224	5			PROPN
ejpam-3347	224	6	n∑	n∑	PROPN
ejpam-3347	224	7	j=1	j=1	PROPN
ejpam-3347	224	8	w2	w2	PROPN
ejpam-3347	224	9	j	j	PROPN
ejpam-3347	224	10	1/2	1/2	PROPN
ejpam-3347	224	11	×	×	PROPN
ejpam-3347	224	12			PROPN
ejpam-3347	224	13	n∑	n∑	PROPN
ejpam-3347	224	14	j=1	j=1	NOUN
ejpam-3347	224	15	(	(	PUNCT
ejpam-3347	224	16	sj	sj	PROPN
ejpam-3347	224	17	,	,	PUNCT
ejpam-3347	224	18	t	t	PROPN
ejpam-3347	224	19	−	−	PROPN
ejpam-3347	224	20	sj	sj	PROPN
ejpam-3347	224	21	,	,	PUNCT
ejpam-3347	224	22	t−1)2	t−1)2	PROPN
ejpam-3347	224	23	1/2	1/2	PROPN
ejpam-3347	224	24	+	+	CCONJ
ejpam-3347	224	25	∆t	∆t	PROPN
ejpam-3347	224	26	(	(	PUNCT
ejpam-3347	224	27	28	28	NUM
ejpam-3347	224	28	)	)	PUNCT
ejpam-3347	224	29	these	these	DET
ejpam-3347	224	30	losses	loss	NOUN
ejpam-3347	224	31	and	and	CCONJ
ejpam-3347	224	32	profits	profit	NOUN
ejpam-3347	224	33	are	be	AUX
ejpam-3347	224	34	expressed	express	VERB
ejpam-3347	224	35	in	in	ADP
ejpam-3347	224	36	the	the	DET
ejpam-3347	224	37	form	form	NOUN
ejpam-3347	224	38	of	of	ADP
ejpam-3347	224	39	a	a	DET
ejpam-3347	224	40	geometric	geometric	ADJ
ejpam-3347	224	41	return	return	NOUN
ejpam-3347	224	42	noted	note	VERB
ejpam-3347	224	43	rt	rt	PROPN
ejpam-3347	224	44	:	:	PUNCT
ejpam-3347	225	1	rt	rt	PROPN
ejpam-3347	225	2	=	=	PUNCT
ejpam-3347	225	3	log	log	PROPN
ejpam-3347	225	4	(	(	PUNCT
ejpam-3347	225	5	pt	pt	NOUN
ejpam-3347	225	6	+	+	CCONJ
ejpam-3347	225	7	∆t	∆t	PROPN
ejpam-3347	225	8	pt−1	pt−1	NOUN
ejpam-3347	225	9	)	)	PUNCT
ejpam-3347	225	10	=	=	PUNCT
ejpam-3347	225	11	log	log	VERB
ejpam-3347	225	12			ADJ
ejpam-3347	225	13	(	(	PUNCT
ejpam-3347	225	14	n∑	n∑	NOUN
ejpam-3347	225	15	j=1	j=1	PROPN
ejpam-3347	225	16	w2	w2	PROPN
ejpam-3347	225	17	j	j	PROPN
ejpam-3347	225	18	)	)	PUNCT
ejpam-3347	225	19	1/2	1/2	NUM
ejpam-3347	225	20	×	×	NOUN
ejpam-3347	225	21	(	(	PUNCT
ejpam-3347	225	22	n∑	n∑	NOUN
ejpam-3347	225	23	j=1	j=1	PROPN
ejpam-3347	225	24	s2	s2	PROPN
ejpam-3347	225	25	j	j	PROPN
ejpam-3347	225	26	,	,	PUNCT
ejpam-3347	225	27	t	t	PROPN
ejpam-3347	225	28	)	)	PUNCT
ejpam-3347	225	29	1/2	1/2	NUM
ejpam-3347	225	30	+	+	NUM
ejpam-3347	225	31	∆t	∆t	PROPN
ejpam-3347	225	32	(	(	PUNCT
ejpam-3347	225	33	n∑	n∑	PROPN
ejpam-3347	225	34	j=1	j=1	PROPN
ejpam-3347	225	35	w2	w2	PROPN
ejpam-3347	225	36	j	j	PROPN
ejpam-3347	225	37	)	)	PUNCT
ejpam-3347	225	38	1/2	1/2	NUM
ejpam-3347	225	39	×	×	NOUN
ejpam-3347	225	40	(	(	PUNCT
ejpam-3347	225	41	n∑	n∑	NOUN
ejpam-3347	225	42	j=1	j=1	PROPN
ejpam-3347	225	43	s2	s2	PROPN
ejpam-3347	225	44	j	j	PROPN
ejpam-3347	225	45	,	,	PUNCT
ejpam-3347	225	46	t−1	t−1	PROPN
ejpam-3347	225	47	)	)	PUNCT
ejpam-3347	225	48	1/2	1/2	NUM
ejpam-3347	225	49			NOUN
ejpam-3347	225	50	(	(	PUNCT
ejpam-3347	225	51	29	29	NUM
ejpam-3347	225	52	)	)	PUNCT
ejpam-3347	225	53	if	if	SCONJ
ejpam-3347	225	54	we	we	PRON
ejpam-3347	225	55	use	use	VERB
ejpam-3347	225	56	the	the	DET
ejpam-3347	225	57	following	follow	VERB
ejpam-3347	225	58	relation	relation	NOUN
ejpam-3347	225	59	;	;	PUNCT
ejpam-3347	225	60	e	e	X
ejpam-3347	225	61	(	(	PUNCT
ejpam-3347	225	62	s2	s2	PROPN
ejpam-3347	225	63	t	t	PROPN
ejpam-3347	225	64	)	)	PUNCT
ejpam-3347	225	65	=	=	PUNCT
ejpam-3347	226	1	[	[	PUNCT
ejpam-3347	226	2	1	1	NUM
ejpam-3347	226	3	n	n	SYM
ejpam-3347	226	4	(	(	PUNCT
ejpam-3347	226	5	σ	σ	PROPN
ejpam-3347	226	6	(	(	PUNCT
ejpam-3347	226	7	st	st	PROPN
ejpam-3347	226	8	)	)	PUNCT
ejpam-3347	226	9	)	)	PUNCT
ejpam-3347	226	10	2	2	NUM
ejpam-3347	227	1	+	+	CCONJ
ejpam-3347	227	2	(	(	PUNCT
ejpam-3347	227	3	e	e	X
ejpam-3347	227	4	(	(	PUNCT
ejpam-3347	227	5	st	st	PROPN
ejpam-3347	227	6	)	)	PUNCT
ejpam-3347	227	7	)	)	PUNCT
ejpam-3347	227	8	2	2	NUM
ejpam-3347	227	9	]	]	SYM
ejpam-3347	227	10	1/2	1/2	NUM
ejpam-3347	227	11	.	.	PUNCT
ejpam-3347	228	1	it	it	PRON
ejpam-3347	228	2	comes	come	VERB
ejpam-3347	228	3	that	that	PRON
ejpam-3347	228	4	:	:	PUNCT
ejpam-3347	229	1	rt	rt	PROPN
ejpam-3347	229	2	=	=	PUNCT
ejpam-3347	229	3	log	log	PROPN
ejpam-3347	229	4	(	(	PUNCT
ejpam-3347	229	5	(	(	PUNCT
ejpam-3347	229	6	[	[	X
ejpam-3347	229	7	(	(	PUNCT
ejpam-3347	229	8	σ(st	σ(st	NOUN
ejpam-3347	229	9	)	)	PUNCT
ejpam-3347	229	10	)	)	PUNCT
ejpam-3347	229	11	2+(e(st	2+(e(st	NUM
ejpam-3347	229	12	)	)	PUNCT
ejpam-3347	229	13	)	)	PUNCT
ejpam-3347	229	14	2	2	NUM
ejpam-3347	229	15	]	]	SYM
ejpam-3347	229	16	)	)	PUNCT
ejpam-3347	229	17	1/2	1/2	NUM
ejpam-3347	229	18	(	(	PUNCT
ejpam-3347	229	19	[	[	X
ejpam-3347	229	20	(	(	PUNCT
ejpam-3347	229	21	σ(st−1))2+(e(st−1))2	σ(st−1))2+(e(st−1))2	NOUN
ejpam-3347	229	22	]	]	PUNCT
ejpam-3347	229	23	)	)	PUNCT
ejpam-3347	229	24	1/2	1/2	NUM
ejpam-3347	229	25	+	+	NUM
ejpam-3347	229	26	n×∆t	n×∆t	NOUN
ejpam-3347	229	27	(	(	PUNCT
ejpam-3347	229	28	[	[	X
ejpam-3347	229	29	(	(	PUNCT
ejpam-3347	229	30	σ(w))2+(e(w))2	σ(w))2+(e(w))2	PROPN
ejpam-3347	229	31	]	]	PUNCT
ejpam-3347	229	32	)	)	PUNCT
ejpam-3347	229	33	1/2×([(σ(st−1))2+(e(st−1))2	1/2×([(σ(st−1))2+(e(st−1))2	NUM
ejpam-3347	229	34	]	]	PUNCT
ejpam-3347	229	35	)	)	PUNCT
ejpam-3347	229	36	1/2	1/2	NUM
ejpam-3347	229	37	)	)	PUNCT
ejpam-3347	229	38	(	(	PUNCT
ejpam-3347	229	39	30	30	X
ejpam-3347	229	40	)	)	PUNCT
ejpam-3347	229	41	it	it	PRON
ejpam-3347	229	42	is	be	AUX
ejpam-3347	229	43	assumed	assume	VERB
ejpam-3347	229	44	that	that	SCONJ
ejpam-3347	229	45	the	the	DET
ejpam-3347	229	46	return	return	NOUN
ejpam-3347	229	47	on	on	ADP
ejpam-3347	229	48	the	the	DET
ejpam-3347	229	49	date	date	NOUN
ejpam-3347	229	50	t	t	PROPN
ejpam-3347	229	51	,	,	PUNCT
ejpam-3347	229	52	i.e.	i.e.	X
ejpam-3347	229	53	rt	rt	PROPN
ejpam-3347	229	54	,	,	PUNCT
ejpam-3347	229	55	is	be	AUX
ejpam-3347	229	56	a	a	DET
ejpam-3347	229	57	real	real	ADV
ejpam-3347	229	58	random	random	ADJ
ejpam-3347	229	59	variable	variable	NOUN
ejpam-3347	229	60	.	.	PUNCT
ejpam-3347	230	1	corollary	corollary	ADJ
ejpam-3347	230	2	1	1	NUM
ejpam-3347	230	3	.	.	PUNCT
ejpam-3347	231	1	let	let	VERB
ejpam-3347	231	2	w	w	NOUN
ejpam-3347	231	3	=	=	SYM
ejpam-3347	231	4	(	(	PUNCT
ejpam-3347	231	5	w1	w1	NOUN
ejpam-3347	231	6	,	,	PUNCT
ejpam-3347	231	7	...	...	PUNCT
ejpam-3347	231	8	,	,	PUNCT
ejpam-3347	231	9	wn)t	wn)t	PROPN
ejpam-3347	231	10	∈	∈	PROPN
ejpam-3347	231	11	rn	rn	PROPN
ejpam-3347	231	12	a	a	DET
ejpam-3347	231	13	portfolio	portfolio	NOUN
ejpam-3347	231	14	consisting	consist	VERB
ejpam-3347	231	15	of	of	ADP
ejpam-3347	231	16	n	n	DET
ejpam-3347	231	17	capital	capital	NOUN
ejpam-3347	231	18	(	(	PUNCT
ejpam-3347	231	19	the	the	DET
ejpam-3347	231	20	allocation	allocation	NOUN
ejpam-3347	231	21	of	of	ADP
ejpam-3347	231	22	capital	capital	NOUN
ejpam-3347	231	23	)	)	PUNCT
ejpam-3347	231	24	and	and	CCONJ
ejpam-3347	231	25	st	st	PROPN
ejpam-3347	231	26	=	=	SYM
ejpam-3347	231	27	(	(	PUNCT
ejpam-3347	231	28	s1,t	s1,t	PROPN
ejpam-3347	231	29	,	,	PUNCT
ejpam-3347	231	30	...	...	PUNCT
ejpam-3347	231	31	,	,	PUNCT
ejpam-3347	231	32	sn	sn	PROPN
ejpam-3347	231	33	,	,	PUNCT
ejpam-3347	231	34	t	t	PROPN
ejpam-3347	231	35	)	)	PUNCT
ejpam-3347	231	36	t	t	PROPN
ejpam-3347	231	37	the	the	DET
ejpam-3347	231	38	non	non	ADJ
ejpam-3347	231	39	-	-	ADJ
ejpam-3347	231	40	negative	negative	ADJ
ejpam-3347	231	41	random	random	ADJ
ejpam-3347	231	42	vector	vector	NOUN
ejpam-3347	231	43	representing	represent	VERB
ejpam-3347	231	44	the	the	DET
ejpam-3347	231	45	capital	capital	NOUN
ejpam-3347	231	46	at	at	ADP
ejpam-3347	231	47	the	the	DET
ejpam-3347	231	48	moment	moment	NOUN
ejpam-3347	231	49	t.	t.	NOUN
ejpam-3347	231	50	then	then	ADV
ejpam-3347	231	51	geometric	geometric	ADJ
ejpam-3347	231	52	yield	yield	NOUN
ejpam-3347	231	53	rt	rt	PROPN
ejpam-3347	231	54	'	'	PUNCT
ejpam-3347	231	55	n×∆t	n×∆t	PROPN
ejpam-3347	231	56	(	(	PUNCT
ejpam-3347	231	57	[	[	PUNCT
ejpam-3347	231	58	(	(	PUNCT
ejpam-3347	231	59	σ	σ	PROPN
ejpam-3347	231	60	(	(	PUNCT
ejpam-3347	231	61	w))2	w))2	NOUN
ejpam-3347	231	62	+	+	CCONJ
ejpam-3347	231	63	(	(	PUNCT
ejpam-3347	231	64	e	e	X
ejpam-3347	231	65	(	(	PUNCT
ejpam-3347	231	66	w))2	w))2	NOUN
ejpam-3347	231	67	]	]	PUNCT
ejpam-3347	231	68	)	)	PUNCT
ejpam-3347	231	69	1/2	1/2	NUM
ejpam-3347	231	70	×	×	NOUN
ejpam-3347	231	71	(	(	PUNCT
ejpam-3347	231	72	[	[	PUNCT
ejpam-3347	231	73	(	(	PUNCT
ejpam-3347	231	74	σ	σ	PROPN
ejpam-3347	231	75	(	(	PUNCT
ejpam-3347	231	76	st	st	PROPN
ejpam-3347	231	77	)	)	PUNCT
ejpam-3347	231	78	)	)	PUNCT
ejpam-3347	231	79	2	2	NUM
ejpam-3347	232	1	+	+	CCONJ
ejpam-3347	232	2	(	(	PUNCT
ejpam-3347	232	3	e	e	X
ejpam-3347	232	4	(	(	PUNCT
ejpam-3347	232	5	st	st	PROPN
ejpam-3347	232	6	)	)	PUNCT
ejpam-3347	232	7	)	)	PUNCT
ejpam-3347	232	8	2	2	NUM
ejpam-3347	232	9	]	]	SYM
ejpam-3347	232	10	)	)	PUNCT
ejpam-3347	232	11	1/2	1/2	NUM
ejpam-3347	232	12	(	(	PUNCT
ejpam-3347	232	13	31	31	NUM
ejpam-3347	232	14	)	)	PUNCT
ejpam-3347	232	15	where	where	SCONJ
ejpam-3347	232	16	σ	σ	PROPN
ejpam-3347	232	17	(	(	PUNCT
ejpam-3347	232	18	·	·	PUNCT
ejpam-3347	232	19	)	)	PUNCT
ejpam-3347	232	20	is	be	AUX
ejpam-3347	232	21	a	a	DET
ejpam-3347	232	22	standard	standard	ADJ
ejpam-3347	232	23	deviation	deviation	NOUN
ejpam-3347	232	24	and	and	CCONJ
ejpam-3347	232	25	e	e	NOUN
ejpam-3347	232	26	(	(	PUNCT
ejpam-3347	232	27	·	·	PUNCT
ejpam-3347	232	28	)	)	PUNCT
ejpam-3347	232	29	is	be	AUX
ejpam-3347	232	30	a	a	DET
ejpam-3347	232	31	mean	mean	NOUN
ejpam-3347	232	32	and	and	CCONJ
ejpam-3347	232	33	with	with	ADP
ejpam-3347	232	34	∆t	∆t	PROPN
ejpam-3347	232	35	all	all	DET
ejpam-3347	232	36	the	the	DET
ejpam-3347	232	37	interim	interim	ADJ
ejpam-3347	232	38	payments	payment	NOUN
ejpam-3347	232	39	obtained	obtain	VERB
ejpam-3347	232	40	between	between	ADP
ejpam-3347	232	41	the	the	DET
ejpam-3347	232	42	dates	date	NOUN
ejpam-3347	232	43	t−	t−	PROPN
ejpam-3347	232	44	1	1	NUM
ejpam-3347	232	45	and	and	CCONJ
ejpam-3347	232	46	t.	t.	NOUN
ejpam-3347	232	47	references	reference	NOUN
ejpam-3347	232	48	205	205	NUM
ejpam-3347	232	49	proof	proof	NOUN
ejpam-3347	232	50	.	.	PUNCT
ejpam-3347	233	1	by	by	ADP
ejpam-3347	233	2	taking	take	VERB
ejpam-3347	233	3	the	the	DET
ejpam-3347	233	4	relationship	relationship	NOUN
ejpam-3347	233	5	(	(	PUNCT
ejpam-3347	233	6	24	24	NUM
ejpam-3347	233	7	)	)	PUNCT
ejpam-3347	233	8	and	and	CCONJ
ejpam-3347	233	9	as	as	SCONJ
ejpam-3347	233	10	st	st	PROPN
ejpam-3347	233	11	and	and	CCONJ
ejpam-3347	233	12	st−1	st−1	PROPN
ejpam-3347	233	13	are	be	AUX
ejpam-3347	233	14	of	of	ADP
ejpam-3347	233	15	the	the	DET
ejpam-3347	233	16	same	same	ADJ
ejpam-3347	233	17	nature	nature	NOUN
ejpam-3347	233	18	we	we	PRON
ejpam-3347	233	19	have	have	VERB
ejpam-3347	233	20	:	:	PUNCT
ejpam-3347	233	21	σ	σ	PROPN
ejpam-3347	233	22	(	(	PUNCT
ejpam-3347	233	23	st	st	PROPN
ejpam-3347	233	24	)	)	PUNCT
ejpam-3347	233	25	'	'	PART
ejpam-3347	233	26	σ	σ	PROPN
ejpam-3347	233	27	(	(	PUNCT
ejpam-3347	233	28	st−1	st−1	NOUN
ejpam-3347	233	29	)	)	PUNCT
ejpam-3347	233	30	and	and	CCONJ
ejpam-3347	233	31	e	e	PROPN
ejpam-3347	233	32	(	(	PUNCT
ejpam-3347	233	33	st	st	PROPN
ejpam-3347	233	34	)	)	PUNCT
ejpam-3347	233	35	'	'	PART
ejpam-3347	233	36	e	e	NOUN
ejpam-3347	233	37	(	(	PUNCT
ejpam-3347	233	38	st−1	st−1	NOUN
ejpam-3347	233	39	)	)	PUNCT
ejpam-3347	233	40	.	.	PUNCT
ejpam-3347	234	1	and	and	CCONJ
ejpam-3347	234	2	view	view	VERB
ejpam-3347	234	3	the	the	DET
ejpam-3347	234	4	limited	limited	ADJ
ejpam-3347	234	5	developmental	developmental	ADJ
ejpam-3347	234	6	formula	formula	NOUN
ejpam-3347	234	7	in	in	ADP
ejpam-3347	234	8	the	the	DET
ejpam-3347	234	9	neighborhood	neighborhood	NOUN
ejpam-3347	234	10	of	of	ADP
ejpam-3347	234	11	zero	zero	NUM
ejpam-3347	234	12	log(1	log(1	NOUN
ejpam-3347	235	1	+	+	CCONJ
ejpam-3347	235	2	x	x	X
ejpam-3347	235	3	)	)	PUNCT
ejpam-3347	235	4	'	'	PUNCT
ejpam-3347	235	5	x	x	NOUN
ejpam-3347	236	1	it	it	PRON
ejpam-3347	236	2	comes	come	VERB
ejpam-3347	236	3	that	that	DET
ejpam-3347	236	4	rt	rt	PROPN
ejpam-3347	236	5	=	=	PRON
ejpam-3347	236	6	log	log	PROPN
ejpam-3347	236	7	1	1	PROPN
ejpam-3347	237	1	+	+	NUM
ejpam-3347	237	2	n×∆t	n×∆t	X
ejpam-3347	237	3	(	(	PUNCT
ejpam-3347	237	4	[	[	PUNCT
ejpam-3347	237	5	(	(	PUNCT
ejpam-3347	237	6	σ	σ	PROPN
ejpam-3347	237	7	(	(	PUNCT
ejpam-3347	237	8	w))2	w))2	NOUN
ejpam-3347	237	9	+	+	CCONJ
ejpam-3347	237	10	(	(	PUNCT
ejpam-3347	237	11	e	e	X
ejpam-3347	237	12	(	(	PUNCT
ejpam-3347	237	13	w))2	w))2	NOUN
ejpam-3347	237	14	]	]	PUNCT
ejpam-3347	237	15	)	)	PUNCT
ejpam-3347	237	16	1/2	1/2	NUM
ejpam-3347	237	17	×	×	NOUN
ejpam-3347	237	18	(	(	PUNCT
ejpam-3347	237	19	[	[	PUNCT
ejpam-3347	237	20	(	(	PUNCT
ejpam-3347	237	21	σ	σ	PROPN
ejpam-3347	237	22	(	(	PUNCT
ejpam-3347	237	23	st	st	PROPN
ejpam-3347	237	24	)	)	PUNCT
ejpam-3347	237	25	)	)	PUNCT
ejpam-3347	237	26	2	2	NUM
ejpam-3347	238	1	+	+	CCONJ
ejpam-3347	238	2	(	(	PUNCT
ejpam-3347	238	3	e	e	X
ejpam-3347	238	4	(	(	PUNCT
ejpam-3347	238	5	st	st	PROPN
ejpam-3347	238	6	)	)	PUNCT
ejpam-3347	238	7	)	)	PUNCT
ejpam-3347	238	8	2	2	NUM
ejpam-3347	238	9	]	]	PUNCT
ejpam-3347	238	10	)	)	PUNCT
ejpam-3347	238	11	1/2	1/2	NUM
ejpam-3347	238	12			NOUN
ejpam-3347	238	13	hence	hence	ADV
ejpam-3347	238	14	the	the	DET
ejpam-3347	238	15	result	result	NOUN
ejpam-3347	238	16	.	.	PUNCT
ejpam-3347	239	1	3.4	3.4	NUM
ejpam-3347	239	2	.	.	PUNCT
ejpam-3347	239	3	conclusion	conclusion	NOUN
ejpam-3347	239	4	and	and	CCONJ
ejpam-3347	239	5	discussion	discussion	NOUN
ejpam-3347	239	6	we	we	PRON
ejpam-3347	239	7	thought	think	VERB
ejpam-3347	239	8	to	to	PART
ejpam-3347	239	9	introduce	introduce	VERB
ejpam-3347	239	10	the	the	DET
ejpam-3347	239	11	notion	notion	NOUN
ejpam-3347	239	12	of	of	ADP
ejpam-3347	239	13	product	product	NOUN
ejpam-3347	239	14	in	in	ADP
ejpam-3347	239	15	the	the	DET
ejpam-3347	239	16	stochastic	stochastic	ADJ
ejpam-3347	239	17	modeling	modeling	NOUN
ejpam-3347	239	18	of	of	ADP
ejpam-3347	239	19	the	the	DET
ejpam-3347	239	20	copula	copula	NOUN
ejpam-3347	239	21	and	and	CCONJ
ejpam-3347	239	22	the	the	DET
ejpam-3347	239	23	value	value	NOUN
ejpam-3347	239	24	at	at	ADP
ejpam-3347	239	25	risk	risk	NOUN
ejpam-3347	239	26	.	.	PUNCT
ejpam-3347	240	1	because	because	SCONJ
ejpam-3347	240	2	it	it	PRON
ejpam-3347	240	3	allows	allow	VERB
ejpam-3347	240	4	us	we	PRON
ejpam-3347	240	5	to	to	PART
ejpam-3347	240	6	combine	combine	VERB
ejpam-3347	240	7	precisely	precisely	ADV
ejpam-3347	240	8	these	these	DET
ejpam-3347	240	9	two	two	NUM
ejpam-3347	240	10	notions	notion	NOUN
ejpam-3347	240	11	(	(	PUNCT
ejpam-3347	240	12	copula	copula	NOUN
ejpam-3347	240	13	,	,	PUNCT
ejpam-3347	240	14	var	var	NOUN
ejpam-3347	240	15	)	)	PUNCT
ejpam-3347	240	16	.	.	PUNCT
ejpam-3347	241	1	one	one	NUM
ejpam-3347	241	2	of	of	ADP
ejpam-3347	241	3	the	the	DET
ejpam-3347	241	4	characteristics	characteristic	NOUN
ejpam-3347	241	5	of	of	ADP
ejpam-3347	241	6	the	the	DET
ejpam-3347	241	7	scalar	scalar	ADJ
ejpam-3347	241	8	product	product	NOUN
ejpam-3347	241	9	is	be	AUX
ejpam-3347	241	10	the	the	DET
ejpam-3347	241	11	fact	fact	NOUN
ejpam-3347	241	12	that	that	SCONJ
ejpam-3347	241	13	it	it	PRON
ejpam-3347	241	14	makes	make	VERB
ejpam-3347	241	15	it	it	PRON
ejpam-3347	241	16	possible	possible	ADJ
ejpam-3347	241	17	to	to	PART
ejpam-3347	241	18	move	move	VERB
ejpam-3347	241	19	the	the	DET
ejpam-3347	241	20	diferential	diferential	NOUN
ejpam-3347	241	21	from	from	ADP
ejpam-3347	241	22	one	one	NUM
ejpam-3347	241	23	component	component	NOUN
ejpam-3347	241	24	to	to	ADP
ejpam-3347	241	25	another	another	PRON
ejpam-3347	241	26	.	.	PUNCT
ejpam-3347	242	1	the	the	DET
ejpam-3347	242	2	different	different	ADJ
ejpam-3347	242	3	relations	relation	NOUN
ejpam-3347	242	4	that	that	PRON
ejpam-3347	242	5	we	we	PRON
ejpam-3347	242	6	obtained	obtain	VERB
ejpam-3347	242	7	in	in	ADP
ejpam-3347	242	8	this	this	DET
ejpam-3347	242	9	document	document	NOUN
ejpam-3347	242	10	allow	allow	VERB
ejpam-3347	242	11	to	to	PART
ejpam-3347	242	12	establish	establish	VERB
ejpam-3347	242	13	a	a	DET
ejpam-3347	242	14	close	close	ADJ
ejpam-3347	242	15	link	link	NOUN
ejpam-3347	242	16	between	between	ADP
ejpam-3347	242	17	copula	copula	NOUN
ejpam-3347	242	18	and	and	CCONJ
ejpam-3347	242	19	the	the	DET
ejpam-3347	242	20	value	value	NOUN
ejpam-3347	242	21	at	at	ADP
ejpam-3347	242	22	risk	risk	NOUN
ejpam-3347	242	23	through	through	ADP
ejpam-3347	242	24	an	an	DET
ejpam-3347	242	25	analytical	analytical	ADJ
ejpam-3347	242	26	expression	expression	NOUN
ejpam-3347	242	27	with	with	ADP
ejpam-3347	242	28	the	the	DET
ejpam-3347	242	29	norms	norm	NOUN
ejpam-3347	242	30	.	.	PUNCT
ejpam-3347	243	1	it	it	PRON
ejpam-3347	243	2	becomes	become	VERB
ejpam-3347	243	3	quite	quite	ADV
ejpam-3347	243	4	easy	easy	ADJ
ejpam-3347	243	5	to	to	PART
ejpam-3347	243	6	calculate	calculate	VERB
ejpam-3347	243	7	the	the	DET
ejpam-3347	243	8	values	value	NOUN
ejpam-3347	243	9	of	of	ADP
ejpam-3347	243	10	var	var	NOUN
ejpam-3347	243	11	when	when	SCONJ
ejpam-3347	243	12	we	we	PRON
ejpam-3347	243	13	know	know	VERB
ejpam-3347	243	14	the	the	DET
ejpam-3347	243	15	value	value	NOUN
ejpam-3347	243	16	of	of	ADP
ejpam-3347	243	17	the	the	DET
ejpam-3347	243	18	copula	copula	NOUN
ejpam-3347	243	19	and	and	CCONJ
ejpam-3347	243	20	the	the	DET
ejpam-3347	243	21	type	type	NOUN
ejpam-3347	243	22	of	of	ADP
ejpam-3347	243	23	copula	copula	NOUN
ejpam-3347	243	24	.	.	PUNCT
ejpam-3347	244	1	references	reference	NOUN
ejpam-3347	244	2	[	[	X
ejpam-3347	244	3	1	1	NUM
ejpam-3347	244	4	]	]	PUNCT
ejpam-3347	244	5	artzner	artzner	NOUN
ejpam-3347	244	6	,	,	PUNCT
ejpam-3347	244	7	p.	p.	PROPN
ejpam-3347	244	8	,	,	PUNCT
ejpam-3347	244	9	delbaen	delbaen	PROPN
ejpam-3347	244	10	,	,	PUNCT
ejpam-3347	244	11	f.	f.	PROPN
ejpam-3347	244	12	,	,	PUNCT
ejpam-3347	244	13	eber	eber	PROPN
ejpam-3347	244	14	,	,	PUNCT
ejpam-3347	244	15	j.-m	j.-m	PROPN
ejpam-3347	244	16	.	.	PUNCT
ejpam-3347	244	17	,	,	PUNCT
ejpam-3347	244	18	and	and	CCONJ
ejpam-3347	244	19	heath	heath	PROPN
ejpam-3347	244	20	,	,	PUNCT
ejpam-3347	244	21	d.	d.	PROPN
ejpam-3347	244	22	(	(	PUNCT
ejpam-3347	244	23	1999	1999	NUM
ejpam-3347	244	24	)	)	PUNCT
ejpam-3347	244	25	.	.	PUNCT
ejpam-3347	245	1	“	"	PUNCT
ejpam-3347	245	2	coherent	coherent	ADJ
ejpam-3347	245	3	measures	measure	NOUN
ejpam-3347	245	4	of	of	ADP
ejpam-3347	245	5	risk	risk	NOUN
ejpam-3347	245	6	.	.	PUNCT
ejpam-3347	246	1	”mathematical	”mathematical	ADJ
ejpam-3347	246	2	finance	finance	NOUN
ejpam-3347	246	3	,	,	PUNCT
ejpam-3347	246	4	9	9	NUM
ejpam-3347	246	5	(	(	PUNCT
ejpam-3347	246	6	3	3	NUM
ejpam-3347	246	7	):	):	PUNCT
ejpam-3347	246	8	203	203	NUM
ejpam-3347	246	9	-	-	SYM
ejpam-3347	246	10	228	228	NUM
ejpam-3347	246	11	.	.	PUNCT
ejpam-3347	247	1	[	[	X
ejpam-3347	247	2	2	2	X
ejpam-3347	247	3	]	]	X
ejpam-3347	247	4	cardin	cardin	NOUN
ejpam-3347	247	5	m.	m.	NOUN
ejpam-3347	247	6	,	,	PUNCT
ejpam-3347	247	7	(	(	PUNCT
ejpam-3347	247	8	2010	2010	NUM
ejpam-3347	247	9	)	)	PUNCT
ejpam-3347	247	10	some	some	DET
ejpam-3347	247	11	classes	class	NOUN
ejpam-3347	247	12	of	of	ADP
ejpam-3347	247	13	multivariate	multivariate	NOUN
ejpam-3347	247	14	risk	risk	NOUN
ejpam-3347	247	15	measures	measure	NOUN
ejpam-3347	247	16	,	,	PUNCT
ejpam-3347	247	17	springer	springer	NOUN
ejpam-3347	247	18	pp	pp	ADP
ejpam-3347	247	19	63	63	NUM
ejpam-3347	247	20	-	-	SYM
ejpam-3347	247	21	730	730	NUM
ejpam-3347	247	22	doi	doi	NOUN
ejpam-3347	247	23	:	:	PUNCT
ejpam-3347	247	24	10.1007/978	10.1007/978	NUM
ejpam-3347	247	25	-	-	SYM
ejpam-3347	247	26	88	88	NUM
ejpam-3347	247	27	-	-	PUNCT
ejpam-3347	247	28	470	470	NUM
ejpam-3347	247	29	-	-	PUNCT
ejpam-3347	247	30	1481	1481	NUM
ejpam-3347	247	31	-	-	SYM
ejpam-3347	247	32	7	7	NUM
ejpam-3347	247	33	7	7	NUM
ejpam-3347	247	34	[	[	X
ejpam-3347	247	35	3	3	NUM
ejpam-3347	247	36	]	]	PUNCT
ejpam-3347	247	37	cousin	cousin	PROPN
ejpam-3347	247	38	a.	a.	PROPN
ejpam-3347	247	39	,	,	PUNCT
ejpam-3347	247	40	di	di	PROPN
ejpam-3347	247	41	bernardino	bernardino	PROPN
ejpam-3347	247	42	e.	e.	PROPN
ejpam-3347	247	43	(	(	PUNCT
ejpam-3347	247	44	2012	2012	NUM
ejpam-3347	247	45	)	)	PUNCT
ejpam-3347	247	46	a	a	DET
ejpam-3347	247	47	multivariate	multivariate	NOUN
ejpam-3347	247	48	extension	extension	NOUN
ejpam-3347	247	49	of	of	ADP
ejpam-3347	247	50	value	value	NOUN
ejpam-3347	247	51	-	-	PUNCT
ejpam-3347	247	52	at	at	ADP
ejpam-3347	247	53	-	-	PUNCT
ejpam-3347	247	54	risk	risk	NOUN
ejpam-3347	247	55	and	and	CCONJ
ejpam-3347	247	56	conditionaltail	conditionaltail	NOUN
ejpam-3347	247	57	-	-	PUNCT
ejpam-3347	247	58	expectation	expectation	NOUN
ejpam-3347	247	59	[	[	X
ejpam-3347	247	60	4	4	X
ejpam-3347	247	61	]	]	X
ejpam-3347	247	62	basel	basel	PROPN
ejpam-3347	247	63	ii	ii	PROPN
ejpam-3347	247	64	,	,	PUNCT
ejpam-3347	247	65	2006basel	2006basel	PROPN
ejpam-3347	247	66	committee	committee	NOUN
ejpam-3347	247	67	on	on	ADP
ejpam-3347	247	68	banking	banking	NOUN
ejpam-3347	247	69	supervision	supervision	NOUN
ejpam-3347	247	70	,	,	PUNCT
ejpam-3347	247	71	international	international	ADJ
ejpam-3347	247	72	convergence	convergence	NOUN
ejpam-3347	247	73	of	of	ADP
ejpam-3347	247	74	capital	capital	NOUN
ejpam-3347	247	75	measurement	measurement	NOUN
ejpam-3347	247	76	and	and	CCONJ
ejpam-3347	247	77	capital	capital	NOUN
ejpam-3347	247	78	standards	standard	NOUN
ejpam-3347	247	79	.	.	PUNCT
ejpam-3347	248	1	basel	basel	PROPN
ejpam-3347	248	2	,	,	PUNCT
ejpam-3347	248	3	june	june	PROPN
ejpam-3347	248	4	2006	2006	NUM
ejpam-3347	248	5	,	,	PUNCT
ejpam-3347	248	6	http://www.bis.org	http://www.bis.org	PROPN
ejpam-3347	248	7	.	.	PUNCT
ejpam-3347	249	1	[	[	X
ejpam-3347	249	2	5	5	NUM
ejpam-3347	249	3	]	]	PUNCT
ejpam-3347	249	4	bouy	bouy	NOUN
ejpam-3347	249	5	e.(2002	e.(2002	NOUN
ejpam-3347	249	6	)	)	PUNCT
ejpam-3347	249	7	multivariate	multivariate	NOUN
ejpam-3347	249	8	extremes	extreme	NOUN
ejpam-3347	249	9	at	at	ADP
ejpam-3347	249	10	work	work	NOUN
ejpam-3347	249	11	for	for	ADP
ejpam-3347	249	12	portfolio	portfolio	NOUN
ejpam-3347	249	13	risk	risk	NOUN
ejpam-3347	249	14	measurement	measurement	NOUN
ejpam-3347	249	15	.	.	PUNCT
ejpam-3347	250	1	warwick	warwick	PROPN
ejpam-3347	250	2	business	business	PROPN
ejpam-3347	250	3	school	school	PROPN
ejpam-3347	250	4	working	working	PROPN
ejpam-3347	250	5	paper	paper	NOUN
ejpam-3347	250	6	series	series	NOUN
ejpam-3347	250	7	,	,	PUNCT
ejpam-3347	250	8	wp01	wp01	PROPN
ejpam-3347	250	9	-	-	PUNCT
ejpam-3347	250	10	10	10	NUM
ejpam-3347	250	11	.	.	PUNCT
ejpam-3347	251	1	[	[	X
ejpam-3347	251	2	6	6	NUM
ejpam-3347	251	3	]	]	PUNCT
ejpam-3347	251	4	charpentier	charpentier	NOUN
ejpam-3347	251	5	,	,	PUNCT
ejpam-3347	251	6	a.	a.	NOUN
ejpam-3347	251	7	and	and	CCONJ
ejpam-3347	251	8	segers	seger	NOUN
ejpam-3347	251	9	,	,	PUNCT
ejpam-3347	251	10	j.	j.	PROPN
ejpam-3347	251	11	(	(	PUNCT
ejpam-3347	251	12	2009	2009	NUM
ejpam-3347	251	13	)	)	PUNCT
ejpam-3347	251	14	.	.	PUNCT
ejpam-3347	252	1	tails	tail	NOUN
ejpam-3347	252	2	of	of	ADP
ejpam-3347	252	3	multivariate	multivariate	NOUN
ejpam-3347	252	4	archimedean	archimedean	ADJ
ejpam-3347	252	5	copulas	copula	NOUN
ejpam-3347	252	6	.	.	PUNCT
ejpam-3347	253	1	j.	j.	PROPN
ejpam-3347	253	2	multivariate	multivariate	PROPN
ejpam-3347	253	3	anal	anal	PROPN
ejpam-3347	253	4	.	.	PUNCT
ejpam-3347	254	1	100	100	NUM
ejpam-3347	254	2	,	,	PUNCT
ejpam-3347	254	3	1521–1537	1521–1537	NUM
ejpam-3347	254	4	.	.	PUNCT
ejpam-3347	254	5	mathscinet	mathscinet	NOUN
ejpam-3347	254	6	:	:	PUNCT
ejpam-3347	254	7	mr2514145	mr2514145	NOUN
ejpam-3347	254	8	doi:10.1016	doi:10.1016	PROPN
ejpam-3347	254	9	/	/	SYM
ejpam-3347	254	10	j.jmva.2008.12.015	j.jmva.2008.12.015	PROPN
ejpam-3347	254	11	references	reference	VERB
ejpam-3347	254	12	206	206	NUM
ejpam-3347	255	1	[	[	X
ejpam-3347	255	2	7	7	NUM
ejpam-3347	255	3	]	]	X
ejpam-3347	255	4	joe	joe	PROPN
ejpam-3347	255	5	,	,	PUNCT
ejpam-3347	255	6	h.	h.	PROPN
ejpam-3347	255	7	(	(	PUNCT
ejpam-3347	255	8	1997	1997	NUM
ejpam-3347	255	9	)	)	PUNCT
ejpam-3347	255	10	.	.	PUNCT
ejpam-3347	256	1	multivariate	multivariate	NOUN
ejpam-3347	256	2	models	model	NOUN
ejpam-3347	256	3	and	and	CCONJ
ejpam-3347	256	4	dependence	dependence	NOUN
ejpam-3347	256	5	concepts	concept	NOUN
ejpam-3347	256	6	monographs	monograph	NOUN
ejpam-3347	256	7	on	on	ADP
ejpam-3347	256	8	statistics	statistic	NOUN
ejpam-3347	256	9	and	and	CCONJ
ejpam-3347	256	10	applied	applied	ADJ
ejpam-3347	256	11	probabilty	probabilty	NOUN
ejpam-3347	256	12	73	73	NUM
ejpam-3347	256	13	,	,	PUNCT
ejpam-3347	256	14	chapman	chapman	NOUN
ejpam-3347	256	15	and	and	CCONJ
ejpam-3347	256	16	hall	hall	PROPN
ejpam-3347	256	17	,	,	PUNCT
ejpam-3347	256	18	london	london	PROPN
ejpam-3347	256	19	.	.	PUNCT
ejpam-3347	257	1	[	[	X
ejpam-3347	257	2	8	8	NUM
ejpam-3347	257	3	]	]	X
ejpam-3347	257	4	patton	patton	PROPN
ejpam-3347	257	5	,	,	PUNCT
ejpam-3347	257	6	a.	a.	PROPN
ejpam-3347	257	7	j.	j.	PROPN
ejpam-3347	257	8	(	(	PUNCT
ejpam-3347	257	9	2001	2001	NUM
ejpam-3347	257	10	)	)	PUNCT
ejpam-3347	257	11	,	,	PUNCT
ejpam-3347	257	12	modelling	model	VERB
ejpam-3347	257	13	time	time	NOUN
ejpam-3347	257	14	-	-	PUNCT
ejpam-3347	257	15	varying	vary	VERB
ejpam-3347	257	16	exchange	exchange	NOUN
ejpam-3347	257	17	rate	rate	NOUN
ejpam-3347	257	18	dependence	dependence	NOUN
ejpam-3347	257	19	using	use	VERB
ejpam-3347	257	20	the	the	DET
ejpam-3347	257	21	conditional	conditional	ADJ
ejpam-3347	257	22	copula	copula	NOUN
ejpam-3347	257	23	,	,	PUNCT
ejpam-3347	257	24	phd	phd	NOUN
ejpam-3347	257	25	thesis	thesis	NOUN
ejpam-3347	257	26	,	,	PUNCT
ejpam-3347	257	27	department	department	NOUN
ejpam-3347	257	28	of	of	ADP
ejpam-3347	257	29	economics	economics	PROPN
ejpam-3347	257	30	,	,	PUNCT
ejpam-3347	257	31	ucsd	ucsd	PROPN
ejpam-3347	257	32	.	.	PUNCT
ejpam-3347	258	1	[	[	X
ejpam-3347	258	2	9	9	NUM
ejpam-3347	258	3	]	]	X
ejpam-3347	258	4	nelsen	nelsen	PROPN
ejpam-3347	258	5	,	,	PUNCT
ejpam-3347	258	6	r.	r.	PROPN
ejpam-3347	258	7	b.	b.	PROPN
ejpam-3347	258	8	(	(	PUNCT
ejpam-3347	258	9	1999	1999	NUM
ejpam-3347	258	10	)	)	PUNCT
ejpam-3347	258	11	.	.	PUNCT
ejpam-3347	259	1	an	an	DET
ejpam-3347	259	2	introduction	introduction	NOUN
ejpam-3347	259	3	to	to	ADP
ejpam-3347	259	4	copulas	copula	NOUN
ejpam-3347	259	5	.	.	PUNCT
ejpam-3347	260	1	springer	springer	NOUN
ejpam-3347	260	2	,	,	PUNCT
ejpam-3347	260	3	new	new	PROPN
ejpam-3347	260	4	york	york	PROPN
ejpam-3347	260	5	.	.	PUNCT
ejpam-3347	261	1	[	[	X
ejpam-3347	261	2	10	10	NUM
ejpam-3347	261	3	]	]	X
ejpam-3347	261	4	patton	patton	PROPN
ejpam-3347	261	5	,	,	PUNCT
ejpam-3347	261	6	a.j	a.j	PROPN
ejpam-3347	261	7	.	.	PROPN
ejpam-3347	261	8	,	,	PUNCT
ejpam-3347	261	9	(	(	PUNCT
ejpam-3347	261	10	2006	2006	NUM
ejpam-3347	261	11	)	)	PUNCT
ejpam-3347	261	12	,	,	PUNCT
ejpam-3347	261	13	modelling	model	VERB
ejpam-3347	261	14	asymmetric	asymmetric	ADJ
ejpam-3347	261	15	exchange	exchange	NOUN
ejpam-3347	261	16	rate	rate	NOUN
ejpam-3347	261	17	dependence	dependence	NOUN
ejpam-3347	261	18	,	,	PUNCT
ejpam-3347	261	19	international	international	ADJ
ejpam-3347	261	20	economic	economic	ADJ
ejpam-3347	261	21	review	review	PROPN
ejpam-3347	261	22	,	,	PUNCT
ejpam-3347	261	23	47(2	47(2	PROPN
ejpam-3347	261	24	)	)	PUNCT
ejpam-3347	261	25	,	,	PUNCT
ejpam-3347	261	26	527	527	NUM
ejpam-3347	261	27	-	-	SYM
ejpam-3347	261	28	556	556	NUM
ejpam-3347	261	29	.	.	PUNCT
ejpam-3347	262	1	[	[	X
ejpam-3347	262	2	11	11	NUM
ejpam-3347	262	3	]	]	X
ejpam-3347	262	4	basel	basel	PROPN
ejpam-3347	262	5	committee	committee	PROPN
ejpam-3347	262	6	on	on	ADP
ejpam-3347	262	7	banking	banking	NOUN
ejpam-3347	262	8	supervision	supervision	NOUN
ejpam-3347	262	9	,	,	PUNCT
ejpam-3347	262	10	international	international	ADJ
ejpam-3347	262	11	convergence	convergence	NOUN
ejpam-3347	262	12	of	of	ADP
ejpam-3347	262	13	capital	capital	NOUN
ejpam-3347	262	14	measurement	measurement	NOUN
ejpam-3347	262	15	and	and	CCONJ
ejpam-3347	262	16	capital	capital	NOUN
ejpam-3347	262	17	standards	standard	NOUN
ejpam-3347	262	18	,	,	PUNCT
ejpam-3347	262	19	basel	basel	PROPN
ejpam-3347	262	20	,	,	PUNCT
ejpam-3347	262	21	june	june	PROPN
ejpam-3347	262	22	2006	2006	NUM
ejpam-3347	262	23	,	,	PUNCT
ejpam-3347	262	24	www.bis.org	www.bis.org	PROPN
ejpam-3347	262	25	.	.	PUNCT
ejpam-3347	263	1	[	[	X
ejpam-3347	263	2	12	12	NUM
ejpam-3347	263	3	]	]	X
ejpam-3347	263	4	soustra	soustra	PROPN
ejpam-3347	263	5	,	,	PUNCT
ejpam-3347	263	6	f.	f.	PROPN
ejpam-3347	263	7	(	(	PUNCT
ejpam-3347	263	8	2006	2006	NUM
ejpam-3347	263	9	)	)	PUNCT
ejpam-3347	263	10	,	,	PUNCT
ejpam-3347	263	11	‘	'	PUNCT
ejpam-3347	263	12	pricing	pricing	NOUN
ejpam-3347	263	13	of	of	ADP
ejpam-3347	263	14	synthetic	synthetic	ADJ
ejpam-3347	263	15	cdo	cdo	ADJ
ejpam-3347	263	16	tranches	tranche	NOUN
ejpam-3347	263	17	,	,	PUNCT
ejpam-3347	263	18	analysis	analysis	NOUN
ejpam-3347	263	19	of	of	ADP
ejpam-3347	263	20	base	base	NOUN
ejpam-3347	263	21	correlation	correlation	NOUN
ejpam-3347	263	22	and	and	CCONJ
ejpam-3347	263	23	an	an	DET
ejpam-3347	263	24	introduction	introduction	NOUN
ejpam-3347	263	25	to	to	ADP
ejpam-3347	263	26	dynamic	dynamic	ADJ
ejpam-3347	263	27	copulas	copula	NOUN
ejpam-3347	263	28	’	'	PUNCT
ejpam-3347	263	29	,	,	PUNCT
ejpam-3347	263	30	m	m	PROPN
ejpam-3347	263	31	emoire	emoire	NOUN
ejpam-3347	263	32	de	de	X
ejpam-3347	263	33	maitrise	maitrise	PROPN
ejpam-3347	263	34	,	,	PUNCT
ejpam-3347	263	35	hec	hec	PROPN
ejpam-3347	263	36	montr	montr	PROPN
ejpam-3347	263	37	eal	eal	PROPN
ejpam-3347	263	38	.	.	PUNCT
ejpam-3347	264	1	[	[	X
ejpam-3347	264	2	13	13	NUM
ejpam-3347	264	3	]	]	PUNCT
ejpam-3347	264	4	embrechts	embrecht	NOUN
ejpam-3347	264	5	,	,	PUNCT
ejpam-3347	264	6	p.	p.	NOUN
ejpam-3347	264	7	mikosch	mikosch	PROPN
ejpam-3347	264	8	,	,	PUNCT
ejpam-3347	264	9	t.	t.	PROPN
ejpam-3347	264	10	klppelberg	klppelberg	PROPN
ejpam-3347	264	11	,	,	PUNCT
ejpam-3347	264	12	c.	c.	PROPN
ejpam-3347	264	13	(	(	PUNCT
ejpam-3347	264	14	1997	1997	NUM
ejpam-3347	264	15	)	)	PUNCT
ejpam-3347	264	16	.	.	PUNCT
ejpam-3347	265	1	“	"	PUNCT
ejpam-3347	265	2	modelling	model	VERB
ejpam-3347	265	3	extremal	extremal	ADJ
ejpam-3347	265	4	events	event	NOUN
ejpam-3347	265	5	:	:	PUNCT
ejpam-3347	265	6	for	for	ADP
ejpam-3347	265	7	insurance	insurance	NOUN
ejpam-3347	265	8	and	and	CCONJ
ejpam-3347	265	9	finance	finance	NOUN
ejpam-3347	265	10	.	.	PUNCT
ejpam-3347	265	11	”springer	”springer	NOUN
ejpam-3347	265	12	-	-	PUNCT
ejpam-3347	265	13	verlag	verlag	PROPN
ejpam-3347	265	14	,	,	PUNCT
ejpam-3347	265	15	london	london	PROPN
ejpam-3347	265	16	.	.	PUNCT
ejpam-3347	266	1	[	[	X
ejpam-3347	266	2	14	14	NUM
ejpam-3347	266	3	]	]	PUNCT
ejpam-3347	266	4	embrechts	embrecht	NOUN
ejpam-3347	266	5	,	,	PUNCT
ejpam-3347	266	6	p.	p.	NOUN
ejpam-3347	266	7	,	,	PUNCT
ejpam-3347	266	8	a.	a.	PROPN
ejpam-3347	266	9	mcneil	mcneil	PROPN
ejpam-3347	266	10	and	and	CCONJ
ejpam-3347	266	11	d.	d.	PROPN
ejpam-3347	266	12	straumann	straumann	PROPN
ejpam-3347	266	13	(	(	PUNCT
ejpam-3347	266	14	2002	2002	NUM
ejpam-3347	266	15	)	)	PUNCT
ejpam-3347	266	16	,	,	PUNCT
ejpam-3347	266	17	correlation	correlation	NOUN
ejpam-3347	266	18	and	and	CCONJ
ejpam-3347	266	19	dependence	dependence	NOUN
ejpam-3347	266	20	in	in	ADP
ejpam-3347	266	21	risk	risk	NOUN
ejpam-3347	266	22	management	management	NOUN
ejpam-3347	266	23	:	:	PUNCT
ejpam-3347	266	24	properties	property	NOUN
ejpam-3347	266	25	and	and	CCONJ
ejpam-3347	266	26	pitfalls	pitfall	NOUN
ejpam-3347	266	27	,	,	PUNCT
ejpam-3347	266	28	in	in	ADP
ejpam-3347	266	29	m.	m.	NOUN
ejpam-3347	266	30	dempster	dempster	PROPN
ejpam-3347	266	31	(	(	PUNCT
ejpam-3347	266	32	ed	ed	NOUN
ejpam-3347	266	33	.	.	PUNCT
ejpam-3347	266	34	)	)	PUNCT
ejpam-3347	266	35	,	,	PUNCT
ejpam-3347	266	36	risk	risk	NOUN
ejpam-3347	266	37	management	management	NOUN
ejpam-3347	266	38	:	:	PUNCT
ejpam-3347	266	39	value	value	NOUN
ejpam-3347	266	40	at	at	ADP
ejpam-3347	266	41	risk	risk	NOUN
ejpam-3347	266	42	and	and	CCONJ
ejpam-3347	266	43	beyond	beyond	ADP
ejpam-3347	266	44	,	,	PUNCT
ejpam-3347	266	45	cambridge	cambridge	PROPN
ejpam-3347	266	46	university	university	PROPN
ejpam-3347	266	47	press	press	NOUN
ejpam-3347	266	48	,	,	PUNCT
ejpam-3347	266	49	pp	pp	ADP
ejpam-3347	266	50	.	.	PUNCT
ejpam-3347	267	1	176	176	NUM
ejpam-3347	267	2	-	-	SYM
ejpam-3347	267	3	223	223	NUM
ejpam-3347	267	4	.	.	PUNCT
ejpam-3347	268	1	[	[	X
ejpam-3347	268	2	15	15	NUM
ejpam-3347	268	3	]	]	X
ejpam-3347	268	4	rockafeller	rockafeller	PROPN
ejpam-3347	268	5	rt	rt	PROPN
ejpam-3347	268	6	(	(	PUNCT
ejpam-3347	268	7	2007	2007	NUM
ejpam-3347	268	8	)	)	PUNCT
ejpam-3347	268	9	,	,	PUNCT
ejpam-3347	268	10	coherent	coherent	ADJ
ejpam-3347	268	11	approaches	approach	NOUN
ejpam-3347	268	12	to	to	PART
ejpam-3347	268	13	risk	risk	VERB
ejpam-3347	268	14	in	in	ADP
ejpam-3347	268	15	optimization	optimization	NOUN
ejpam-3347	268	16	under	under	ADP
ejpam-3347	268	17	uncertainty	uncertainty	NOUN
ejpam-3347	268	18	.	.	PUNCT
ejpam-3347	269	1	tutorials	tutorial	NOUN
ejpam-3347	269	2	in	in	ADP
ejpam-3347	269	3	operations	operation	NOUN
ejpam-3347	269	4	research	research	NOUN
ejpam-3347	269	5	informs	inform	VERB
ejpam-3347	269	6	,	,	PUNCT
ejpam-3347	269	7	38	38	NUM
ejpam-3347	269	8	-	-	SYM
ejpam-3347	269	9	61	61	NUM
ejpam-3347	269	10	.	.	PUNCT
ejpam-3347	270	1	[	[	X
ejpam-3347	270	2	16	16	NUM
ejpam-3347	270	3	]	]	PUNCT
ejpam-3347	270	4	rootzn	rootzn	ADJ
ejpam-3347	270	5	,	,	PUNCT
ejpam-3347	270	6	h.	h.	PROPN
ejpam-3347	270	7	and	and	CCONJ
ejpam-3347	270	8	klppelberg	klppelberg	PROPN
ejpam-3347	270	9	c.	c.	PROPN
ejpam-3347	270	10	(	(	PUNCT
ejpam-3347	270	11	1999	1999	NUM
ejpam-3347	270	12	)	)	PUNCT
ejpam-3347	270	13	.	.	PUNCT
ejpam-3347	271	1	“	"	PUNCT
ejpam-3347	271	2	a	a	DET
ejpam-3347	271	3	single	single	ADJ
ejpam-3347	271	4	number	number	NOUN
ejpam-3347	271	5	ca	can	AUX
ejpam-3347	271	6	n’t	not	PART
ejpam-3347	271	7	hedge	hedge	VERB
ejpam-3347	271	8	against	against	ADP
ejpam-3347	271	9	economic	economic	ADJ
ejpam-3347	271	10	catastrophes	catastrophe	NOUN
ejpam-3347	271	11	”	"	PUNCT
ejpam-3347	271	12	working	working	NOUN
ejpam-3347	271	13	paper	paper	NOUN
ejpam-3347	271	14	,	,	PUNCT
ejpam-3347	271	15	munich	munich	PROPN
ejpam-3347	271	16	university	university	PROPN
ejpam-3347	271	17	of	of	ADP
ejpam-3347	271	18	technology	technology	NOUN
ejpam-3347	271	19	.	.	PUNCT
ejpam-3347	272	1	[	[	X
ejpam-3347	272	2	17	17	NUM
ejpam-3347	272	3	]	]	X
ejpam-3347	272	4	nelsen	nelsen	PROPN
ejpam-3347	272	5	,	,	PUNCT
ejpam-3347	272	6	r.b	r.b	PROPN
ejpam-3347	272	7	.	.	PROPN
ejpam-3347	272	8	(	(	PUNCT
ejpam-3347	272	9	1999	1999	NUM
ejpam-3347	272	10	)	)	PUNCT
ejpam-3347	272	11	.	.	PUNCT
ejpam-3347	273	1	an	an	DET
ejpam-3347	273	2	introduction	introduction	NOUN
ejpam-3347	273	3	to	to	ADP
ejpam-3347	273	4	copulaslectures	copulaslecture	NOUN
ejpam-3347	273	5	notes	note	NOUN
ejpam-3347	273	6	in	in	ADP
ejpam-3347	273	7	statistics	statistic	NOUN
ejpam-3347	273	8	139	139	NUM
ejpam-3347	273	9	,	,	PUNCT
ejpam-3347	273	10	springer	springer	NOUN
ejpam-3347	273	11	-	-	PUNCT
ejpam-3347	273	12	verlag	verlag	PROPN
ejpam-3347	273	13	(	(	PUNCT
ejpam-3347	273	14	isbn	isbn	PROPN
ejpam-3347	273	15	10	10	NUM
ejpam-3347	273	16	:	:	SYM
ejpam-3347	273	17	0387986235	0387986235	NUM
ejpam-3347	273	18	/	/	SYM
ejpam-3347	273	19	isbn	isbn	ADJ
ejpam-3347	273	20	13	13	NUM
ejpam-3347	273	21	:	:	SYM
ejpam-3347	273	22	9780387986234	9780387986234	NUM
ejpam-3347	273	23	)	)	PUNCT
ejpam-3347	274	1	[	[	X
ejpam-3347	274	2	18	18	NUM
ejpam-3347	274	3	]	]	X
ejpam-3347	274	4	basel	basel	PROPN
ejpam-3347	274	5	committee	committee	PROPN
ejpam-3347	274	6	on	on	ADP
ejpam-3347	274	7	banking	banking	NOUN
ejpam-3347	274	8	supervision	supervision	NOUN
ejpam-3347	274	9	,	,	PUNCT
ejpam-3347	274	10	2010	2010	NUM
ejpam-3347	274	11	.	.	PUNCT
ejpam-3347	275	1	basel	basel	PROPN
ejpam-3347	275	2	iii	iii	PROPN
ejpam-3347	275	3	:	:	PUNCT
ejpam-3347	275	4	a	a	DET
ejpam-3347	275	5	global	global	ADJ
ejpam-3347	275	6	regulatory	regulatory	ADJ
ejpam-3347	275	7	framework	framework	NOUN
ejpam-3347	275	8	for	for	ADP
ejpam-3347	275	9	more	more	ADV
ejpam-3347	275	10	resilient	resilient	ADJ
ejpam-3347	275	11	banks	bank	NOUN
ejpam-3347	275	12	and	and	CCONJ
ejpam-3347	275	13	banking	banking	NOUN
ejpam-3347	275	14	systems	system	NOUN
ejpam-3347	275	15	.	.	PUNCT
ejpam-3347	276	1	http://www.bis.org/publ/bcbs189	http://www.bis.org/publ/bcbs189	ADJ
ejpam-3347	276	2	dec2010.pdf	dec2010.pdf	PROPN
ejpam-3347	276	3	,	,	PUNCT
ejpam-3347	276	4	december	december	PROPN
ejpam-3347	276	5	.	.	PUNCT
ejpam-3347	277	1	[	[	X
ejpam-3347	277	2	19	19	NUM
ejpam-3347	277	3	]	]	SYM
ejpam-3347	277	4	beirlant	beirlant	PROPN
ejpam-3347	277	5	,	,	PUNCT
ejpam-3347	277	6	j.	j.	PROPN
ejpam-3347	277	7	,	,	PUNCT
ejpam-3347	277	8	goegebeur	goegebeur	PROPN
ejpam-3347	277	9	,	,	PUNCT
ejpam-3347	277	10	y.	y.	PROPN
ejpam-3347	277	11	,	,	PUNCT
ejpam-3347	277	12	segers	seger	NOUN
ejpam-3347	277	13	,	,	PUNCT
ejpam-3347	277	14	j.	j.	PROPN
ejpam-3347	277	15	,	,	PUNCT
ejpam-3347	277	16	and	and	CCONJ
ejpam-3347	277	17	teugels	teugel	NOUN
ejpam-3347	277	18	,	,	PUNCT
ejpam-3347	277	19	j.	j.	PROPN
ejpam-3347	277	20	(	(	PUNCT
ejpam-3347	277	21	2005	2005	NUM
ejpam-3347	277	22	)	)	PUNCT
ejpam-3347	277	23	.	.	PUNCT
ejpam-3347	278	1	statistics	statistic	NOUN
ejpam-3347	278	2	of	of	ADP
ejpam-3347	278	3	extremes	extreme	NOUN
ejpam-3347	278	4	:	:	PUNCT
ejpam-3347	278	5	theory	theory	NOUN
ejpam-3347	278	6	and	and	CCONJ
ejpam-3347	278	7	application	application	NOUN
ejpam-3347	278	8	-wiley	-wiley	PROPN
ejpam-3347	278	9	,	,	PUNCT
ejpam-3347	278	10	chichester	chichester	PROPN
ejpam-3347	278	11	,	,	PUNCT
ejpam-3347	278	12	england	england	PROPN
ejpam-3347	278	13	.	.	PUNCT
ejpam-3347	279	1	[	[	X
ejpam-3347	279	2	23	23	NUM
ejpam-3347	279	3	]	]	X
ejpam-3347	279	4	carreau	carreau	PROPN
ejpam-3347	279	5	j.	j.	PROPN
ejpam-3347	279	6	(	(	PUNCT
ejpam-3347	279	7	2004	2004	NUM
ejpam-3347	279	8	)	)	PUNCT
ejpam-3347	279	9	.	.	PUNCT
ejpam-3347	280	1	estimation	estimation	NOUN
ejpam-3347	280	2	de	de	ADP
ejpam-3347	280	3	densit	densit	PROPN
ejpam-3347	280	4	conditionnelle	conditionnelle	VERB
ejpam-3347	280	5	lorsque	lorsque	ADJ
ejpam-3347	280	6	l’hyppothse	l’hyppothse	PROPN
ejpam-3347	280	7	de	de	X
ejpam-3347	280	8	normalit	normalit	ADJ
ejpam-3347	280	9	est	est	X
ejpam-3347	280	10	insatisfaisante	insatisfaisante	NOUN
ejpam-3347	280	11	thse	thse	X
ejpam-3347	280	12	de	de	X
ejpam-3347	280	13	doctorat	doctorat	PROPN
ejpam-3347	280	14	.	.	PUNCT
ejpam-3347	281	1	[	[	X
ejpam-3347	281	2	21	21	NUM
ejpam-3347	281	3	]	]	X
ejpam-3347	281	4	clauss	clauss	ADJ
ejpam-3347	281	5	,	,	PUNCT
ejpam-3347	281	6	p.	p.	NOUN
ejpam-3347	281	7	(	(	PUNCT
ejpam-3347	281	8	2008	2008	NUM
ejpam-3347	281	9	)	)	PUNCT
ejpam-3347	281	10	.	.	PUNCT
ejpam-3347	282	1	thorie	thorie	PROPN
ejpam-3347	282	2	des	des	PROPN
ejpam-3347	282	3	copules	copules	PROPN
ejpam-3347	282	4	elments	elment	NOUN
ejpam-3347	282	5	de	de	X
ejpam-3347	282	6	cours	cours	X
ejpam-3347	282	7	sur	sur	PROPN
ejpam-3347	282	8	les	les	PROPN
ejpam-3347	282	9	copules	copule	NOUN
ejpam-3347	282	10	multivariesensai	multivariesensai	ADJ
ejpam-3347	282	11	.	.	PUNCT
ejpam-3347	283	1	[	[	X
ejpam-3347	283	2	22	22	NUM
ejpam-3347	283	3	]	]	PUNCT
ejpam-3347	283	4	yves	yve	NOUN
ejpam-3347	283	5	bernadin	bernadin	VERB
ejpam-3347	283	6	vini	vini	NOUN
ejpam-3347	283	7	loyara	loyara	PROPN
ejpam-3347	283	8	,	,	PUNCT
ejpam-3347	283	9	remi	remi	PROPN
ejpam-3347	283	10	guillaume	guillaume	PROPN
ejpam-3347	283	11	bagr	bagr	PROPN
ejpam-3347	283	12	and	and	CCONJ
ejpam-3347	283	13	diakarya	diakarya	ADJ
ejpam-3347	283	14	barro	barro	PROPN
ejpam-3347	283	15	.	.	PUNCT
ejpam-3347	284	1	(	(	PUNCT
ejpam-3347	284	2	2017	2017	NUM
ejpam-3347	284	3	)	)	PUNCT
ejpam-3347	284	4	.	.	PUNCT
ejpam-3347	285	1	multivariate	multivariate	NOUN
ejpam-3347	285	2	risk	risk	NOUN
ejpam-3347	285	3	modeling	modeling	NOUN
ejpam-3347	285	4	for	for	ADP
ejpam-3347	285	5	financial	financial	ADJ
ejpam-3347	285	6	portfolio	portfolio	NOUN
ejpam-3347	285	7	management	management	NOUN
ejpam-3347	285	8	and	and	CCONJ
ejpam-3347	285	9	climate	climate	NOUN
ejpam-3347	285	10	application	application	NOUN
ejpam-3347	285	11	.	.	PUNCT
ejpam-3347	286	1	far	far	PROPN
ejpam-3347	286	2	east	east	PROPN
ejpam-3347	286	3	journal	journal	PROPN
ejpam-3347	286	4	of	of	ADP
ejpam-3347	286	5	mathematical	mathematical	ADJ
ejpam-3347	286	6	sciences	sciences	PROPN
ejpam-3347	286	7	(	(	PUNCT
ejpam-3347	286	8	fjms	fjms	NOUN
ejpam-3347	286	9	)	)	PUNCT
ejpam-3347	286	10	.	.	PUNCT
ejpam-3347	287	1	references	reference	NOUN
ejpam-3347	287	2	207	207	NUM
ejpam-3347	287	3	[	[	X
ejpam-3347	287	4	23	23	NUM
ejpam-3347	287	5	]	]	PUNCT
ejpam-3347	287	6	karl	karl	PROPN
ejpam-3347	287	7	friedrich	friedrich	PROPN
ejpam-3347	287	8	siburg	siburg	PROPN
ejpam-3347	287	9	,	,	PUNCT
ejpam-3347	287	10	pavel	pavel	PROPN
ejpam-3347	287	11	a.	a.	NOUN
ejpam-3347	287	12	stoimenov	stoimenov	PROPN
ejpam-3347	287	13	.	.	PUNCT
ejpam-3347	288	1	(	(	PUNCT
ejpam-3347	288	2	2007	2007	NUM
ejpam-3347	288	3	)	)	PUNCT
ejpam-3347	288	4	.	.	PUNCT
ejpam-3347	289	1	a	a	DET
ejpam-3347	289	2	scalar	scalar	ADJ
ejpam-3347	289	3	product	product	NOUN
ejpam-3347	289	4	for	for	ADP
ejpam-3347	289	5	copulas	copula	NOUN
ejpam-3347	289	6	.	.	PUNCT
ejpam-3347	290	1	journal	journal	PROPN
ejpam-3347	290	2	of	of	ADP
ejpam-3347	290	3	mathematical	mathematical	ADJ
ejpam-3347	290	4	analysis	analysis	NOUN
ejpam-3347	290	5	and	and	CCONJ
ejpam-3347	290	6	application	application	NOUN
ejpam-3347	290	7	.	.	PUNCT