id	sid	tid	token	lemma	pos
ejpam-4385	1	1	european	european	PROPN
ejpam-4385	1	2	journal	journal	PROPN
ejpam-4385	1	3	of	of	ADP
ejpam-4385	1	4	pure	pure	ADJ
ejpam-4385	1	5	and	and	CCONJ
ejpam-4385	1	6	applied	apply	VERB
ejpam-4385	1	7	mathematics	mathematic	NOUN
ejpam-4385	1	8	vol	vol	NOUN
ejpam-4385	1	9	.	.	PROPN
ejpam-4385	2	1	15	15	NUM
ejpam-4385	2	2	,	,	PUNCT
ejpam-4385	2	3	no	no	INTJ
ejpam-4385	2	4	.	.	NOUN
ejpam-4385	2	5	3	3	NUM
ejpam-4385	2	6	,	,	PUNCT
ejpam-4385	2	7	2022	2022	NUM
ejpam-4385	2	8	,	,	PUNCT
ejpam-4385	2	9	948	948	NUM
ejpam-4385	2	10	-	-	SYM
ejpam-4385	2	11	970	970	NUM
ejpam-4385	2	12	issn	issn	PROPN
ejpam-4385	2	13	1307	1307	NUM
ejpam-4385	2	14	-	-	SYM
ejpam-4385	2	15	5543	5543	NUM
ejpam-4385	2	16	–	–	PUNCT
ejpam-4385	2	17	ejpam.com	ejpam.com	X
ejpam-4385	2	18	published	publish	VERB
ejpam-4385	2	19	by	by	ADP
ejpam-4385	2	20	new	new	PROPN
ejpam-4385	2	21	york	york	PROPN
ejpam-4385	2	22	business	business	PROPN
ejpam-4385	2	23	global	global	ADJ
ejpam-4385	2	24	british	british	ADJ
ejpam-4385	2	25	call	call	NOUN
ejpam-4385	2	26	option	option	NOUN
ejpam-4385	2	27	on	on	ADP
ejpam-4385	2	28	stocks	stock	NOUN
ejpam-4385	2	29	under	under	ADP
ejpam-4385	2	30	stochastic	stochastic	ADJ
ejpam-4385	2	31	interest	interest	NOUN
ejpam-4385	2	32	rate	rate	NOUN
ejpam-4385	2	33	kreanne	kreanne	PROPN
ejpam-4385	2	34	falcasantos1,∗	falcasantos1,∗	PROPN
ejpam-4385	2	35	,	,	PUNCT
ejpam-4385	2	36	felipe	felipe	PROPN
ejpam-4385	2	37	r.	r.	PROPN
ejpam-4385	2	38	sumalpong	sumalpong	PROPN
ejpam-4385	2	39	jr.2	jr.2	PROPN
ejpam-4385	2	40	1	1	NUM
ejpam-4385	2	41	mathematics	mathematics	PROPN
ejpam-4385	2	42	department	department	NOUN
ejpam-4385	2	43	,	,	PUNCT
ejpam-4385	2	44	college	college	NOUN
ejpam-4385	2	45	of	of	ADP
ejpam-4385	2	46	science	science	NOUN
ejpam-4385	2	47	and	and	CCONJ
ejpam-4385	2	48	information	information	NOUN
ejpam-4385	2	49	technology	technology	NOUN
ejpam-4385	2	50	,	,	PUNCT
ejpam-4385	2	51	ateneo	ateneo	PROPN
ejpam-4385	2	52	de	de	PROPN
ejpam-4385	2	53	zamboanga	zamboanga	PROPN
ejpam-4385	2	54	university	university	PROPN
ejpam-4385	2	55	,	,	PUNCT
ejpam-4385	2	56	7000	7000	NUM
ejpam-4385	2	57	,	,	PUNCT
ejpam-4385	2	58	zamboanga	zamboanga	PROPN
ejpam-4385	2	59	city	city	PROPN
ejpam-4385	2	60	,	,	PUNCT
ejpam-4385	2	61	philippines	philippines	PROPN
ejpam-4385	2	62	2	2	NUM
ejpam-4385	2	63	department	department	NOUN
ejpam-4385	2	64	of	of	ADP
ejpam-4385	2	65	mathematics	mathematic	NOUN
ejpam-4385	2	66	and	and	CCONJ
ejpam-4385	2	67	statistics	statistic	NOUN
ejpam-4385	2	68	,	,	PUNCT
ejpam-4385	2	69	college	college	NOUN
ejpam-4385	2	70	of	of	ADP
ejpam-4385	2	71	science	science	NOUN
ejpam-4385	2	72	and	and	CCONJ
ejpam-4385	2	73	mathematics	mathematic	NOUN
ejpam-4385	2	74	,	,	PUNCT
ejpam-4385	2	75	mindanao	mindanao	PROPN
ejpam-4385	2	76	state	state	PROPN
ejpam-4385	2	77	university	university	PROPN
ejpam-4385	2	78	-	-	PUNCT
ejpam-4385	2	79	iligan	iligan	PROPN
ejpam-4385	2	80	institute	institute	PROPN
ejpam-4385	2	81	of	of	ADP
ejpam-4385	2	82	technology	technology	PROPN
ejpam-4385	2	83	,	,	PUNCT
ejpam-4385	2	84	9200	9200	NUM
ejpam-4385	2	85	,	,	PUNCT
ejpam-4385	2	86	iligan	iligan	ADJ
ejpam-4385	2	87	city	city	NOUN
ejpam-4385	2	88	,	,	PUNCT
ejpam-4385	2	89	philippines	philippine	NOUN
ejpam-4385	2	90	abstract	abstract	ADJ
ejpam-4385	2	91	.	.	PUNCT
ejpam-4385	3	1	the	the	DET
ejpam-4385	3	2	closed	closed	ADJ
ejpam-4385	3	3	form	form	NOUN
ejpam-4385	3	4	expression	expression	NOUN
ejpam-4385	3	5	for	for	ADP
ejpam-4385	3	6	the	the	DET
ejpam-4385	3	7	price	price	NOUN
ejpam-4385	3	8	of	of	ADP
ejpam-4385	3	9	the	the	DET
ejpam-4385	3	10	british	british	ADJ
ejpam-4385	3	11	put	put	VERB
ejpam-4385	3	12	and	and	CCONJ
ejpam-4385	3	13	call	call	VERB
ejpam-4385	3	14	options	option	NOUN
ejpam-4385	3	15	have	have	AUX
ejpam-4385	3	16	long	long	ADV
ejpam-4385	3	17	been	be	AUX
ejpam-4385	3	18	established	establish	VERB
ejpam-4385	3	19	where	where	SCONJ
ejpam-4385	3	20	both	both	DET
ejpam-4385	3	21	interest	interest	NOUN
ejpam-4385	3	22	rate	rate	NOUN
ejpam-4385	3	23	and	and	CCONJ
ejpam-4385	3	24	volatility	volatility	NOUN
ejpam-4385	3	25	are	be	AUX
ejpam-4385	3	26	assumed	assume	VERB
ejpam-4385	3	27	to	to	PART
ejpam-4385	3	28	be	be	AUX
ejpam-4385	3	29	constant	constant	ADJ
ejpam-4385	3	30	.	.	PUNCT
ejpam-4385	4	1	in	in	ADP
ejpam-4385	4	2	reality	reality	NOUN
ejpam-4385	4	3	,	,	PUNCT
ejpam-4385	4	4	these	these	DET
ejpam-4385	4	5	assumptions	assumption	NOUN
ejpam-4385	4	6	do	do	AUX
ejpam-4385	4	7	not	not	PART
ejpam-4385	4	8	fully	fully	ADV
ejpam-4385	4	9	reflect	reflect	VERB
ejpam-4385	4	10	the	the	DET
ejpam-4385	4	11	variable	variable	ADJ
ejpam-4385	4	12	nature	nature	NOUN
ejpam-4385	4	13	of	of	ADP
ejpam-4385	4	14	the	the	DET
ejpam-4385	4	15	financial	financial	ADJ
ejpam-4385	4	16	markets	market	NOUN
ejpam-4385	4	17	.	.	PUNCT
ejpam-4385	5	1	in	in	ADP
ejpam-4385	5	2	this	this	DET
ejpam-4385	5	3	paper	paper	NOUN
ejpam-4385	5	4	,	,	PUNCT
ejpam-4385	5	5	we	we	PRON
ejpam-4385	5	6	derived	derive	VERB
ejpam-4385	5	7	a	a	DET
ejpam-4385	5	8	closed	closed	ADJ
ejpam-4385	5	9	form	form	NOUN
ejpam-4385	5	10	expression	expression	NOUN
ejpam-4385	5	11	for	for	ADP
ejpam-4385	5	12	the	the	DET
ejpam-4385	5	13	arbitrage	arbitrage	NOUN
ejpam-4385	5	14	-	-	PUNCT
ejpam-4385	5	15	free	free	ADJ
ejpam-4385	5	16	price	price	NOUN
ejpam-4385	5	17	of	of	ADP
ejpam-4385	5	18	the	the	DET
ejpam-4385	5	19	british	british	ADJ
ejpam-4385	5	20	call	call	NOUN
ejpam-4385	5	21	option	option	NOUN
ejpam-4385	5	22	by	by	ADP
ejpam-4385	5	23	assuming	assume	VERB
ejpam-4385	5	24	stochastic	stochastic	ADJ
ejpam-4385	5	25	interest	interest	NOUN
ejpam-4385	5	26	rate	rate	NOUN
ejpam-4385	5	27	which	which	PRON
ejpam-4385	5	28	follows	follow	VERB
ejpam-4385	5	29	the	the	DET
ejpam-4385	5	30	cox	cox	PROPN
ejpam-4385	5	31	-	-	PUNCT
ejpam-4385	5	32	ingersoll	ingersoll	PROPN
ejpam-4385	5	33	-	-	PUNCT
ejpam-4385	5	34	ross	ross	PROPN
ejpam-4385	5	35	model	model	NOUN
ejpam-4385	5	36	and	and	CCONJ
ejpam-4385	5	37	constant	constant	ADJ
ejpam-4385	5	38	volatility	volatility	NOUN
ejpam-4385	5	39	as	as	ADP
ejpam-4385	5	40	v	v	NOUN
ejpam-4385	5	41	(	(	PUNCT
ejpam-4385	5	42	t	t	PROPN
ejpam-4385	5	43	,	,	PUNCT
ejpam-4385	5	44	rt	rt	PROPN
ejpam-4385	5	45	,	,	PUNCT
ejpam-4385	5	46	x	x	NOUN
ejpam-4385	5	47	)	)	PUNCT
ejpam-4385	5	48	=	=	SYM
ejpam-4385	5	49	p(t	p(t	NOUN
ejpam-4385	5	50	,	,	PUNCT
ejpam-4385	5	51	rt;t	rt;t	PROPN
ejpam-4385	5	52	)	)	PUNCT
ejpam-4385	6	1	+	+	CCONJ
ejpam-4385	6	2	∫	∫	PROPN
ejpam-4385	6	3	t	t	PROPN
ejpam-4385	6	4	t	t	PROPN
ejpam-4385	6	5	j(t	j(t	PROPN
ejpam-4385	6	6	,	,	PUNCT
ejpam-4385	6	7	rt	rt	PROPN
ejpam-4385	6	8	,	,	PUNCT
ejpam-4385	6	9	x	x	NOUN
ejpam-4385	6	10	,	,	PUNCT
ejpam-4385	6	11	v	v	NOUN
ejpam-4385	6	12	,	,	PUNCT
ejpam-4385	6	13	bd(v	bd(v	PUNCT
ejpam-4385	6	14	,	,	PUNCT
ejpam-4385	6	15	rv))dv	rv))dv	PROPN
ejpam-4385	6	16	,	,	PUNCT
ejpam-4385	6	17	where	where	SCONJ
ejpam-4385	6	18	the	the	DET
ejpam-4385	6	19	first	first	ADJ
ejpam-4385	6	20	term	term	NOUN
ejpam-4385	6	21	is	be	AUX
ejpam-4385	6	22	the	the	DET
ejpam-4385	6	23	arbitrage	arbitrage	NOUN
ejpam-4385	6	24	-	-	PUNCT
ejpam-4385	6	25	free	free	ADJ
ejpam-4385	6	26	price	price	NOUN
ejpam-4385	6	27	of	of	ADP
ejpam-4385	6	28	the	the	DET
ejpam-4385	6	29	european	european	ADJ
ejpam-4385	6	30	call	call	NOUN
ejpam-4385	6	31	option	option	NOUN
ejpam-4385	6	32	under	under	ADP
ejpam-4385	6	33	stochastic	stochastic	ADJ
ejpam-4385	6	34	interest	interest	NOUN
ejpam-4385	6	35	rate	rate	NOUN
ejpam-4385	6	36	and	and	CCONJ
ejpam-4385	6	37	the	the	DET
ejpam-4385	6	38	second	second	ADJ
ejpam-4385	6	39	term	term	NOUN
ejpam-4385	6	40	is	be	AUX
ejpam-4385	6	41	the	the	DET
ejpam-4385	6	42	early	early	ADJ
ejpam-4385	6	43	-	-	PUNCT
ejpam-4385	6	44	exercise	exercise	NOUN
ejpam-4385	6	45	premmium	premmium	NOUN
ejpam-4385	6	46	.	.	PUNCT
ejpam-4385	7	1	we	we	PRON
ejpam-4385	7	2	have	have	AUX
ejpam-4385	7	3	also	also	ADV
ejpam-4385	7	4	shown	show	VERB
ejpam-4385	7	5	that	that	SCONJ
ejpam-4385	7	6	the	the	DET
ejpam-4385	7	7	price	price	NOUN
ejpam-4385	7	8	function	function	NOUN
ejpam-4385	7	9	of	of	ADP
ejpam-4385	7	10	the	the	DET
ejpam-4385	7	11	british	british	ADJ
ejpam-4385	7	12	call	call	NOUN
ejpam-4385	7	13	option	option	NOUN
ejpam-4385	7	14	satisfies	satisfy	VERB
ejpam-4385	7	15	the	the	DET
ejpam-4385	7	16	partial	partial	ADJ
ejpam-4385	7	17	differential	differential	NOUN
ejpam-4385	7	18	equation	equation	NOUN
ejpam-4385	7	19	given	give	VERB
ejpam-4385	7	20	by	by	ADP
ejpam-4385	7	21	∂v	∂v	PROPN
ejpam-4385	7	22	∂t	∂t	PROPN
ejpam-4385	8	1	+	+	CCONJ
ejpam-4385	8	2	1	1	NUM
ejpam-4385	8	3	2	2	NUM
ejpam-4385	8	4	σ2	σ2	NOUN
ejpam-4385	8	5	1x	1x	NUM
ejpam-4385	8	6	2	2	NUM
ejpam-4385	8	7	t	t	PROPN
ejpam-4385	8	8	∂2v	∂2v	X
ejpam-4385	8	9	∂x2	∂x2	PROPN
ejpam-4385	8	10	+	+	X
ejpam-4385	8	11	ρσ1σ2	ρσ1σ2	PROPN
ejpam-4385	8	12	√	√	PROPN
ejpam-4385	8	13	rt	rt	PROPN
ejpam-4385	8	14	∂2v	∂2v	PROPN
ejpam-4385	8	15	∂x∂r	∂x∂r	VERB
ejpam-4385	9	1	+	+	CCONJ
ejpam-4385	9	2	1	1	NUM
ejpam-4385	9	3	2	2	NUM
ejpam-4385	9	4	σ2	σ2	NOUN
ejpam-4385	9	5	2rt	2rt	NOUN
ejpam-4385	9	6	∂2v	∂2v	PROPN
ejpam-4385	9	7	∂r2	∂r2	PROPN
ejpam-4385	9	8	+	+	CCONJ
ejpam-4385	9	9	∂v	∂v	PROPN
ejpam-4385	9	10	∂x	∂x	PROPN
ejpam-4385	9	11	rtxt	rtxt	NOUN
ejpam-4385	9	12	+	+	CCONJ
ejpam-4385	10	1	[	[	X
ejpam-4385	10	2	aθ	aθ	INTJ
ejpam-4385	10	3	−	−	PROPN
ejpam-4385	10	4	(	(	PUNCT
ejpam-4385	10	5	a+	a+	X
ejpam-4385	10	6	λσ)r	λσ)r	X
ejpam-4385	10	7	]	]	X
ejpam-4385	10	8	∂v	∂v	PROPN
ejpam-4385	10	9	∂r	∂r	INTJ
ejpam-4385	11	1	−	−	PROPN
ejpam-4385	11	2	rtv	rtv	NOUN
ejpam-4385	11	3	=	=	SYM
ejpam-4385	11	4	0	0	PROPN
ejpam-4385	11	5	.	.	PUNCT
ejpam-4385	12	1	moreover	moreover	ADV
ejpam-4385	12	2	,	,	PUNCT
ejpam-4385	12	3	we	we	PRON
ejpam-4385	12	4	have	have	AUX
ejpam-4385	12	5	shown	show	VERB
ejpam-4385	12	6	that	that	SCONJ
ejpam-4385	12	7	the	the	DET
ejpam-4385	12	8	contract	contract	NOUN
ejpam-4385	12	9	drift	drift	NOUN
ejpam-4385	12	10	satisfies	satisfie	NOUN
ejpam-4385	12	11	µc	µc	VERB
ejpam-4385	12	12	<	<	X
ejpam-4385	12	13	rt+ρσ1σ2	rt+ρσ1σ2	ADJ
ejpam-4385	12	14	√	√	PROPN
ejpam-4385	12	15	rtλ(0	rtλ(0	NOUN
ejpam-4385	12	16	,	,	PUNCT
ejpam-4385	12	17	t+u	t+u	NUM
ejpam-4385	12	18	)	)	PUNCT
ejpam-4385	12	19	for	for	ADP
ejpam-4385	12	20	u	u	PROPN
ejpam-4385	12	21	∈	∈	PROPN
ejpam-4385	13	1	[	[	X
ejpam-4385	13	2	0	0	NUM
ejpam-4385	13	3	,	,	PUNCT
ejpam-4385	13	4	τ	τ	X
ejpam-4385	13	5	]	]	PUNCT
ejpam-4385	13	6	and	and	CCONJ
ejpam-4385	13	7	t	t	PROPN
ejpam-4385	13	8	∈	∈	PROPN
ejpam-4385	14	1	[	[	X
ejpam-4385	14	2	0	0	NUM
ejpam-4385	14	3	,	,	PUNCT
ejpam-4385	14	4	t	t	X
ejpam-4385	14	5	]	]	PUNCT
ejpam-4385	14	6	.	.	PUNCT
ejpam-4385	15	1	2020	2020	NUM
ejpam-4385	15	2	mathematics	mathematic	NOUN
ejpam-4385	15	3	subject	subject	NOUN
ejpam-4385	15	4	classifications	classification	NOUN
ejpam-4385	15	5	:	:	PUNCT
ejpam-4385	15	6	35a01	35a01	NUM
ejpam-4385	15	7	,	,	PUNCT
ejpam-4385	15	8	35a02	35a02	NUM
ejpam-4385	15	9	,	,	PUNCT
ejpam-4385	15	10	35c05	35c05	NUM
ejpam-4385	15	11	,	,	PUNCT
ejpam-4385	15	12	35c15	35c15	NUM
ejpam-4385	15	13	,	,	PUNCT
ejpam-4385	15	14	35r35	35r35	NUM
ejpam-4385	15	15	,	,	PUNCT
ejpam-4385	15	16	60h15	60h15	NUM
ejpam-4385	15	17	,	,	PUNCT
ejpam-4385	15	18	60h35	60h35	NUM
ejpam-4385	15	19	,	,	PUNCT
ejpam-4385	15	20	60j65	60j65	NUM
ejpam-4385	15	21	key	key	ADJ
ejpam-4385	15	22	words	word	NOUN
ejpam-4385	15	23	and	and	CCONJ
ejpam-4385	15	24	phrases	phrase	NOUN
ejpam-4385	15	25	:	:	PUNCT
ejpam-4385	15	26	british	british	ADJ
ejpam-4385	15	27	call	call	NOUN
ejpam-4385	15	28	option	option	NOUN
ejpam-4385	15	29	,	,	PUNCT
ejpam-4385	15	30	american	american	ADJ
ejpam-4385	15	31	call	call	NOUN
ejpam-4385	15	32	option	option	NOUN
ejpam-4385	15	33	,	,	PUNCT
ejpam-4385	15	34	european	european	ADJ
ejpam-4385	15	35	call	call	NOUN
ejpam-4385	15	36	option	option	NOUN
ejpam-4385	15	37	,	,	PUNCT
ejpam-4385	15	38	arbitrage	arbitrage	NOUN
ejpam-4385	15	39	-	-	PUNCT
ejpam-4385	15	40	free	free	ADJ
ejpam-4385	15	41	price	price	NOUN
ejpam-4385	15	42	,	,	PUNCT
ejpam-4385	15	43	cox	cox	PROPN
ejpam-4385	15	44	-	-	PUNCT
ejpam-4385	15	45	ingersoll	ingersoll	PROPN
ejpam-4385	15	46	-	-	PUNCT
ejpam-4385	15	47	ross	ross	PROPN
ejpam-4385	15	48	model	model	NOUN
ejpam-4385	15	49	,	,	PUNCT
ejpam-4385	15	50	rational	rational	ADJ
ejpam-4385	15	51	exercise	exercise	NOUN
ejpam-4385	15	52	boundary	boundary	NOUN
ejpam-4385	15	53	,	,	PUNCT
ejpam-4385	15	54	geometric	geometric	ADJ
ejpam-4385	15	55	brownian	brownian	ADJ
ejpam-4385	15	56	motion	motion	NOUN
ejpam-4385	15	57	or	or	CCONJ
ejpam-4385	15	58	wiener	wiener	NOUN
ejpam-4385	15	59	process	process	NOUN
ejpam-4385	15	60	,	,	PUNCT
ejpam-4385	15	61	optimal	optimal	ADJ
ejpam-4385	15	62	stopping	stopping	NOUN
ejpam-4385	15	63	time	time	NOUN
ejpam-4385	15	64	,	,	PUNCT
ejpam-4385	15	65	free	free	ADJ
ejpam-4385	15	66	boundary	boundary	ADJ
ejpam-4385	15	67	problem	problem	NOUN
ejpam-4385	15	68	∗corresponding	∗corresponde	VERB
ejpam-4385	15	69	author	author	NOUN
ejpam-4385	15	70	.	.	PUNCT
ejpam-4385	16	1	doi	doi	NOUN
ejpam-4385	16	2	:	:	PUNCT
ejpam-4385	16	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4385	https://doi.org/10.29020/nybg.ejpam.v15i3.4385	PROPN
ejpam-4385	16	4	email	email	NOUN
ejpam-4385	16	5	addresses	address	NOUN
ejpam-4385	16	6	:	:	PUNCT
ejpam-4385	16	7	falcasantoskrel@adzu.edu.ph	falcasantoskrel@adzu.edu.ph	PROPN
ejpam-4385	16	8	(	(	PUNCT
ejpam-4385	16	9	k.	k.	PROPN
ejpam-4385	16	10	falcasantos	falcasanto	NOUN
ejpam-4385	16	11	)	)	PUNCT
ejpam-4385	16	12	,	,	PUNCT
ejpam-4385	16	13	felipejr.sumalpong@g.msuiit.edu.ph	felipejr.sumalpong@g.msuiit.edu.ph	PROPN
ejpam-4385	16	14	(	(	PUNCT
ejpam-4385	16	15	r.	r.	PROPN
ejpam-4385	16	16	sumalpong	sumalpong	PROPN
ejpam-4385	16	17	)	)	PUNCT
ejpam-4385	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4385	17	1	948	948	NUM
ejpam-4385	18	1	©	©	PROPN
ejpam-4385	18	2	2022	2022	NUM
ejpam-4385	18	3	ejpam	ejpam	VERB
ejpam-4385	18	4	all	all	DET
ejpam-4385	18	5	rights	right	NOUN
ejpam-4385	18	6	reserved	reserve	VERB
ejpam-4385	18	7	.	.	PUNCT
ejpam-4385	19	1	k.	k.	PROPN
ejpam-4385	19	2	falcasantos	falcasantos	PROPN
ejpam-4385	19	3	,	,	PUNCT
ejpam-4385	19	4	f.	f.	PROPN
ejpam-4385	19	5	sumalpong	sumalpong	PROPN
ejpam-4385	19	6	/	/	SYM
ejpam-4385	19	7	eur	eur	PROPN
ejpam-4385	19	8	.	.	PUNCT
ejpam-4385	20	1	j.	j.	PROPN
ejpam-4385	20	2	pure	pure	PROPN
ejpam-4385	20	3	appl	appl	PROPN
ejpam-4385	20	4	.	.	PROPN
ejpam-4385	20	5	math	math	PROPN
ejpam-4385	20	6	,	,	PUNCT
ejpam-4385	20	7	15	15	NUM
ejpam-4385	20	8	(	(	PUNCT
ejpam-4385	20	9	3	3	NUM
ejpam-4385	20	10	)	)	PUNCT
ejpam-4385	20	11	(	(	PUNCT
ejpam-4385	20	12	2022	2022	NUM
ejpam-4385	20	13	)	)	PUNCT
ejpam-4385	20	14	,	,	PUNCT
ejpam-4385	20	15	948	948	NUM
ejpam-4385	20	16	-	-	SYM
ejpam-4385	20	17	970	970	NUM
ejpam-4385	20	18	949	949	NUM
ejpam-4385	20	19	1	1	NUM
ejpam-4385	20	20	.	.	PUNCT
ejpam-4385	20	21	introduction	introduction	NOUN
ejpam-4385	20	22	over	over	ADP
ejpam-4385	20	23	the	the	DET
ejpam-4385	20	24	years	year	NOUN
ejpam-4385	20	25	,	,	PUNCT
ejpam-4385	20	26	derivatives	derivative	NOUN
ejpam-4385	20	27	have	have	AUX
ejpam-4385	20	28	become	become	VERB
ejpam-4385	20	29	increasingly	increasingly	ADV
ejpam-4385	20	30	important	important	ADJ
ejpam-4385	20	31	in	in	ADP
ejpam-4385	20	32	the	the	DET
ejpam-4385	20	33	global	global	ADJ
ejpam-4385	20	34	financial	financial	ADJ
ejpam-4385	20	35	market	market	NOUN
ejpam-4385	20	36	,	,	PUNCT
ejpam-4385	20	37	with	with	ADP
ejpam-4385	20	38	great	great	ADJ
ejpam-4385	20	39	impact	impact	NOUN
ejpam-4385	20	40	on	on	ADP
ejpam-4385	20	41	national	national	ADJ
ejpam-4385	20	42	economics	economic	NOUN
ejpam-4385	20	43	.	.	PUNCT
ejpam-4385	21	1	they	they	PRON
ejpam-4385	21	2	are	be	AUX
ejpam-4385	21	3	embedded	embed	VERB
ejpam-4385	21	4	in	in	ADP
ejpam-4385	21	5	capital	capital	NOUN
ejpam-4385	21	6	investment	investment	NOUN
ejpam-4385	21	7	opportunities	opportunity	NOUN
ejpam-4385	21	8	,	,	PUNCT
ejpam-4385	21	9	added	add	VERB
ejpam-4385	21	10	to	to	AUX
ejpam-4385	21	11	bond	bond	VERB
ejpam-4385	21	12	issues[5	issues[5	PROPN
ejpam-4385	21	13	]	]	PUNCT
ejpam-4385	21	14	,	,	PUNCT
ejpam-4385	21	15	used	use	VERB
ejpam-4385	21	16	as	as	ADP
ejpam-4385	21	17	price	price	NOUN
ejpam-4385	21	18	discovery	discovery	NOUN
ejpam-4385	21	19	and	and	CCONJ
ejpam-4385	21	20	price	price	NOUN
ejpam-4385	21	21	stabilizer	stabilizer	NOUN
ejpam-4385	21	22	[	[	X
ejpam-4385	21	23	14	14	NUM
ejpam-4385	21	24	]	]	PUNCT
ejpam-4385	21	25	and	and	CCONJ
ejpam-4385	21	26	so	so	ADV
ejpam-4385	21	27	on	on	ADV
ejpam-4385	21	28	.	.	PUNCT
ejpam-4385	22	1	the	the	DET
ejpam-4385	22	2	most	most	ADV
ejpam-4385	22	3	common	common	ADJ
ejpam-4385	22	4	forms	form	NOUN
ejpam-4385	22	5	of	of	ADP
ejpam-4385	22	6	derivatives	derivative	NOUN
ejpam-4385	22	7	is	be	AUX
ejpam-4385	22	8	an	an	DET
ejpam-4385	22	9	option	option	NOUN
ejpam-4385	22	10	.	.	PUNCT
ejpam-4385	23	1	an	an	DET
ejpam-4385	23	2	option	option	NOUN
ejpam-4385	23	3	is	be	AUX
ejpam-4385	23	4	defined	define	VERB
ejpam-4385	23	5	to	to	PART
ejpam-4385	23	6	be	be	AUX
ejpam-4385	23	7	a	a	DET
ejpam-4385	23	8	contract	contract	NOUN
ejpam-4385	23	9	between	between	ADP
ejpam-4385	23	10	two	two	NUM
ejpam-4385	23	11	parties	party	NOUN
ejpam-4385	23	12	granting	grant	VERB
ejpam-4385	23	13	one	one	NUM
ejpam-4385	23	14	party	party	NOUN
ejpam-4385	23	15	the	the	DET
ejpam-4385	23	16	opportunity	opportunity	NOUN
ejpam-4385	23	17	to	to	PART
ejpam-4385	23	18	buy	buy	VERB
ejpam-4385	23	19	or	or	CCONJ
ejpam-4385	23	20	sell	sell	VERB
ejpam-4385	23	21	a	a	DET
ejpam-4385	23	22	security	security	NOUN
ejpam-4385	23	23	from	from	ADP
ejpam-4385	23	24	or	or	CCONJ
ejpam-4385	23	25	to	to	ADP
ejpam-4385	23	26	the	the	DET
ejpam-4385	23	27	other	other	ADJ
ejpam-4385	23	28	party	party	NOUN
ejpam-4385	23	29	at	at	ADP
ejpam-4385	23	30	a	a	DET
ejpam-4385	23	31	specified	specify	VERB
ejpam-4385	23	32	price	price	NOUN
ejpam-4385	23	33	also	also	ADV
ejpam-4385	23	34	known	know	VERB
ejpam-4385	23	35	as	as	ADP
ejpam-4385	23	36	strike	strike	NOUN
ejpam-4385	23	37	price	price	NOUN
ejpam-4385	23	38	on	on	ADP
ejpam-4385	23	39	or	or	CCONJ
ejpam-4385	23	40	before	before	ADP
ejpam-4385	23	41	a	a	DET
ejpam-4385	23	42	specified	specified	ADJ
ejpam-4385	23	43	maturity	maturity	NOUN
ejpam-4385	23	44	date	date	NOUN
ejpam-4385	24	1	[	[	X
ejpam-4385	24	2	7	7	NUM
ejpam-4385	24	3	]	]	PUNCT
ejpam-4385	24	4	.	.	PUNCT
ejpam-4385	25	1	the	the	DET
ejpam-4385	25	2	two	two	NUM
ejpam-4385	25	3	parties	party	NOUN
ejpam-4385	25	4	involved	involve	VERB
ejpam-4385	25	5	are	be	AUX
ejpam-4385	25	6	called	call	VERB
ejpam-4385	25	7	the	the	DET
ejpam-4385	25	8	buyer	buyer	NOUN
ejpam-4385	25	9	and	and	CCONJ
ejpam-4385	25	10	seller	seller	NOUN
ejpam-4385	25	11	of	of	ADP
ejpam-4385	25	12	the	the	DET
ejpam-4385	25	13	option	option	NOUN
ejpam-4385	25	14	.	.	PUNCT
ejpam-4385	26	1	the	the	DET
ejpam-4385	26	2	buyer	buyer	NOUN
ejpam-4385	26	3	has	have	VERB
ejpam-4385	26	4	the	the	DET
ejpam-4385	26	5	right	right	NOUN
ejpam-4385	26	6	but	but	CCONJ
ejpam-4385	26	7	not	not	PART
ejpam-4385	26	8	the	the	DET
ejpam-4385	26	9	obligation	obligation	NOUN
ejpam-4385	26	10	to	to	PART
ejpam-4385	26	11	exercise	exercise	VERB
ejpam-4385	26	12	the	the	DET
ejpam-4385	26	13	option	option	NOUN
ejpam-4385	26	14	.	.	PUNCT
ejpam-4385	27	1	in	in	ADP
ejpam-4385	27	2	order	order	NOUN
ejpam-4385	27	3	to	to	PART
ejpam-4385	27	4	acquire	acquire	VERB
ejpam-4385	27	5	the	the	DET
ejpam-4385	27	6	option	option	NOUN
ejpam-4385	27	7	,	,	PUNCT
ejpam-4385	27	8	the	the	DET
ejpam-4385	27	9	buyer	buyer	NOUN
ejpam-4385	27	10	should	should	AUX
ejpam-4385	27	11	pay	pay	VERB
ejpam-4385	27	12	the	the	DET
ejpam-4385	27	13	option	option	NOUN
ejpam-4385	27	14	price	price	NOUN
ejpam-4385	27	15	,	,	PUNCT
ejpam-4385	27	16	which	which	PRON
ejpam-4385	27	17	is	be	AUX
ejpam-4385	27	18	also	also	ADV
ejpam-4385	27	19	known	know	VERB
ejpam-4385	27	20	as	as	ADP
ejpam-4385	27	21	premium	premium	NOUN
ejpam-4385	27	22	to	to	ADP
ejpam-4385	27	23	the	the	DET
ejpam-4385	27	24	seller	seller	NOUN
ejpam-4385	27	25	[	[	X
ejpam-4385	27	26	7	7	NUM
ejpam-4385	27	27	]	]	PUNCT
ejpam-4385	27	28	.	.	PUNCT
ejpam-4385	28	1	in	in	ADP
ejpam-4385	28	2	2013	2013	NUM
ejpam-4385	28	3	,	,	PUNCT
ejpam-4385	28	4	g.peskir	g.peskir	PUNCT
ejpam-4385	28	5	and	and	CCONJ
ejpam-4385	28	6	f.	f.	PROPN
ejpam-4385	28	7	samee	samee	PROPN
ejpam-4385	28	8	introduced	introduce	VERB
ejpam-4385	28	9	a	a	DET
ejpam-4385	28	10	new	new	ADJ
ejpam-4385	28	11	type	type	NOUN
ejpam-4385	28	12	of	of	ADP
ejpam-4385	28	13	call	call	NOUN
ejpam-4385	28	14	option	option	NOUN
ejpam-4385	28	15	called	call	VERB
ejpam-4385	28	16	british	british	ADJ
ejpam-4385	28	17	call	call	NOUN
ejpam-4385	28	18	options	option	NOUN
ejpam-4385	28	19	where	where	SCONJ
ejpam-4385	28	20	the	the	DET
ejpam-4385	28	21	holder	holder	NOUN
ejpam-4385	28	22	enjoys	enjoy	VERB
ejpam-4385	28	23	the	the	DET
ejpam-4385	28	24	early	early	ADJ
ejpam-4385	28	25	exercise	exercise	NOUN
ejpam-4385	28	26	feature	feature	NOUN
ejpam-4385	28	27	of	of	ADP
ejpam-4385	28	28	the	the	DET
ejpam-4385	28	29	american	american	ADJ
ejpam-4385	28	30	option	option	NOUN
ejpam-4385	28	31	whereupon	whereupon	ADV
ejpam-4385	28	32	his	his	PRON
ejpam-4385	28	33	payoff	payoff	NOUN
ejpam-4385	28	34	is	be	AUX
ejpam-4385	28	35	the	the	DET
ejpam-4385	28	36	best	good	ADJ
ejpam-4385	28	37	prediction	prediction	NOUN
ejpam-4385	28	38	of	of	ADP
ejpam-4385	28	39	the	the	DET
ejpam-4385	28	40	european	european	PROPN
ejpam-4385	28	41	payoff	payoff	NOUN
ejpam-4385	28	42	under	under	ADP
ejpam-4385	28	43	the	the	DET
ejpam-4385	28	44	hypothesis	hypothesis	NOUN
ejpam-4385	28	45	that	that	PRON
ejpam-4385	28	46	the	the	DET
ejpam-4385	28	47	true	true	ADJ
ejpam-4385	28	48	drift	drift	NOUN
ejpam-4385	28	49	of	of	ADP
ejpam-4385	28	50	the	the	DET
ejpam-4385	28	51	stock	stock	NOUN
ejpam-4385	28	52	price	price	NOUN
ejpam-4385	28	53	equals	equal	VERB
ejpam-4385	28	54	the	the	DET
ejpam-4385	28	55	contract	contract	NOUN
ejpam-4385	28	56	drift	drift	NOUN
ejpam-4385	29	1	[	[	X
ejpam-4385	29	2	11	11	NUM
ejpam-4385	29	3	]	]	PUNCT
ejpam-4385	29	4	.	.	PUNCT
ejpam-4385	30	1	british	british	ADJ
ejpam-4385	30	2	option	option	NOUN
ejpam-4385	30	3	provides	provide	VERB
ejpam-4385	30	4	its	its	PRON
ejpam-4385	30	5	holder	holder	NOUN
ejpam-4385	30	6	with	with	ADP
ejpam-4385	30	7	a	a	DET
ejpam-4385	30	8	protection	protection	NOUN
ejpam-4385	30	9	mechanism	mechanism	NOUN
ejpam-4385	30	10	against	against	ADP
ejpam-4385	30	11	unfavorable	unfavorable	ADJ
ejpam-4385	30	12	stock	stock	NOUN
ejpam-4385	30	13	price	price	NOUN
ejpam-4385	30	14	movements	movement	NOUN
ejpam-4385	30	15	as	as	ADV
ejpam-4385	30	16	well	well	ADV
ejpam-4385	30	17	as	as	ADP
ejpam-4385	30	18	securing	secure	VERB
ejpam-4385	30	19	higher	high	ADJ
ejpam-4385	30	20	returns	return	NOUN
ejpam-4385	30	21	when	when	SCONJ
ejpam-4385	30	22	the	the	DET
ejpam-4385	30	23	movements	movement	NOUN
ejpam-4385	30	24	are	be	AUX
ejpam-4385	30	25	favourable	favourable	ADJ
ejpam-4385	30	26	.	.	PUNCT
ejpam-4385	31	1	the	the	DET
ejpam-4385	31	2	motivation	motivation	NOUN
ejpam-4385	31	3	for	for	ADP
ejpam-4385	31	4	the	the	DET
ejpam-4385	31	5	british	british	ADJ
ejpam-4385	31	6	call	call	NOUN
ejpam-4385	31	7	option	option	NOUN
ejpam-4385	31	8	starts	start	VERB
ejpam-4385	31	9	from	from	ADP
ejpam-4385	31	10	the	the	DET
ejpam-4385	31	11	difference	difference	NOUN
ejpam-4385	31	12	between	between	ADP
ejpam-4385	31	13	the	the	DET
ejpam-4385	31	14	paid	pay	VERB
ejpam-4385	31	15	premium	premium	NOUN
ejpam-4385	31	16	and	and	CCONJ
ejpam-4385	31	17	the	the	DET
ejpam-4385	31	18	expected	expect	VERB
ejpam-4385	31	19	payoff	payoff	NOUN
ejpam-4385	31	20	when	when	SCONJ
ejpam-4385	31	21	the	the	DET
ejpam-4385	31	22	true	true	ADJ
ejpam-4385	31	23	drift	drift	NOUN
ejpam-4385	31	24	deviates	deviate	VERB
ejpam-4385	31	25	from	from	ADP
ejpam-4385	31	26	the	the	DET
ejpam-4385	31	27	risk	risk	NOUN
ejpam-4385	31	28	-	-	PUNCT
ejpam-4385	31	29	free	free	ADJ
ejpam-4385	31	30	rate	rate	NOUN
ejpam-4385	31	31	.	.	PUNCT
ejpam-4385	32	1	an	an	DET
ejpam-4385	32	2	added	add	VERB
ejpam-4385	32	3	feature	feature	NOUN
ejpam-4385	32	4	is	be	AUX
ejpam-4385	32	5	built	build	VERB
ejpam-4385	32	6	into	into	ADP
ejpam-4385	32	7	this	this	DET
ejpam-4385	32	8	instrument	instrument	NOUN
ejpam-4385	32	9	which	which	PRON
ejpam-4385	32	10	aim	aim	VERB
ejpam-4385	32	11	at	at	ADP
ejpam-4385	32	12	both	both	PRON
ejpam-4385	32	13	providing	provide	VERB
ejpam-4385	32	14	protection	protection	NOUN
ejpam-4385	32	15	against	against	ADP
ejpam-4385	32	16	unfavourable	unfavourable	ADJ
ejpam-4385	32	17	price	price	NOUN
ejpam-4385	32	18	movements	movement	NOUN
ejpam-4385	32	19	as	as	ADV
ejpam-4385	32	20	well	well	ADV
ejpam-4385	32	21	as	as	ADP
ejpam-4385	32	22	securing	secure	VERB
ejpam-4385	32	23	higher	high	ADJ
ejpam-4385	32	24	returns	return	NOUN
ejpam-4385	32	25	when	when	SCONJ
ejpam-4385	32	26	these	these	DET
ejpam-4385	32	27	movements	movement	NOUN
ejpam-4385	32	28	are	be	AUX
ejpam-4385	32	29	favourable	favourable	ADJ
ejpam-4385	32	30	[	[	X
ejpam-4385	32	31	11	11	NUM
ejpam-4385	32	32	]	]	PUNCT
ejpam-4385	32	33	.	.	PUNCT
ejpam-4385	33	1	accordingly	accordingly	ADV
ejpam-4385	33	2	,	,	PUNCT
ejpam-4385	33	3	the	the	DET
ejpam-4385	33	4	value	value	NOUN
ejpam-4385	33	5	function	function	NOUN
ejpam-4385	33	6	of	of	ADP
ejpam-4385	33	7	the	the	DET
ejpam-4385	33	8	british	british	ADJ
ejpam-4385	33	9	call	call	NOUN
ejpam-4385	33	10	option	option	NOUN
ejpam-4385	33	11	is	be	AUX
ejpam-4385	33	12	similar	similar	ADJ
ejpam-4385	33	13	to	to	ADP
ejpam-4385	33	14	american	american	ADJ
ejpam-4385	33	15	call	call	NOUN
ejpam-4385	33	16	option	option	NOUN
ejpam-4385	33	17	but	but	CCONJ
ejpam-4385	33	18	they	they	PRON
ejpam-4385	33	19	differ	differ	VERB
ejpam-4385	33	20	on	on	ADP
ejpam-4385	33	21	their	their	PRON
ejpam-4385	33	22	respective	respective	ADJ
ejpam-4385	33	23	boundary	boundary	ADJ
ejpam-4385	33	24	functions	function	NOUN
ejpam-4385	33	25	.	.	PUNCT
ejpam-4385	34	1	the	the	DET
ejpam-4385	34	2	closed	closed	ADJ
ejpam-4385	34	3	form	form	NOUN
ejpam-4385	34	4	expression	expression	NOUN
ejpam-4385	34	5	for	for	ADP
ejpam-4385	34	6	the	the	DET
ejpam-4385	34	7	price	price	NOUN
ejpam-4385	34	8	of	of	ADP
ejpam-4385	34	9	the	the	DET
ejpam-4385	34	10	british	british	ADJ
ejpam-4385	34	11	call	call	NOUN
ejpam-4385	34	12	option	option	NOUN
ejpam-4385	34	13	has	have	AUX
ejpam-4385	34	14	been	be	AUX
ejpam-4385	34	15	derived	derive	VERB
ejpam-4385	34	16	by	by	ADP
ejpam-4385	34	17	peskir	peskir	NOUN
ejpam-4385	34	18	and	and	CCONJ
ejpam-4385	34	19	samee	samee	PROPN
ejpam-4385	34	20	(	(	PUNCT
ejpam-4385	34	21	2013	2013	NUM
ejpam-4385	34	22	)	)	PUNCT
ejpam-4385	34	23	by	by	ADP
ejpam-4385	34	24	assuming	assume	VERB
ejpam-4385	34	25	constant	constant	ADJ
ejpam-4385	34	26	interest	interest	NOUN
ejpam-4385	34	27	rate	rate	NOUN
ejpam-4385	34	28	and	and	CCONJ
ejpam-4385	34	29	constant	constant	ADJ
ejpam-4385	34	30	volatility	volatility	NOUN
ejpam-4385	34	31	.	.	PUNCT
ejpam-4385	35	1	however	however	ADV
ejpam-4385	35	2	,	,	PUNCT
ejpam-4385	35	3	the	the	DET
ejpam-4385	35	4	assumptions	assumption	NOUN
ejpam-4385	35	5	of	of	ADP
ejpam-4385	35	6	constant	constant	ADJ
ejpam-4385	35	7	interest	interest	NOUN
ejpam-4385	35	8	rate	rate	NOUN
ejpam-4385	35	9	and	and	CCONJ
ejpam-4385	35	10	constant	constant	ADJ
ejpam-4385	35	11	volatility	volatility	NOUN
ejpam-4385	35	12	fail	fail	VERB
ejpam-4385	35	13	to	to	PART
ejpam-4385	35	14	reflect	reflect	VERB
ejpam-4385	35	15	the	the	DET
ejpam-4385	35	16	fact	fact	NOUN
ejpam-4385	35	17	that	that	SCONJ
ejpam-4385	35	18	these	these	DET
ejpam-4385	35	19	market	market	NOUN
ejpam-4385	35	20	rates	rate	NOUN
ejpam-4385	35	21	are	be	AUX
ejpam-4385	35	22	stochastic	stochastic	ADJ
ejpam-4385	35	23	in	in	ADP
ejpam-4385	35	24	the	the	DET
ejpam-4385	35	25	real	real	ADJ
ejpam-4385	35	26	world	world	NOUN
ejpam-4385	35	27	.	.	PUNCT
ejpam-4385	36	1	this	this	DET
ejpam-4385	36	2	paper	paper	NOUN
ejpam-4385	36	3	extends	extend	VERB
ejpam-4385	36	4	the	the	DET
ejpam-4385	36	5	results	result	NOUN
ejpam-4385	36	6	in	in	ADP
ejpam-4385	36	7	[	[	X
ejpam-4385	36	8	11	11	NUM
ejpam-4385	36	9	]	]	PUNCT
ejpam-4385	36	10	to	to	PART
ejpam-4385	36	11	address	address	VERB
ejpam-4385	36	12	the	the	DET
ejpam-4385	36	13	mentioned	mention	VERB
ejpam-4385	36	14	shortcomings	shortcoming	NOUN
ejpam-4385	36	15	by	by	ADP
ejpam-4385	36	16	considering	consider	VERB
ejpam-4385	36	17	british	british	ADJ
ejpam-4385	36	18	call	call	NOUN
ejpam-4385	36	19	option	option	NOUN
ejpam-4385	36	20	under	under	ADP
ejpam-4385	36	21	stochastic	stochastic	ADJ
ejpam-4385	36	22	interest	interest	NOUN
ejpam-4385	36	23	rate	rate	NOUN
ejpam-4385	36	24	and	and	CCONJ
ejpam-4385	36	25	constant	constant	ADJ
ejpam-4385	36	26	volatility	volatility	NOUN
ejpam-4385	36	27	.	.	PUNCT
ejpam-4385	37	1	in	in	ADP
ejpam-4385	37	2	particular	particular	ADJ
ejpam-4385	37	3	,	,	PUNCT
ejpam-4385	37	4	it	it	PRON
ejpam-4385	37	5	will	will	AUX
ejpam-4385	37	6	be	be	AUX
ejpam-4385	37	7	assumed	assume	VERB
ejpam-4385	37	8	that	that	SCONJ
ejpam-4385	37	9	the	the	DET
ejpam-4385	37	10	short	short	ADJ
ejpam-4385	37	11	rate	rate	NOUN
ejpam-4385	37	12	follows	follow	VERB
ejpam-4385	37	13	the	the	DET
ejpam-4385	37	14	cox	cox	PROPN
ejpam-4385	37	15	-	-	PUNCT
ejpam-4385	37	16	ingersoll	ingersoll	PROPN
ejpam-4385	37	17	-	-	PUNCT
ejpam-4385	37	18	ross	ross	PROPN
ejpam-4385	37	19	(	(	PUNCT
ejpam-4385	37	20	cir	cir	NOUN
ejpam-4385	37	21	)	)	PUNCT
ejpam-4385	37	22	model	model	NOUN
ejpam-4385	37	23	.	.	PUNCT
ejpam-4385	38	1	furthermore	furthermore	ADV
ejpam-4385	38	2	,	,	PUNCT
ejpam-4385	38	3	this	this	DET
ejpam-4385	38	4	paper	paper	NOUN
ejpam-4385	38	5	focuses	focus	VERB
ejpam-4385	38	6	on	on	ADP
ejpam-4385	38	7	the	the	DET
ejpam-4385	38	8	theoretical	theoretical	ADJ
ejpam-4385	38	9	framework	framework	NOUN
ejpam-4385	38	10	of	of	ADP
ejpam-4385	38	11	british	british	ADJ
ejpam-4385	38	12	option	option	NOUN
ejpam-4385	38	13	pricing	pricing	NOUN
ejpam-4385	38	14	.	.	PUNCT
ejpam-4385	39	1	actual	actual	ADJ
ejpam-4385	39	2	implementation	implementation	NOUN
ejpam-4385	39	3	through	through	ADP
ejpam-4385	39	4	simulation	simulation	NOUN
ejpam-4385	39	5	and	and	CCONJ
ejpam-4385	39	6	numerical	numerical	ADJ
ejpam-4385	39	7	approximation	approximation	NOUN
ejpam-4385	39	8	will	will	AUX
ejpam-4385	39	9	not	not	PART
ejpam-4385	39	10	be	be	AUX
ejpam-4385	39	11	included	include	VERB
ejpam-4385	39	12	.	.	PUNCT
ejpam-4385	40	1	2	2	X
ejpam-4385	40	2	.	.	X
ejpam-4385	40	3	setting	setting	NOUN
ejpam-4385	40	4	of	of	ADP
ejpam-4385	40	5	the	the	DET
ejpam-4385	40	6	problem	problem	NOUN
ejpam-4385	40	7	let	let	VERB
ejpam-4385	40	8	us	we	PRON
ejpam-4385	40	9	consider	consider	VERB
ejpam-4385	40	10	the	the	DET
ejpam-4385	40	11	financial	financial	ADJ
ejpam-4385	40	12	market	market	NOUN
ejpam-4385	40	13	consisting	consist	VERB
ejpam-4385	40	14	of	of	ADP
ejpam-4385	40	15	a	a	DET
ejpam-4385	40	16	risky	risky	ADJ
ejpam-4385	40	17	stock	stock	NOUN
ejpam-4385	40	18	with	with	ADP
ejpam-4385	40	19	price	price	NOUN
ejpam-4385	40	20	process	process	NOUN
ejpam-4385	40	21	x	x	PUNCT
ejpam-4385	40	22	=	=	SYM
ejpam-4385	40	23	(	(	PUNCT
ejpam-4385	40	24	xt	xt	NUM
ejpam-4385	40	25	:	:	PUNCT
ejpam-4385	40	26	t	t	PROPN
ejpam-4385	40	27	∈	∈	PROPN
ejpam-4385	41	1	[	[	X
ejpam-4385	41	2	0	0	NUM
ejpam-4385	41	3	,	,	PUNCT
ejpam-4385	41	4	t	t	X
ejpam-4385	41	5	]	]	PUNCT
ejpam-4385	41	6	)	)	PUNCT
ejpam-4385	41	7	and	and	CCONJ
ejpam-4385	41	8	a	a	DET
ejpam-4385	41	9	zero	zero	NUM
ejpam-4385	41	10	-	-	PUNCT
ejpam-4385	41	11	coupon	coupon	NOUN
ejpam-4385	41	12	bond	bond	NOUN
ejpam-4385	41	13	with	with	ADP
ejpam-4385	41	14	price	price	NOUN
ejpam-4385	41	15	process	process	NOUN
ejpam-4385	41	16	p	p	X
ejpam-4385	41	17	=	=	PUNCT
ejpam-4385	41	18	(	(	PUNCT
ejpam-4385	41	19	pt	pt	X
ejpam-4385	41	20	:	:	PUNCT
ejpam-4385	41	21	t	t	PROPN
ejpam-4385	41	22	∈	∈	PROPN
ejpam-4385	42	1	[	[	X
ejpam-4385	42	2	0	0	NUM
ejpam-4385	42	3	,	,	PUNCT
ejpam-4385	42	4	t	t	X
ejpam-4385	42	5	]	]	PUNCT
ejpam-4385	42	6	)	)	PUNCT
ejpam-4385	42	7	where	where	SCONJ
ejpam-4385	42	8	the	the	DET
ejpam-4385	42	9	prices	price	NOUN
ejpam-4385	42	10	respectively	respectively	ADV
ejpam-4385	42	11	evolve	evolve	VERB
ejpam-4385	42	12	as	as	ADP
ejpam-4385	42	13	dxt	dxt	PROPN
ejpam-4385	42	14	=	=	PROPN
ejpam-4385	42	15	µxtdt+	µxtdt+	ADP
ejpam-4385	42	16	σ1xtdwt	σ1xtdwt	PROPN
ejpam-4385	42	17	,	,	PUNCT
ejpam-4385	42	18	(	(	PUNCT
ejpam-4385	42	19	1	1	X
ejpam-4385	42	20	)	)	PUNCT
ejpam-4385	42	21	dpt	dpt	PROPN
ejpam-4385	42	22	=	=	PUNCT
ejpam-4385	42	23	rtptdt−	rtptdt−	PROPN
ejpam-4385	42	24	λ(t	λ(t	PROPN
ejpam-4385	42	25	,	,	PUNCT
ejpam-4385	42	26	t	t	PROPN
ejpam-4385	42	27	)	)	PUNCT
ejpam-4385	42	28	σ2ptdw̄t	σ2ptdw̄t	NUM
ejpam-4385	42	29	,	,	PUNCT
ejpam-4385	42	30	(	(	PUNCT
ejpam-4385	42	31	2	2	X
ejpam-4385	42	32	)	)	PUNCT
ejpam-4385	42	33	k.	k.	NOUN
ejpam-4385	42	34	falcasantos	falcasantos	PROPN
ejpam-4385	42	35	,	,	PUNCT
ejpam-4385	42	36	f.	f.	PROPN
ejpam-4385	42	37	sumalpong	sumalpong	PROPN
ejpam-4385	42	38	/	/	SYM
ejpam-4385	42	39	eur	eur	PROPN
ejpam-4385	42	40	.	.	PUNCT
ejpam-4385	43	1	j.	j.	PROPN
ejpam-4385	43	2	pure	pure	PROPN
ejpam-4385	43	3	appl	appl	PROPN
ejpam-4385	43	4	.	.	PROPN
ejpam-4385	43	5	math	math	PROPN
ejpam-4385	43	6	,	,	PUNCT
ejpam-4385	43	7	15	15	NUM
ejpam-4385	43	8	(	(	PUNCT
ejpam-4385	43	9	3	3	NUM
ejpam-4385	43	10	)	)	PUNCT
ejpam-4385	43	11	(	(	PUNCT
ejpam-4385	43	12	2022	2022	NUM
ejpam-4385	43	13	)	)	PUNCT
ejpam-4385	43	14	,	,	PUNCT
ejpam-4385	43	15	948	948	NUM
ejpam-4385	43	16	-	-	SYM
ejpam-4385	43	17	970	970	NUM
ejpam-4385	43	18	950	950	NUM
ejpam-4385	43	19	where	where	SCONJ
ejpam-4385	43	20	µ	µ	X
ejpam-4385	43	21	∈	∈	NOUN
ejpam-4385	43	22	r	r	NOUN
ejpam-4385	43	23	is	be	AUX
ejpam-4385	43	24	the	the	DET
ejpam-4385	43	25	appreciation	appreciation	NOUN
ejpam-4385	43	26	rate	rate	NOUN
ejpam-4385	43	27	,	,	PUNCT
ejpam-4385	43	28	σ1	σ1	PROPN
ejpam-4385	43	29	and	and	CCONJ
ejpam-4385	43	30	σ2	σ2	PROPN
ejpam-4385	43	31	are	be	AUX
ejpam-4385	43	32	volatility	volatility	NOUN
ejpam-4385	43	33	coefficients	coefficient	NOUN
ejpam-4385	43	34	,	,	PUNCT
ejpam-4385	43	35	w	w	NOUN
ejpam-4385	43	36	=	=	SYM
ejpam-4385	43	37	(	(	PUNCT
ejpam-4385	43	38	wt)t≥0	wt)t≥0	NOUN
ejpam-4385	43	39	and	and	CCONJ
ejpam-4385	43	40	w̄	w̄	NOUN
ejpam-4385	43	41	=	=	SYM
ejpam-4385	43	42	(	(	PUNCT
ejpam-4385	43	43	w̄t)t≥0	w̄t)t≥0	NOUN
ejpam-4385	43	44	are	be	AUX
ejpam-4385	43	45	standard	standard	ADJ
ejpam-4385	43	46	wiener	wiener	NOUN
ejpam-4385	43	47	processes	process	NOUN
ejpam-4385	43	48	defined	define	VERB
ejpam-4385	43	49	on	on	ADP
ejpam-4385	43	50	a	a	DET
ejpam-4385	43	51	probability	probability	NOUN
ejpam-4385	43	52	space	space	NOUN
ejpam-4385	43	53	(	(	PUNCT
ejpam-4385	43	54	ω	ω	PROPN
ejpam-4385	43	55	,	,	PUNCT
ejpam-4385	43	56	f	f	PROPN
ejpam-4385	43	57	,	,	PUNCT
ejpam-4385	43	58	p	p	NOUN
ejpam-4385	43	59	)	)	PUNCT
ejpam-4385	43	60	with	with	ADP
ejpam-4385	43	61	cov(dwt	cov(dwt	NOUN
ejpam-4385	43	62	·	·	PUNCT
ejpam-4385	43	63	dw̄t	dw̄t	X
ejpam-4385	43	64	)	)	PUNCT
ejpam-4385	43	65	=	=	SYM
ejpam-4385	43	66	ρdt	ρdt	NOUN
ejpam-4385	43	67	,	,	PUNCT
ejpam-4385	43	68	(	(	PUNCT
ejpam-4385	43	69	|ρ|	|ρ|	X
ejpam-4385	43	70	<	<	X
ejpam-4385	43	71	1	1	NUM
ejpam-4385	43	72	)	)	PUNCT
ejpam-4385	43	73	,	,	PUNCT
ejpam-4385	43	74	(	(	PUNCT
ejpam-4385	43	75	see	see	VERB
ejpam-4385	43	76	[	[	X
ejpam-4385	43	77	1	1	NUM
ejpam-4385	43	78	]	]	PUNCT
ejpam-4385	43	79	)	)	PUNCT
ejpam-4385	43	80	rt	rt	PROPN
ejpam-4385	43	81	follows	follow	VERB
ejpam-4385	43	82	the	the	DET
ejpam-4385	43	83	cox	cox	PROPN
ejpam-4385	43	84	-	-	PUNCT
ejpam-4385	43	85	ingersoll	ingersoll	PROPN
ejpam-4385	43	86	-	-	PUNCT
ejpam-4385	43	87	ross	ross	PROPN
ejpam-4385	43	88	(	(	PUNCT
ejpam-4385	43	89	cir	cir	NOUN
ejpam-4385	43	90	)	)	PUNCT
ejpam-4385	43	91	model	model	NOUN
ejpam-4385	43	92	drt	drt	PROPN
ejpam-4385	44	1	=	=	PUNCT
ejpam-4385	44	2	a(θ	a(θ	PROPN
ejpam-4385	44	3	−	−	NOUN
ejpam-4385	44	4	rt)dt+	rt)dt+	NOUN
ejpam-4385	44	5	σ2	σ2	PROPN
ejpam-4385	44	6	√	√	PROPN
ejpam-4385	44	7	rtdw̄t	rtdw̄t	PROPN
ejpam-4385	45	1	(	(	PUNCT
ejpam-4385	45	2	3	3	NUM
ejpam-4385	45	3	)	)	PUNCT
ejpam-4385	45	4	where	where	SCONJ
ejpam-4385	45	5	a	a	DET
ejpam-4385	45	6	,	,	PUNCT
ejpam-4385	45	7	θ	θ	PROPN
ejpam-4385	45	8	,	,	PUNCT
ejpam-4385	45	9	σ2	σ2	NOUN
ejpam-4385	45	10	are	be	AUX
ejpam-4385	45	11	positive	positive	ADJ
ejpam-4385	45	12	constants	constant	NOUN
ejpam-4385	45	13	and	and	CCONJ
ejpam-4385	45	14	the	the	DET
ejpam-4385	45	15	market	market	NOUN
ejpam-4385	45	16	price	price	NOUN
ejpam-4385	45	17	of	of	ADP
ejpam-4385	45	18	risk	risk	NOUN
ejpam-4385	45	19	is	be	AUX
ejpam-4385	45	20	given	give	VERB
ejpam-4385	45	21	by	by	ADP
ejpam-4385	45	22	λ(t	λ(t	NOUN
ejpam-4385	45	23	,	,	PUNCT
ejpam-4385	45	24	t	t	NOUN
ejpam-4385	45	25	)	)	PUNCT
ejpam-4385	46	1	=	=	PUNCT
ejpam-4385	46	2	λ	λ	NOUN
ejpam-4385	46	3	√	√	NUM
ejpam-4385	47	1	rt	rt	INTJ
ejpam-4385	47	2	.	.	PUNCT
ejpam-4385	48	1	in	in	ADP
ejpam-4385	48	2	this	this	DET
ejpam-4385	48	3	model	model	NOUN
ejpam-4385	48	4	,	,	PUNCT
ejpam-4385	48	5	the	the	DET
ejpam-4385	48	6	standard	standard	ADJ
ejpam-4385	48	7	deviation	deviation	NOUN
ejpam-4385	48	8	of	of	ADP
ejpam-4385	48	9	the	the	DET
ejpam-4385	48	10	stochastic	stochastic	ADJ
ejpam-4385	48	11	term	term	NOUN
ejpam-4385	48	12	σ2	σ2	PROPN
ejpam-4385	48	13	√	√	PROPN
ejpam-4385	48	14	rtdw̄t	rtdw̄t	PROPN
ejpam-4385	48	15	is	be	AUX
ejpam-4385	48	16	proportional	proportional	ADJ
ejpam-4385	48	17	to	to	ADP
ejpam-4385	48	18	the	the	DET
ejpam-4385	48	19	square	square	ADJ
ejpam-4385	48	20	root	root	NOUN
ejpam-4385	48	21	of	of	ADP
ejpam-4385	48	22	the	the	DET
ejpam-4385	48	23	interest	interest	NOUN
ejpam-4385	48	24	rate	rate	NOUN
ejpam-4385	48	25	,	,	PUNCT
ejpam-4385	48	26	that	that	ADV
ejpam-4385	48	27	is	is	ADV
ejpam-4385	48	28	,	,	PUNCT
ejpam-4385	48	29	as	as	ADP
ejpam-4385	48	30	the	the	DET
ejpam-4385	48	31	rate	rate	NOUN
ejpam-4385	48	32	increases	increase	NOUN
ejpam-4385	48	33	,	,	PUNCT
ejpam-4385	48	34	the	the	DET
ejpam-4385	48	35	standard	standard	ADJ
ejpam-4385	48	36	deviation	deviation	NOUN
ejpam-4385	48	37	also	also	ADV
ejpam-4385	48	38	increases	increase	VERB
ejpam-4385	48	39	and	and	CCONJ
ejpam-4385	48	40	as	as	ADP
ejpam-4385	48	41	the	the	DET
ejpam-4385	48	42	interest	interest	NOUN
ejpam-4385	48	43	rate	rate	NOUN
ejpam-4385	48	44	approaches	approach	NOUN
ejpam-4385	48	45	zero	zero	NUM
ejpam-4385	48	46	,	,	PUNCT
ejpam-4385	48	47	σ2	σ2	PROPN
ejpam-4385	48	48	√	√	NUM
ejpam-4385	48	49	rtdw̄t	rtdw̄t	NOUN
ejpam-4385	49	1	also	also	ADV
ejpam-4385	49	2	approaches	approach	VERB
ejpam-4385	49	3	zero	zero	NUM
ejpam-4385	49	4	.	.	PUNCT
ejpam-4385	50	1	moreover	moreover	ADV
ejpam-4385	50	2	this	this	DET
ejpam-4385	50	3	model	model	NOUN
ejpam-4385	50	4	is	be	AUX
ejpam-4385	50	5	a	a	DET
ejpam-4385	50	6	mean	mean	ADJ
ejpam-4385	50	7	reverting	revert	VERB
ejpam-4385	50	8	process	process	NOUN
ejpam-4385	50	9	,	,	PUNCT
ejpam-4385	50	10	that	that	ADV
ejpam-4385	50	11	is	is	ADV
ejpam-4385	50	12	,	,	PUNCT
ejpam-4385	50	13	when	when	SCONJ
ejpam-4385	50	14	rt	rt	PROPN
ejpam-4385	50	15	>	>	X
ejpam-4385	50	16	θ	θ	PROPN
ejpam-4385	50	17	the	the	DET
ejpam-4385	50	18	drift	drift	NOUN
ejpam-4385	50	19	is	be	AUX
ejpam-4385	50	20	negative	negative	ADJ
ejpam-4385	50	21	and	and	CCONJ
ejpam-4385	50	22	when	when	SCONJ
ejpam-4385	50	23	rt	rt	PROPN
ejpam-4385	50	24	<	<	X
ejpam-4385	50	25	θ	θ	PROPN
ejpam-4385	50	26	,	,	PUNCT
ejpam-4385	50	27	the	the	DET
ejpam-4385	50	28	drift	drift	NOUN
ejpam-4385	50	29	is	be	AUX
ejpam-4385	50	30	positive	positive	ADJ
ejpam-4385	50	31	where	where	SCONJ
ejpam-4385	50	32	a	a	PRON
ejpam-4385	50	33	is	be	AUX
ejpam-4385	50	34	the	the	DET
ejpam-4385	50	35	speed	speed	NOUN
ejpam-4385	50	36	of	of	ADP
ejpam-4385	50	37	the	the	DET
ejpam-4385	50	38	mean	mean	ADJ
ejpam-4385	50	39	reversion	reversion	NOUN
ejpam-4385	50	40	and	and	CCONJ
ejpam-4385	50	41	θ	θ	PROPN
ejpam-4385	50	42	is	be	AUX
ejpam-4385	50	43	the	the	DET
ejpam-4385	50	44	equilibrium	equilibrium	NOUN
ejpam-4385	50	45	level	level	NOUN
ejpam-4385	50	46	.	.	PUNCT
ejpam-4385	51	1	the	the	DET
ejpam-4385	51	2	deterministic	deterministic	ADJ
ejpam-4385	51	3	part	part	NOUN
ejpam-4385	51	4	of	of	ADP
ejpam-4385	51	5	the	the	DET
ejpam-4385	51	6	solution	solution	NOUN
ejpam-4385	51	7	of	of	ADP
ejpam-4385	51	8	(	(	PUNCT
ejpam-4385	51	9	3	3	NUM
ejpam-4385	51	10	)	)	PUNCT
ejpam-4385	51	11	is	be	AUX
ejpam-4385	51	12	given	give	VERB
ejpam-4385	51	13	by	by	ADP
ejpam-4385	51	14	rt	rt	PROPN
ejpam-4385	51	15	=	=	SYM
ejpam-4385	51	16	θ	θ	PROPN
ejpam-4385	51	17	+	+	PUNCT
ejpam-4385	51	18	(	(	PUNCT
ejpam-4385	51	19	r0	r0	NOUN
ejpam-4385	51	20	−	−	PROPN
ejpam-4385	51	21	θ)e−at	θ)e−at	NOUN
ejpam-4385	51	22	.	.	PUNCT
ejpam-4385	52	1	(	(	PUNCT
ejpam-4385	52	2	4	4	X
ejpam-4385	52	3	)	)	PUNCT
ejpam-4385	52	4	note	note	NOUN
ejpam-4385	52	5	that	that	SCONJ
ejpam-4385	52	6	the	the	DET
ejpam-4385	52	7	price	price	NOUN
ejpam-4385	52	8	pt	pt	NOUN
ejpam-4385	52	9	=	=	SYM
ejpam-4385	52	10	p	p	PROPN
ejpam-4385	52	11	(	(	PUNCT
ejpam-4385	52	12	t	t	PROPN
ejpam-4385	52	13	,	,	PUNCT
ejpam-4385	52	14	r;t	r;t	ADJ
ejpam-4385	52	15	)	)	PUNCT
ejpam-4385	52	16	of	of	ADP
ejpam-4385	52	17	a	a	DET
ejpam-4385	52	18	zero	zero	NUM
ejpam-4385	52	19	coupon	coupon	NOUN
ejpam-4385	52	20	bond	bond	NOUN
ejpam-4385	52	21	satisfies	satisfy	VERB
ejpam-4385	52	22	the	the	DET
ejpam-4385	52	23	partial	partial	ADJ
ejpam-4385	52	24	differential	differential	NOUN
ejpam-4385	52	25	equation	equation	NOUN
ejpam-4385	52	26	(	(	PUNCT
ejpam-4385	52	27	see	see	VERB
ejpam-4385	52	28	[	[	X
ejpam-4385	52	29	4	4	NUM
ejpam-4385	52	30	]	]	PUNCT
ejpam-4385	52	31	)	)	PUNCT
ejpam-4385	53	1	∂p	∂p	PROPN
ejpam-4385	53	2	∂t	∂t	PROPN
ejpam-4385	54	1	+	+	PUNCT
ejpam-4385	54	2	[	[	X
ejpam-4385	54	3	aθ	aθ	INTJ
ejpam-4385	54	4	−	−	PROPN
ejpam-4385	54	5	(	(	PUNCT
ejpam-4385	54	6	a+	a+	X
ejpam-4385	54	7	λσ)r	λσ)r	X
ejpam-4385	54	8	]	]	X
ejpam-4385	54	9	∂p	∂p	PROPN
ejpam-4385	54	10	∂r	∂r	PROPN
ejpam-4385	55	1	+	+	CCONJ
ejpam-4385	55	2	1	1	NUM
ejpam-4385	55	3	2	2	NUM
ejpam-4385	55	4	σ2	σ2	NOUN
ejpam-4385	55	5	2r	2r	NUM
ejpam-4385	55	6	∂2p	∂2p	NOUN
ejpam-4385	55	7	∂r2	∂r2	PROPN
ejpam-4385	55	8	−	−	PROPN
ejpam-4385	55	9	rp	rp	NOUN
ejpam-4385	55	10	=	=	NOUN
ejpam-4385	55	11	0	0	PROPN
ejpam-4385	56	1	(	(	PUNCT
ejpam-4385	56	2	5	5	NUM
ejpam-4385	56	3	)	)	PUNCT
ejpam-4385	57	1	such	such	ADJ
ejpam-4385	57	2	that	that	SCONJ
ejpam-4385	57	3	p	p	X
ejpam-4385	57	4	(	(	PUNCT
ejpam-4385	57	5	t	t	PROPN
ejpam-4385	57	6	,	,	PUNCT
ejpam-4385	57	7	r;t	r;t	ADJ
ejpam-4385	57	8	)	)	PUNCT
ejpam-4385	57	9	=	=	SYM
ejpam-4385	57	10	1	1	NUM
ejpam-4385	57	11	for	for	ADP
ejpam-4385	57	12	all	all	DET
ejpam-4385	57	13	r	r	NOUN
ejpam-4385	57	14	∈	∈	NOUN
ejpam-4385	57	15	r	r	NOUN
ejpam-4385	57	16	and	and	CCONJ
ejpam-4385	57	17	t	t	NOUN
ejpam-4385	57	18	∈	∈	PROPN
ejpam-4385	58	1	[	[	X
ejpam-4385	58	2	0	0	NUM
ejpam-4385	58	3	,	,	PUNCT
ejpam-4385	58	4	t	t	X
ejpam-4385	58	5	]	]	PUNCT
ejpam-4385	58	6	.	.	PUNCT
ejpam-4385	59	1	the	the	DET
ejpam-4385	59	2	price	price	NOUN
ejpam-4385	59	3	of	of	ADP
ejpam-4385	59	4	a	a	DET
ejpam-4385	59	5	zero	zero	NUM
ejpam-4385	59	6	-	-	PUNCT
ejpam-4385	59	7	coupon	coupon	NOUN
ejpam-4385	59	8	bond	bond	NOUN
ejpam-4385	59	9	at	at	ADP
ejpam-4385	59	10	time	time	NOUN
ejpam-4385	59	11	t	t	NOUN
ejpam-4385	59	12	with	with	ADP
ejpam-4385	59	13	maturity	maturity	NOUN
ejpam-4385	59	14	time	time	NOUN
ejpam-4385	59	15	t	t	PROPN
ejpam-4385	59	16	using	use	VERB
ejpam-4385	59	17	the	the	DET
ejpam-4385	59	18	risk	risk	NOUN
ejpam-4385	59	19	neutral	neutral	ADJ
ejpam-4385	59	20	valuation	valuation	NOUN
ejpam-4385	59	21	framework	framework	NOUN
ejpam-4385	59	22	is	be	AUX
ejpam-4385	59	23	given	give	VERB
ejpam-4385	59	24	by	by	ADP
ejpam-4385	59	25	p	p	PROPN
ejpam-4385	59	26	(	(	PUNCT
ejpam-4385	59	27	t	t	PROPN
ejpam-4385	59	28	,	,	PUNCT
ejpam-4385	59	29	rt	rt	PROPN
ejpam-4385	59	30	,	,	PUNCT
ejpam-4385	59	31	t	t	PROPN
ejpam-4385	59	32	)	)	PUNCT
ejpam-4385	59	33	=	=	PUNCT
ejpam-4385	60	1	e[e−	e[e−	PROPN
ejpam-4385	60	2	∫	∫	PROPN
ejpam-4385	60	3	t	t	PROPN
ejpam-4385	60	4	t	t	PROPN
ejpam-4385	60	5	rudu|ft	rudu|ft	PROPN
ejpam-4385	60	6	]	]	X
ejpam-4385	60	7	,	,	PUNCT
ejpam-4385	60	8	(	(	PUNCT
ejpam-4385	60	9	see	see	VERB
ejpam-4385	60	10	[	[	X
ejpam-4385	60	11	8	8	NUM
ejpam-4385	60	12	]	]	SYM
ejpam-4385	60	13	)	)	PUNCT
ejpam-4385	60	14	(	(	PUNCT
ejpam-4385	60	15	6	6	NUM
ejpam-4385	60	16	)	)	PUNCT
ejpam-4385	60	17	where	where	SCONJ
ejpam-4385	60	18	ft	ft	PROPN
ejpam-4385	60	19	denotes	denote	VERB
ejpam-4385	60	20	the	the	DET
ejpam-4385	60	21	natural	natural	ADJ
ejpam-4385	60	22	filtration	filtration	NOUN
ejpam-4385	60	23	generated	generate	VERB
ejpam-4385	60	24	by	by	ADP
ejpam-4385	60	25	the	the	DET
ejpam-4385	60	26	price	price	NOUN
ejpam-4385	60	27	process	process	NOUN
ejpam-4385	60	28	x.	x.	NOUN
ejpam-4385	61	1	the	the	DET
ejpam-4385	61	2	natural	natural	ADJ
ejpam-4385	61	3	filtration	filtration	NOUN
ejpam-4385	61	4	ft	ft	NOUN
ejpam-4385	61	5	represents	represent	VERB
ejpam-4385	61	6	the	the	DET
ejpam-4385	61	7	information	information	NOUN
ejpam-4385	61	8	generated	generate	VERB
ejpam-4385	61	9	by	by	ADP
ejpam-4385	61	10	the	the	DET
ejpam-4385	61	11	process	process	NOUN
ejpam-4385	61	12	x	x	PUNCT
ejpam-4385	61	13	as	as	SCONJ
ejpam-4385	61	14	time	time	NOUN
ejpam-4385	61	15	progresses	progress	VERB
ejpam-4385	61	16	.	.	PUNCT
ejpam-4385	62	1	note	note	VERB
ejpam-4385	62	2	that	that	SCONJ
ejpam-4385	62	3	the	the	DET
ejpam-4385	62	4	interest	interest	NOUN
ejpam-4385	62	5	rate	rate	NOUN
ejpam-4385	62	6	ru	ru	PROPN
ejpam-4385	62	7	is	be	AUX
ejpam-4385	62	8	a	a	DET
ejpam-4385	62	9	markovian	markovian	ADJ
ejpam-4385	62	10	process	process	NOUN
ejpam-4385	62	11	(	(	PUNCT
ejpam-4385	62	12	see	see	VERB
ejpam-4385	62	13	[	[	X
ejpam-4385	62	14	8	8	NUM
ejpam-4385	62	15	]	]	NUM
ejpam-4385	62	16	)	)	PUNCT
ejpam-4385	62	17	.	.	PUNCT
ejpam-4385	63	1	this	this	PRON
ejpam-4385	63	2	implies	imply	VERB
ejpam-4385	63	3	that	that	SCONJ
ejpam-4385	63	4	,	,	PUNCT
ejpam-4385	63	5	ru	ru	PROPN
ejpam-4385	63	6	is	be	AUX
ejpam-4385	63	7	dependent	dependent	ADJ
ejpam-4385	63	8	on	on	ADP
ejpam-4385	63	9	rt	rt	PROPN
ejpam-4385	63	10	for	for	ADP
ejpam-4385	63	11	u	u	PROPN
ejpam-4385	63	12	>	>	X
ejpam-4385	63	13	t	t	PROPN
ejpam-4385	63	14	,	,	PUNCT
ejpam-4385	63	15	i.e.	i.e.	X
ejpam-4385	63	16	,	,	PUNCT
ejpam-4385	63	17	ru	ru	PROPN
ejpam-4385	63	18	is	be	AUX
ejpam-4385	63	19	a	a	DET
ejpam-4385	63	20	function	function	NOUN
ejpam-4385	63	21	of	of	ADP
ejpam-4385	63	22	rt	rt	PROPN
ejpam-4385	63	23	.	.	PUNCT
ejpam-4385	64	1	we	we	PRON
ejpam-4385	64	2	then	then	ADV
ejpam-4385	64	3	have	have	VERB
ejpam-4385	64	4	,	,	PUNCT
ejpam-4385	64	5	p	p	X
ejpam-4385	64	6	(	(	PUNCT
ejpam-4385	64	7	t	t	PROPN
ejpam-4385	64	8	,	,	PUNCT
ejpam-4385	64	9	rt	rt	PROPN
ejpam-4385	64	10	,	,	PUNCT
ejpam-4385	64	11	t	t	PROPN
ejpam-4385	64	12	)	)	PUNCT
ejpam-4385	64	13	=	=	PUNCT
ejpam-4385	65	1	e[e−	e[e−	PROPN
ejpam-4385	65	2	∫	∫	PROPN
ejpam-4385	65	3	t	t	PROPN
ejpam-4385	65	4	t	t	PROPN
ejpam-4385	65	5	rudu|ft	rudu|ft	PROPN
ejpam-4385	65	6	]	]	PUNCT
ejpam-4385	65	7	.	.	PUNCT
ejpam-4385	66	1	=	=	PUNCT
ejpam-4385	67	1	e[e−	e[e−	PROPN
ejpam-4385	67	2	∫	∫	PROPN
ejpam-4385	67	3	t	t	PROPN
ejpam-4385	67	4	t	t	NOUN
ejpam-4385	67	5	rudu|rt	rudu|rt	PROPN
ejpam-4385	67	6	]	]	PUNCT
ejpam-4385	67	7	where	where	SCONJ
ejpam-4385	67	8	e	e	NOUN
ejpam-4385	67	9	is	be	AUX
ejpam-4385	67	10	taken	take	VERB
ejpam-4385	67	11	with	with	ADP
ejpam-4385	67	12	respect	respect	NOUN
ejpam-4385	67	13	to	to	ADP
ejpam-4385	67	14	the	the	DET
ejpam-4385	67	15	probability	probability	NOUN
ejpam-4385	67	16	measure	measure	NOUN
ejpam-4385	68	1	p.	p.	NOUN
ejpam-4385	68	2	the	the	DET
ejpam-4385	68	3	solution	solution	NOUN
ejpam-4385	68	4	to	to	ADP
ejpam-4385	68	5	the	the	DET
ejpam-4385	68	6	partial	partial	ADJ
ejpam-4385	68	7	differential	differential	NOUN
ejpam-4385	68	8	equation	equation	NOUN
ejpam-4385	68	9	(	(	PUNCT
ejpam-4385	68	10	5	5	NUM
ejpam-4385	68	11	)	)	PUNCT
ejpam-4385	68	12	is	be	AUX
ejpam-4385	68	13	given	give	VERB
ejpam-4385	68	14	by	by	ADP
ejpam-4385	68	15	p	p	PROPN
ejpam-4385	68	16	(	(	PUNCT
ejpam-4385	68	17	t	t	PROPN
ejpam-4385	68	18	,	,	PUNCT
ejpam-4385	68	19	r	r	NOUN
ejpam-4385	68	20	,	,	PUNCT
ejpam-4385	68	21	t	t	NOUN
ejpam-4385	68	22	)	)	PUNCT
ejpam-4385	69	1	=	=	PUNCT
ejpam-4385	69	2	e−λ(t	e−λ(t	NOUN
ejpam-4385	69	3	,	,	PUNCT
ejpam-4385	69	4	t	t	NOUN
ejpam-4385	69	5	)	)	PUNCT
ejpam-4385	69	6	r−a(t	r−a(t	PROPN
ejpam-4385	69	7	,	,	PUNCT
ejpam-4385	69	8	t	t	PROPN
ejpam-4385	69	9	)	)	PUNCT
ejpam-4385	69	10	see	see	VERB
ejpam-4385	69	11	[	[	X
ejpam-4385	69	12	4	4	X
ejpam-4385	69	13	]	]	X
ejpam-4385	69	14	(	(	PUNCT
ejpam-4385	69	15	7	7	NUM
ejpam-4385	69	16	)	)	PUNCT
ejpam-4385	69	17	where	where	SCONJ
ejpam-4385	69	18	a(t	a(t	NOUN
ejpam-4385	69	19	,	,	PUNCT
ejpam-4385	69	20	t	t	NOUN
ejpam-4385	69	21	)	)	PUNCT
ejpam-4385	69	22	=	=	PUNCT
ejpam-4385	70	1	2aθ	2aθ	NOUN
ejpam-4385	70	2	γσ2	γσ2	NOUN
ejpam-4385	70	3	[	[	PUNCT
ejpam-4385	70	4	−γ	−γ	NOUN
ejpam-4385	70	5	(	(	PUNCT
ejpam-4385	70	6	t	t	PROPN
ejpam-4385	70	7	−	−	PROPN
ejpam-4385	70	8	t	t	PROPN
ejpam-4385	70	9	h1	h1	PROPN
ejpam-4385	70	10	)	)	PUNCT
ejpam-4385	70	11	−	−	PROPN
ejpam-4385	70	12	h1	h1	VERB
ejpam-4385	70	13	−	−	PROPN
ejpam-4385	70	14	h2	h2	NOUN
ejpam-4385	71	1	h1h2	h1h2	X
ejpam-4385	71	2	ln	ln	NOUN
ejpam-4385	71	3	(	(	PUNCT
ejpam-4385	71	4	h1	h1	PROPN
ejpam-4385	71	5	−	−	PROPN
ejpam-4385	71	6	h2e	h2e	ADJ
ejpam-4385	71	7	γ(t−t	γ(t−t	NOUN
ejpam-4385	71	8	)	)	PUNCT
ejpam-4385	71	9	h1	h1	NOUN
ejpam-4385	71	10	−	−	PROPN
ejpam-4385	71	11	h2	h2	PROPN
ejpam-4385	71	12	)	)	PUNCT
ejpam-4385	71	13	]	]	PUNCT
ejpam-4385	72	1	(	(	PUNCT
ejpam-4385	72	2	8)	8)	NUM
ejpam-4385	72	3	k.	k.	NOUN
ejpam-4385	72	4	falcasantos	falcasanto	NOUN
ejpam-4385	72	5	,	,	PUNCT
ejpam-4385	72	6	f.	f.	PROPN
ejpam-4385	72	7	sumalpong	sumalpong	PROPN
ejpam-4385	72	8	/	/	SYM
ejpam-4385	72	9	eur	eur	PROPN
ejpam-4385	72	10	.	.	PUNCT
ejpam-4385	73	1	j.	j.	PROPN
ejpam-4385	73	2	pure	pure	PROPN
ejpam-4385	73	3	appl	appl	PROPN
ejpam-4385	73	4	.	.	PROPN
ejpam-4385	73	5	math	math	PROPN
ejpam-4385	73	6	,	,	PUNCT
ejpam-4385	73	7	15	15	NUM
ejpam-4385	73	8	(	(	PUNCT
ejpam-4385	73	9	3	3	NUM
ejpam-4385	73	10	)	)	PUNCT
ejpam-4385	73	11	(	(	PUNCT
ejpam-4385	73	12	2022	2022	NUM
ejpam-4385	73	13	)	)	PUNCT
ejpam-4385	73	14	,	,	PUNCT
ejpam-4385	73	15	948	948	NUM
ejpam-4385	73	16	-	-	SYM
ejpam-4385	73	17	970	970	NUM
ejpam-4385	73	18	951	951	NUM
ejpam-4385	73	19	λ(t	λ(t	NOUN
ejpam-4385	73	20	,	,	PUNCT
ejpam-4385	73	21	t	t	NOUN
ejpam-4385	73	22	)	)	PUNCT
ejpam-4385	73	23	=	=	SYM
ejpam-4385	73	24	2	2	NUM
ejpam-4385	73	25	σ2	σ2	PROPN
ejpam-4385	73	26	[	[	PUNCT
ejpam-4385	73	27	1−	1−	NUM
ejpam-4385	73	28	eγ(t−t	eγ(t−t	NOUN
ejpam-4385	73	29	)	)	PUNCT
ejpam-4385	73	30	]	]	PUNCT
ejpam-4385	73	31	[	[	PUNCT
ejpam-4385	73	32	h1e−γ(t−t	h1e−γ(t−t	NUM
ejpam-4385	73	33	)	)	PUNCT
ejpam-4385	73	34	−	−	PROPN
ejpam-4385	73	35	h2	h2	NOUN
ejpam-4385	73	36	]	]	PUNCT
ejpam-4385	73	37	(	(	PUNCT
ejpam-4385	73	38	9	9	X
ejpam-4385	73	39	)	)	PUNCT
ejpam-4385	73	40	γ	γ	NOUN
ejpam-4385	73	41	=	=	SYM
ejpam-4385	73	42	√	√	PROPN
ejpam-4385	73	43	(	(	PUNCT
ejpam-4385	73	44	a+	a+	PUNCT
ejpam-4385	73	45	γ)2	γ)2	NOUN
ejpam-4385	73	46	+	+	CCONJ
ejpam-4385	73	47	2σ2	2σ2	NUM
ejpam-4385	73	48	(	(	PUNCT
ejpam-4385	73	49	10	10	NUM
ejpam-4385	73	50	)	)	PUNCT
ejpam-4385	73	51	h1	h1	NOUN
ejpam-4385	73	52	=	=	SYM
ejpam-4385	73	53	−a+	−a+	X
ejpam-4385	73	54	γ	γ	PROPN
ejpam-4385	73	55	σ2	σ2	PROPN
ejpam-4385	73	56	+	+	CCONJ
ejpam-4385	73	57	γ	γ	PROPN
ejpam-4385	73	58	σ2	σ2	PROPN
ejpam-4385	73	59	(	(	PUNCT
ejpam-4385	73	60	11	11	NUM
ejpam-4385	73	61	)	)	PUNCT
ejpam-4385	73	62	h2	h2	NOUN
ejpam-4385	73	63	=	=	SYM
ejpam-4385	73	64	−a+	−a+	X
ejpam-4385	73	65	γ	γ	PROPN
ejpam-4385	73	66	σ2	σ2	PROPN
ejpam-4385	73	67	−	−	PROPN
ejpam-4385	73	68	γ	γ	PROPN
ejpam-4385	73	69	σ2	σ2	PROPN
ejpam-4385	73	70	(	(	PUNCT
ejpam-4385	73	71	12	12	NUM
ejpam-4385	73	72	)	)	PUNCT
ejpam-4385	73	73	let	let	VERB
ejpam-4385	73	74	us	we	PRON
ejpam-4385	73	75	now	now	ADV
ejpam-4385	73	76	consider	consider	VERB
ejpam-4385	73	77	the	the	DET
ejpam-4385	73	78	british	british	ADJ
ejpam-4385	73	79	call	call	NOUN
ejpam-4385	73	80	option	option	NOUN
ejpam-4385	73	81	on	on	ADP
ejpam-4385	73	82	stock	stock	NOUN
ejpam-4385	73	83	given	give	VERB
ejpam-4385	73	84	the	the	DET
ejpam-4385	73	85	financial	financial	ADJ
ejpam-4385	73	86	market	market	NOUN
ejpam-4385	73	87	described	describe	VERB
ejpam-4385	73	88	above	above	ADV
ejpam-4385	73	89	.	.	PUNCT
ejpam-4385	74	1	moreover	moreover	ADV
ejpam-4385	74	2	,	,	PUNCT
ejpam-4385	74	3	we	we	PRON
ejpam-4385	74	4	assume	assume	VERB
ejpam-4385	74	5	that	that	SCONJ
ejpam-4385	74	6	the	the	DET
ejpam-4385	74	7	stock	stock	NOUN
ejpam-4385	74	8	does	do	AUX
ejpam-4385	74	9	not	not	PART
ejpam-4385	74	10	pay	pay	VERB
ejpam-4385	74	11	dividends	dividend	NOUN
ejpam-4385	74	12	and	and	CCONJ
ejpam-4385	74	13	there	there	PRON
ejpam-4385	74	14	are	be	VERB
ejpam-4385	74	15	no	no	DET
ejpam-4385	74	16	transaction	transaction	NOUN
ejpam-4385	74	17	costs	cost	NOUN
ejpam-4385	74	18	involved	involve	VERB
ejpam-4385	74	19	in	in	ADP
ejpam-4385	74	20	its	its	PRON
ejpam-4385	74	21	trade	trade	NOUN
ejpam-4385	74	22	.	.	PUNCT
ejpam-4385	75	1	in	in	ADP
ejpam-4385	75	2	2013	2013	NUM
ejpam-4385	75	3	,	,	PUNCT
ejpam-4385	75	4	peskir	peskir	NOUN
ejpam-4385	75	5	and	and	CCONJ
ejpam-4385	75	6	samee	samee	PROPN
ejpam-4385	75	7	defined	define	VERB
ejpam-4385	75	8	the	the	DET
ejpam-4385	75	9	british	british	ADJ
ejpam-4385	75	10	call	call	NOUN
ejpam-4385	75	11	option	option	NOUN
ejpam-4385	75	12	with	with	ADP
ejpam-4385	75	13	strike	strike	NOUN
ejpam-4385	75	14	price	price	NOUN
ejpam-4385	75	15	k	k	X
ejpam-4385	75	16	>	>	PUNCT
ejpam-4385	75	17	0	0	PUNCT
ejpam-4385	76	1	and	and	CCONJ
ejpam-4385	76	2	maturity	maturity	NOUN
ejpam-4385	76	3	time	time	NOUN
ejpam-4385	76	4	t	t	PROPN
ejpam-4385	76	5	>	>	X
ejpam-4385	76	6	0	0	PUNCT
ejpam-4385	77	1	in	in	ADP
ejpam-4385	77	2	years	year	NOUN
ejpam-4385	77	3	as	as	SCONJ
ejpam-4385	77	4	follows	follow	VERB
ejpam-4385	77	5	:	:	PUNCT
ejpam-4385	77	6	definition	definition	NOUN
ejpam-4385	77	7	[	[	X
ejpam-4385	77	8	11	11	NUM
ejpam-4385	77	9	]	]	PUNCT
ejpam-4385	77	10	the	the	DET
ejpam-4385	77	11	british	british	ADJ
ejpam-4385	77	12	call	call	NOUN
ejpam-4385	77	13	option	option	NOUN
ejpam-4385	77	14	is	be	AUX
ejpam-4385	77	15	a	a	DET
ejpam-4385	77	16	financial	financial	ADJ
ejpam-4385	77	17	contract	contract	NOUN
ejpam-4385	77	18	between	between	ADP
ejpam-4385	77	19	a	a	DET
ejpam-4385	77	20	seller	seller	NOUN
ejpam-4385	77	21	/	/	SYM
ejpam-4385	77	22	hedger	hedger	NOUN
ejpam-4385	77	23	and	and	CCONJ
ejpam-4385	77	24	a	a	DET
ejpam-4385	77	25	buyer	buyer	NOUN
ejpam-4385	77	26	/	/	SYM
ejpam-4385	77	27	holder	holder	NOUN
ejpam-4385	77	28	entitling	entitle	VERB
ejpam-4385	77	29	the	the	DET
ejpam-4385	77	30	latter	latter	ADJ
ejpam-4385	77	31	to	to	PART
ejpam-4385	77	32	exercise	exercise	VERB
ejpam-4385	77	33	at	at	ADP
ejpam-4385	77	34	any	any	DET
ejpam-4385	77	35	(	(	PUNCT
ejpam-4385	77	36	stopping	stopping	NOUN
ejpam-4385	77	37	)	)	PUNCT
ejpam-4385	77	38	time	time	NOUN
ejpam-4385	77	39	τ	τ	X
ejpam-4385	77	40	prior	prior	ADV
ejpam-4385	77	41	to	to	ADP
ejpam-4385	77	42	t	t	PROPN
ejpam-4385	77	43	whereupon	whereupon	ADV
ejpam-4385	77	44	his	his	PRON
ejpam-4385	77	45	payoff	payoff	NOUN
ejpam-4385	77	46	(	(	PUNCT
ejpam-4385	77	47	deliverable	deliverable	VERB
ejpam-4385	77	48	immediately	immediately	ADV
ejpam-4385	77	49	)	)	PUNCT
ejpam-4385	77	50	is	be	AUX
ejpam-4385	77	51	the	the	DET
ejpam-4385	77	52	‘	'	PUNCT
ejpam-4385	77	53	best	good	ADJ
ejpam-4385	77	54	prediction	prediction	NOUN
ejpam-4385	77	55	’	'	PUNCT
ejpam-4385	77	56	of	of	ADP
ejpam-4385	77	57	the	the	DET
ejpam-4385	77	58	european	european	PROPN
ejpam-4385	77	59	payoff	payoff	PROPN
ejpam-4385	77	60	(	(	PUNCT
ejpam-4385	77	61	xt	xt	ADP
ejpam-4385	77	62	−	−	PROPN
ejpam-4385	77	63	k)+	k)+	PROPN
ejpam-4385	77	64	given	give	VERB
ejpam-4385	77	65	all	all	DET
ejpam-4385	77	66	the	the	DET
ejpam-4385	77	67	information	information	NOUN
ejpam-4385	77	68	up	up	ADP
ejpam-4385	77	69	to	to	ADP
ejpam-4385	77	70	time	time	NOUN
ejpam-4385	77	71	τ	τ	X
ejpam-4385	77	72	under	under	ADP
ejpam-4385	77	73	the	the	DET
ejpam-4385	77	74	hypothesis	hypothesis	NOUN
ejpam-4385	77	75	that	that	PRON
ejpam-4385	77	76	the	the	DET
ejpam-4385	77	77	true	true	ADJ
ejpam-4385	77	78	drift	drift	NOUN
ejpam-4385	77	79	of	of	ADP
ejpam-4385	77	80	the	the	DET
ejpam-4385	77	81	stock	stock	NOUN
ejpam-4385	77	82	price	price	NOUN
ejpam-4385	77	83	equals	equal	VERB
ejpam-4385	77	84	the	the	DET
ejpam-4385	77	85	contract	contract	NOUN
ejpam-4385	77	86	drift	drift	NOUN
ejpam-4385	77	87	µc	µc	PROPN
ejpam-4385	77	88	.	.	PUNCT
ejpam-4385	78	1	in	in	ADP
ejpam-4385	78	2	[	[	X
ejpam-4385	78	3	11	11	NUM
ejpam-4385	78	4	]	]	PUNCT
ejpam-4385	78	5	,	,	PUNCT
ejpam-4385	78	6	the	the	DET
ejpam-4385	78	7	price	price	NOUN
ejpam-4385	78	8	of	of	ADP
ejpam-4385	78	9	the	the	DET
ejpam-4385	78	10	british	british	ADJ
ejpam-4385	78	11	call	call	NOUN
ejpam-4385	78	12	option	option	NOUN
ejpam-4385	78	13	is	be	AUX
ejpam-4385	78	14	derived	derive	VERB
ejpam-4385	78	15	under	under	ADP
ejpam-4385	78	16	the	the	DET
ejpam-4385	78	17	hypothesis	hypothesis	NOUN
ejpam-4385	78	18	that	that	SCONJ
ejpam-4385	78	19	the	the	DET
ejpam-4385	78	20	risk	risk	NOUN
ejpam-4385	78	21	-	-	PUNCT
ejpam-4385	78	22	free	free	ADJ
ejpam-4385	78	23	rate	rate	NOUN
ejpam-4385	78	24	is	be	AUX
ejpam-4385	78	25	constant	constant	ADJ
ejpam-4385	78	26	,	,	PUNCT
ejpam-4385	78	27	that	that	ADV
ejpam-4385	78	28	is	is	ADV
ejpam-4385	78	29	,	,	PUNCT
ejpam-4385	78	30	rt	rt	PROPN
ejpam-4385	78	31	=	=	PUNCT
ejpam-4385	78	32	r	r	NOUN
ejpam-4385	78	33	for	for	ADP
ejpam-4385	78	34	all	all	DET
ejpam-4385	78	35	t	t	NOUN
ejpam-4385	78	36	∈	∈	PROPN
ejpam-4385	79	1	[	[	X
ejpam-4385	79	2	0	0	NUM
ejpam-4385	79	3	,	,	PUNCT
ejpam-4385	79	4	t	t	X
ejpam-4385	79	5	]	]	PUNCT
ejpam-4385	79	6	.	.	PUNCT
ejpam-4385	80	1	hence	hence	ADV
ejpam-4385	80	2	,	,	PUNCT
ejpam-4385	80	3	this	this	DET
ejpam-4385	80	4	paper	paper	NOUN
ejpam-4385	80	5	presents	present	VERB
ejpam-4385	80	6	an	an	DET
ejpam-4385	80	7	extension	extension	NOUN
ejpam-4385	80	8	of	of	ADP
ejpam-4385	80	9	the	the	DET
ejpam-4385	80	10	results	result	NOUN
ejpam-4385	80	11	in	in	ADP
ejpam-4385	80	12	peskir	peskir	NOUN
ejpam-4385	80	13	and	and	CCONJ
ejpam-4385	80	14	samee	samee	PROPN
ejpam-4385	80	15	(	(	PUNCT
ejpam-4385	80	16	2013	2013	NUM
ejpam-4385	80	17	)	)	PUNCT
ejpam-4385	80	18	by	by	ADP
ejpam-4385	80	19	considering	consider	VERB
ejpam-4385	80	20	stochastic	stochastic	ADJ
ejpam-4385	80	21	interest	interest	NOUN
ejpam-4385	80	22	rate	rate	NOUN
ejpam-4385	80	23	.	.	PUNCT
ejpam-4385	81	1	let	let	VERB
ejpam-4385	81	2	(	(	PUNCT
ejpam-4385	81	3	ω	ω	PROPN
ejpam-4385	81	4	,	,	PUNCT
ejpam-4385	81	5	f	f	PROPN
ejpam-4385	81	6	,	,	PUNCT
ejpam-4385	81	7	p	p	NOUN
ejpam-4385	81	8	)	)	PUNCT
ejpam-4385	81	9	denote	denote	VERB
ejpam-4385	81	10	the	the	DET
ejpam-4385	81	11	probability	probability	NOUN
ejpam-4385	81	12	space	space	NOUN
ejpam-4385	81	13	for	for	ADP
ejpam-4385	81	14	which	which	PRON
ejpam-4385	81	15	all	all	DET
ejpam-4385	81	16	the	the	DET
ejpam-4385	81	17	succeeding	succeed	VERB
ejpam-4385	81	18	processes	process	NOUN
ejpam-4385	81	19	are	be	AUX
ejpam-4385	81	20	defined	define	VERB
ejpam-4385	81	21	.	.	PUNCT
ejpam-4385	82	1	let	let	VERB
ejpam-4385	82	2	xt	xt	PART
ejpam-4385	82	3	denote	denote	VERB
ejpam-4385	82	4	the	the	DET
ejpam-4385	82	5	price	price	NOUN
ejpam-4385	82	6	of	of	ADP
ejpam-4385	82	7	a	a	DET
ejpam-4385	82	8	risky	risky	ADJ
ejpam-4385	82	9	stock	stock	NOUN
ejpam-4385	82	10	at	at	ADP
ejpam-4385	82	11	time	time	NOUN
ejpam-4385	82	12	t	t	PROPN
ejpam-4385	82	13	∈	∈	PROPN
ejpam-4385	83	1	[	[	X
ejpam-4385	83	2	0	0	NUM
ejpam-4385	83	3	,	,	PUNCT
ejpam-4385	83	4	t	t	PROPN
ejpam-4385	83	5	]	]	PUNCT
ejpam-4385	83	6	which	which	PRON
ejpam-4385	83	7	satisfies	satisfy	VERB
ejpam-4385	83	8	dxt	dxt	PROPN
ejpam-4385	83	9	=	=	PUNCT
ejpam-4385	83	10	µxtdt	µxtdt	PROPN
ejpam-4385	83	11	+	+	CCONJ
ejpam-4385	83	12	σ1xtdwt	σ1xtdwt	PROPN
ejpam-4385	83	13	.	.	PUNCT
ejpam-4385	84	1	we	we	PRON
ejpam-4385	84	2	note	note	VERB
ejpam-4385	84	3	that	that	SCONJ
ejpam-4385	84	4	the	the	DET
ejpam-4385	84	5	coefficients	coefficient	NOUN
ejpam-4385	84	6	depend	depend	VERB
ejpam-4385	84	7	on	on	ADP
ejpam-4385	84	8	the	the	DET
ejpam-4385	84	9	maturity	maturity	NOUN
ejpam-4385	84	10	time	time	NOUN
ejpam-4385	84	11	t	t	PROPN
ejpam-4385	84	12	as	as	ADV
ejpam-4385	84	13	well	well	ADV
ejpam-4385	84	14	as	as	ADP
ejpam-4385	84	15	the	the	DET
ejpam-4385	84	16	current	current	ADJ
ejpam-4385	84	17	time	time	NOUN
ejpam-4385	84	18	t.	t.	PROPN
ejpam-4385	84	19	let	let	VERB
ejpam-4385	84	20	(	(	PUNCT
ejpam-4385	84	21	f)0≤t≤t	f)0≤t≤t	PROPN
ejpam-4385	84	22	denote	denote	VERB
ejpam-4385	84	23	the	the	DET
ejpam-4385	84	24	natural	natural	ADJ
ejpam-4385	84	25	filtration	filtration	NOUN
ejpam-4385	84	26	generated	generate	VERB
ejpam-4385	84	27	by	by	ADP
ejpam-4385	84	28	the	the	DET
ejpam-4385	84	29	process	process	NOUN
ejpam-4385	84	30	xt	xt	PROPN
ejpam-4385	84	31	.	.	PUNCT
ejpam-4385	85	1	all	all	DET
ejpam-4385	85	2	local	local	ADJ
ejpam-4385	85	3	martingales	martingale	NOUN
ejpam-4385	85	4	involved	involve	VERB
ejpam-4385	85	5	are	be	AUX
ejpam-4385	85	6	with	with	ADP
ejpam-4385	85	7	respect	respect	NOUN
ejpam-4385	85	8	to	to	ADP
ejpam-4385	85	9	the	the	DET
ejpam-4385	85	10	filtration	filtration	NOUN
ejpam-4385	85	11	ft	ft	NOUN
ejpam-4385	85	12	.	.	PUNCT
ejpam-4385	86	1	let	let	VERB
ejpam-4385	86	2	µc	µc	INTJ
ejpam-4385	86	3	>	>	X
ejpam-4385	86	4	0	0	NUM
ejpam-4385	86	5	be	be	AUX
ejpam-4385	86	6	the	the	DET
ejpam-4385	86	7	risk	risk	NOUN
ejpam-4385	86	8	-	-	PUNCT
ejpam-4385	86	9	free	free	ADJ
ejpam-4385	86	10	rate	rate	NOUN
ejpam-4385	86	11	and	and	CCONJ
ejpam-4385	86	12	µ	µ	NOUN
ejpam-4385	86	13	be	be	AUX
ejpam-4385	86	14	the	the	DET
ejpam-4385	86	15	expected	expect	VERB
ejpam-4385	86	16	rate	rate	NOUN
ejpam-4385	86	17	of	of	ADP
ejpam-4385	86	18	return	return	NOUN
ejpam-4385	86	19	(	(	PUNCT
ejpam-4385	86	20	appreciation	appreciation	NOUN
ejpam-4385	86	21	rate	rate	NOUN
ejpam-4385	86	22	)	)	PUNCT
ejpam-4385	86	23	such	such	ADJ
ejpam-4385	86	24	that	that	SCONJ
ejpam-4385	86	25	µc	µc	AUX
ejpam-4385	86	26	̸=	̸=	PROPN
ejpam-4385	86	27	µ.	µ.	NOUN
ejpam-4385	86	28	let	let	VERB
ejpam-4385	86	29	zt	zt	PROPN
ejpam-4385	87	1	:	:	PUNCT
ejpam-4385	87	2	=	=	SYM
ejpam-4385	87	3	exp	exp	PROPN
ejpam-4385	87	4	[	[	X
ejpam-4385	87	5	∫	∫	X
ejpam-4385	87	6	t	t	PROPN
ejpam-4385	87	7	0	0	NUM
ejpam-4385	88	1	β(u)dwu	β(u)dwu	NOUN
ejpam-4385	88	2	−	−	NUM
ejpam-4385	88	3	1	1	NUM
ejpam-4385	88	4	2	2	NUM
ejpam-4385	88	5	∫	∫	NOUN
ejpam-4385	88	6	t	t	PROPN
ejpam-4385	88	7	0	0	NUM
ejpam-4385	88	8	β2(u)du	β2(u)du	PROPN
ejpam-4385	88	9	]	]	PUNCT
ejpam-4385	88	10	for	for	ADP
ejpam-4385	88	11	0	0	NUM
ejpam-4385	88	12	≤	≤	NUM
ejpam-4385	88	13	u	u	NOUN
ejpam-4385	88	14	≤	≤	X
ejpam-4385	88	15	t	t	PROPN
ejpam-4385	88	16	≤	≤	X
ejpam-4385	88	17	t	t	PROPN
ejpam-4385	88	18	where	where	SCONJ
ejpam-4385	88	19	β(t	β(t	PROPN
ejpam-4385	88	20	)	)	PUNCT
ejpam-4385	89	1	:	:	PUNCT
ejpam-4385	89	2	=	=	PRON
ejpam-4385	89	3	µc	µc	ADP
ejpam-4385	89	4	−	−	PROPN
ejpam-4385	89	5	µ	µ	PRON
ejpam-4385	89	6	σ1	σ1	NOUN
ejpam-4385	89	7	is	be	AUX
ejpam-4385	89	8	independent	independent	ADJ
ejpam-4385	89	9	of	of	ADP
ejpam-4385	89	10	t	t	PROPN
ejpam-4385	89	11	.	.	PUNCT
ejpam-4385	90	1	by	by	ADP
ejpam-4385	90	2	itö	itö	NOUN
ejpam-4385	90	3	’s	’s	PART
ejpam-4385	90	4	formula	formula	NOUN
ejpam-4385	90	5	[	[	X
ejpam-4385	90	6	2	2	NUM
ejpam-4385	90	7	]	]	PUNCT
ejpam-4385	90	8	,	,	PUNCT
ejpam-4385	90	9	we	we	PRON
ejpam-4385	90	10	have	have	VERB
ejpam-4385	90	11	dzt	dzt	NOUN
ejpam-4385	90	12	zt	zt	PROPN
ejpam-4385	90	13	=	=	PUNCT
ejpam-4385	90	14	β(t)dwt	β(t)dwt	PROPN
ejpam-4385	90	15	.	.	PUNCT
ejpam-4385	91	1	this	this	PRON
ejpam-4385	91	2	shows	show	VERB
ejpam-4385	91	3	that	that	SCONJ
ejpam-4385	91	4	zt	zt	PROPN
ejpam-4385	91	5	is	be	AUX
ejpam-4385	91	6	a	a	DET
ejpam-4385	91	7	local	local	ADJ
ejpam-4385	91	8	martingale	martingale	NOUN
ejpam-4385	91	9	with	with	ADP
ejpam-4385	91	10	e	e	PROPN
ejpam-4385	91	11	[	[	X
ejpam-4385	91	12	zt	zt	X
ejpam-4385	91	13	]	]	X
ejpam-4385	91	14	=	=	SYM
ejpam-4385	91	15	1	1	NUM
ejpam-4385	91	16	for	for	ADP
ejpam-4385	91	17	0	0	NUM
ejpam-4385	91	18	≤	≤	NUM
ejpam-4385	91	19	t	t	PROPN
ejpam-4385	91	20	≤	≤	PROPN
ejpam-4385	91	21	t	t	PROPN
ejpam-4385	91	22	.	.	PUNCT
ejpam-4385	92	1	k.	k.	PROPN
ejpam-4385	92	2	falcasantos	falcasantos	PROPN
ejpam-4385	92	3	,	,	PUNCT
ejpam-4385	92	4	f.	f.	PROPN
ejpam-4385	92	5	sumalpong	sumalpong	PROPN
ejpam-4385	92	6	/	/	SYM
ejpam-4385	92	7	eur	eur	PROPN
ejpam-4385	92	8	.	.	PUNCT
ejpam-4385	93	1	j.	j.	PROPN
ejpam-4385	93	2	pure	pure	PROPN
ejpam-4385	93	3	appl	appl	PROPN
ejpam-4385	93	4	.	.	PROPN
ejpam-4385	93	5	math	math	PROPN
ejpam-4385	93	6	,	,	PUNCT
ejpam-4385	93	7	15	15	NUM
ejpam-4385	93	8	(	(	PUNCT
ejpam-4385	93	9	3	3	NUM
ejpam-4385	93	10	)	)	PUNCT
ejpam-4385	93	11	(	(	PUNCT
ejpam-4385	93	12	2022	2022	NUM
ejpam-4385	93	13	)	)	PUNCT
ejpam-4385	93	14	,	,	PUNCT
ejpam-4385	93	15	948	948	NUM
ejpam-4385	93	16	-	-	SYM
ejpam-4385	93	17	970	970	NUM
ejpam-4385	93	18	952	952	NUM
ejpam-4385	93	19	moreover	moreover	ADV
ejpam-4385	93	20	,	,	PUNCT
ejpam-4385	93	21	define	define	VERB
ejpam-4385	93	22	the	the	DET
ejpam-4385	93	23	radon	radon	PROPN
ejpam-4385	93	24	-	-	PUNCT
ejpam-4385	93	25	nikodym	nikodym	PROPN
ejpam-4385	93	26	derivative	derivative	NOUN
ejpam-4385	93	27	of	of	ADP
ejpam-4385	93	28	pµc	pµc	PROPN
ejpam-4385	93	29	with	with	ADP
ejpam-4385	93	30	respect	respect	NOUN
ejpam-4385	93	31	to	to	ADP
ejpam-4385	93	32	p	p	NOUN
ejpam-4385	93	33	via	via	ADP
ejpam-4385	93	34	the	the	DET
ejpam-4385	93	35	following	following	NOUN
ejpam-4385	93	36	:	:	PUNCT
ejpam-4385	93	37	dpµc	dpµc	ADJ
ejpam-4385	93	38	dp	dp	NOUN
ejpam-4385	93	39	=	=	NOUN
ejpam-4385	93	40	zt	zt	PROPN
ejpam-4385	93	41	.	.	PUNCT
ejpam-4385	94	1	(	(	PUNCT
ejpam-4385	94	2	13	13	NUM
ejpam-4385	94	3	)	)	PUNCT
ejpam-4385	94	4	by	by	ADP
ejpam-4385	94	5	the	the	DET
ejpam-4385	94	6	generalized	generalize	VERB
ejpam-4385	94	7	girsavanov	girsavanov	NOUN
ejpam-4385	94	8	’s	’s	PART
ejpam-4385	94	9	theorem	theorem	NOUN
ejpam-4385	94	10	(	(	PUNCT
ejpam-4385	94	11	see	see	VERB
ejpam-4385	94	12	lemma	lemma	PROPN
ejpam-4385	94	13	1	1	NUM
ejpam-4385	94	14	in	in	ADP
ejpam-4385	94	15	[	[	X
ejpam-4385	94	16	15	15	NUM
ejpam-4385	94	17	]	]	NUM
ejpam-4385	94	18	)	)	PUNCT
ejpam-4385	94	19	,	,	PUNCT
ejpam-4385	94	20	we	we	PRON
ejpam-4385	94	21	have	have	VERB
ejpam-4385	94	22	wµc	wµc	NOUN
ejpam-4385	94	23	:	:	PUNCT
ejpam-4385	95	1	=	=	SYM
ejpam-4385	95	2	wt	wt	ADP
ejpam-4385	95	3	−	−	NUM
ejpam-4385	95	4	∫	∫	PROPN
ejpam-4385	95	5	t	t	PROPN
ejpam-4385	95	6	0	0	NUM
ejpam-4385	95	7	β(u)du	β(u)du	X
ejpam-4385	95	8	is	be	AUX
ejpam-4385	95	9	a	a	DET
ejpam-4385	95	10	pµc	pµc	ADJ
ejpam-4385	95	11	-	-	PUNCT
ejpam-4385	95	12	brownian	brownian	ADJ
ejpam-4385	95	13	motion	motion	NOUN
ejpam-4385	95	14	.	.	PUNCT
ejpam-4385	96	1	let	let	VERB
ejpam-4385	96	2	eµc	eµc	NOUN
ejpam-4385	96	3	be	be	AUX
ejpam-4385	96	4	an	an	DET
ejpam-4385	96	5	expectation	expectation	NOUN
ejpam-4385	96	6	with	with	ADP
ejpam-4385	96	7	respect	respect	NOUN
ejpam-4385	96	8	to	to	ADP
ejpam-4385	96	9	the	the	DET
ejpam-4385	96	10	measure	measure	NOUN
ejpam-4385	96	11	pµc	pµc	PROPN
ejpam-4385	96	12	.	.	PUNCT
ejpam-4385	97	1	under	under	ADP
ejpam-4385	97	2	the	the	DET
ejpam-4385	97	3	probability	probability	NOUN
ejpam-4385	97	4	pµc	pµc	NOUN
ejpam-4385	97	5	,	,	PUNCT
ejpam-4385	97	6	the	the	DET
ejpam-4385	97	7	stock	stock	NOUN
ejpam-4385	97	8	price	price	NOUN
ejpam-4385	97	9	process	process	NOUN
ejpam-4385	97	10	in	in	ADP
ejpam-4385	97	11	equation	equation	NOUN
ejpam-4385	97	12	(	(	PUNCT
ejpam-4385	97	13	1	1	X
ejpam-4385	97	14	)	)	PUNCT
ejpam-4385	97	15	becomes	become	VERB
ejpam-4385	97	16	dxt	dxt	PROPN
ejpam-4385	97	17	=	=	PUNCT
ejpam-4385	98	1	µcxtdt+	µcxtdt+	X
ejpam-4385	98	2	σ1xtdw	σ1xtdw	VERB
ejpam-4385	98	3	µc	µc	INTJ
ejpam-4385	98	4	t	t	PROPN
ejpam-4385	98	5	(	(	PUNCT
ejpam-4385	98	6	14	14	NUM
ejpam-4385	98	7	)	)	PUNCT
ejpam-4385	98	8	where	where	SCONJ
ejpam-4385	98	9	0	0	NUM
ejpam-4385	98	10	≤	≤	NUM
ejpam-4385	98	11	t	t	PROPN
ejpam-4385	98	12	≤	≤	X
ejpam-4385	98	13	t	t	PROPN
ejpam-4385	98	14	with	with	ADP
ejpam-4385	98	15	x0	x0	PROPN
ejpam-4385	98	16	=	=	PUNCT
ejpam-4385	98	17	x	x	SYM
ejpam-4385	98	18	∈	∈	PROPN
ejpam-4385	98	19	(	(	PUNCT
ejpam-4385	98	20	0,∞	0,∞	NOUN
ejpam-4385	98	21	)	)	PUNCT
ejpam-4385	98	22	.	.	PUNCT
ejpam-4385	99	1	thus	thus	ADV
ejpam-4385	99	2	,	,	PUNCT
ejpam-4385	99	3	law(x(µ)|p	law(x(µ)|p	PROPN
ejpam-4385	99	4	)	)	PUNCT
ejpam-4385	99	5	=	=	SYM
ejpam-4385	99	6	law(x(µc)|pµc	law(x(µc)|pµc	PROPN
ejpam-4385	99	7	)	)	PUNCT
ejpam-4385	99	8	where	where	SCONJ
ejpam-4385	99	9	law	law	NOUN
ejpam-4385	99	10	means	mean	VERB
ejpam-4385	99	11	“	"	PUNCT
ejpam-4385	99	12	distribution	distribution	NOUN
ejpam-4385	99	13	”	"	PUNCT
ejpam-4385	99	14	.	.	PUNCT
ejpam-4385	100	1	furthermore	furthermore	ADV
ejpam-4385	100	2	,	,	PUNCT
ejpam-4385	100	3	making	make	VERB
ejpam-4385	100	4	use	use	NOUN
ejpam-4385	100	5	of	of	ADP
ejpam-4385	100	6	the	the	DET
ejpam-4385	100	7	property	property	NOUN
ejpam-4385	100	8	of	of	ADP
ejpam-4385	100	9	zt	zt	PROPN
ejpam-4385	100	10	,	,	PUNCT
ejpam-4385	100	11	we	we	PRON
ejpam-4385	100	12	have	have	VERB
ejpam-4385	100	13	eµc(x	eµc(x	NOUN
ejpam-4385	100	14	)	)	PUNCT
ejpam-4385	100	15	=	=	SYM
ejpam-4385	100	16	e(ztx	e(ztx	PROPN
ejpam-4385	100	17	)	)	PUNCT
ejpam-4385	100	18	=	=	SYM
ejpam-4385	100	19	e(zt	e(zt	PROPN
ejpam-4385	100	20	)	)	PUNCT
ejpam-4385	100	21	e(x	e(x	NUM
ejpam-4385	100	22	)	)	PUNCT
ejpam-4385	100	23	=	=	SYM
ejpam-4385	100	24	e(x	e(x	NUM
ejpam-4385	100	25	)	)	PUNCT
ejpam-4385	100	26	for	for	ADP
ejpam-4385	100	27	any	any	DET
ejpam-4385	100	28	random	random	ADJ
ejpam-4385	100	29	variable	variable	NOUN
ejpam-4385	100	30	x.	x.	NOUN
ejpam-4385	101	1	thus	thus	ADV
ejpam-4385	101	2	,	,	PUNCT
ejpam-4385	101	3	the	the	DET
ejpam-4385	101	4	payoff	payoff	NOUN
ejpam-4385	101	5	of	of	ADP
ejpam-4385	101	6	the	the	DET
ejpam-4385	101	7	british	british	ADJ
ejpam-4385	101	8	call	call	NOUN
ejpam-4385	101	9	option	option	NOUN
ejpam-4385	101	10	at	at	ADP
ejpam-4385	101	11	a	a	DET
ejpam-4385	101	12	given	give	VERB
ejpam-4385	101	13	stopping	stopping	NOUN
ejpam-4385	101	14	time	time	NOUN
ejpam-4385	101	15	t	t	PROPN
ejpam-4385	101	16	=	=	SYM
ejpam-4385	101	17	τ	τ	PROPN
ejpam-4385	101	18	can	can	AUX
ejpam-4385	101	19	be	be	AUX
ejpam-4385	101	20	written	write	VERB
ejpam-4385	101	21	as	as	ADP
ejpam-4385	101	22	eµc	eµc	PROPN
ejpam-4385	101	23	[	[	X
ejpam-4385	101	24	(	(	PUNCT
ejpam-4385	101	25	xt	xt	X
ejpam-4385	101	26	−k)+|fτ	−k)+|fτ	PROPN
ejpam-4385	101	27	]	]	X
ejpam-4385	101	28	(	(	PUNCT
ejpam-4385	101	29	15	15	NUM
ejpam-4385	101	30	)	)	PUNCT
ejpam-4385	101	31	where	where	SCONJ
ejpam-4385	101	32	the	the	DET
ejpam-4385	101	33	conditional	conditional	ADJ
ejpam-4385	101	34	expectation	expectation	NOUN
ejpam-4385	101	35	is	be	AUX
ejpam-4385	101	36	taken	take	VERB
ejpam-4385	101	37	with	with	ADP
ejpam-4385	101	38	respect	respect	NOUN
ejpam-4385	101	39	to	to	ADP
ejpam-4385	101	40	a	a	DET
ejpam-4385	101	41	new	new	ADJ
ejpam-4385	101	42	(	(	PUNCT
ejpam-4385	101	43	equivalent	equivalent	ADJ
ejpam-4385	101	44	)	)	PUNCT
ejpam-4385	101	45	probability	probability	NOUN
ejpam-4385	101	46	measure	measure	NOUN
ejpam-4385	101	47	pµc	pµc	PROPN
ejpam-4385	101	48	.	.	PUNCT
ejpam-4385	102	1	clearly	clearly	ADV
ejpam-4385	102	2	,	,	PUNCT
ejpam-4385	102	3	when	when	SCONJ
ejpam-4385	102	4	we	we	PRON
ejpam-4385	102	5	exercise	exercise	VERB
ejpam-4385	102	6	the	the	DET
ejpam-4385	102	7	british	british	ADJ
ejpam-4385	102	8	call	call	NOUN
ejpam-4385	102	9	option	option	NOUN
ejpam-4385	102	10	,	,	PUNCT
ejpam-4385	102	11	we	we	PRON
ejpam-4385	102	12	just	just	ADV
ejpam-4385	102	13	substitute	substitute	VERB
ejpam-4385	102	14	the	the	DET
ejpam-4385	102	15	contract	contract	NOUN
ejpam-4385	102	16	drift	drift	NOUN
ejpam-4385	102	17	µc	µc	ADP
ejpam-4385	102	18	to	to	ADP
ejpam-4385	102	19	the	the	DET
ejpam-4385	102	20	true	true	ADJ
ejpam-4385	102	21	(	(	PUNCT
ejpam-4385	102	22	unknown	unknown	ADJ
ejpam-4385	102	23	)	)	PUNCT
ejpam-4385	102	24	drift	drift	NOUN
ejpam-4385	102	25	µ	µ	PROPN
ejpam-4385	102	26	of	of	ADP
ejpam-4385	102	27	the	the	DET
ejpam-4385	102	28	stock	stock	NOUN
ejpam-4385	102	29	price	price	NOUN
ejpam-4385	102	30	for	for	ADP
ejpam-4385	102	31	the	the	DET
ejpam-4385	102	32	remaining	remain	VERB
ejpam-4385	102	33	term	term	NOUN
ejpam-4385	102	34	of	of	ADP
ejpam-4385	102	35	the	the	DET
ejpam-4385	102	36	contract	contract	NOUN
ejpam-4385	102	37	.	.	PUNCT
ejpam-4385	103	1	3	3	X
ejpam-4385	103	2	.	.	X
ejpam-4385	103	3	payoff	payoff	PROPN
ejpam-4385	103	4	,	,	PUNCT
ejpam-4385	103	5	premium	premium	NOUN
ejpam-4385	103	6	and	and	CCONJ
ejpam-4385	103	7	the	the	DET
ejpam-4385	103	8	price	price	NOUN
ejpam-4385	103	9	process	process	NOUN
ejpam-4385	103	10	of	of	ADP
ejpam-4385	103	11	the	the	DET
ejpam-4385	103	12	british	british	ADJ
ejpam-4385	103	13	call	call	NOUN
ejpam-4385	103	14	option	option	NOUN
ejpam-4385	103	15	using	use	VERB
ejpam-4385	103	16	the	the	DET
ejpam-4385	103	17	properties	property	NOUN
ejpam-4385	103	18	of	of	ADP
ejpam-4385	103	19	the	the	DET
ejpam-4385	103	20	wiener	wiener	NOUN
ejpam-4385	103	21	process	process	NOUN
ejpam-4385	103	22	wµc	wµc	NOUN
ejpam-4385	103	23	on	on	ADP
ejpam-4385	103	24	x	x	X
ejpam-4385	103	25	(	(	PUNCT
ejpam-4385	103	26	stationary	stationary	ADJ
ejpam-4385	103	27	and	and	CCONJ
ejpam-4385	103	28	independent	independent	ADJ
ejpam-4385	103	29	increments	increment	NOUN
ejpam-4385	103	30	of	of	ADP
ejpam-4385	103	31	wµc	wµc	NOUN
ejpam-4385	103	32	on	on	ADP
ejpam-4385	103	33	x	x	NOUN
ejpam-4385	103	34	)	)	PUNCT
ejpam-4385	103	35	,	,	PUNCT
ejpam-4385	103	36	implies	imply	VERB
ejpam-4385	103	37	that	that	SCONJ
ejpam-4385	103	38	eµc	eµc	PROPN
ejpam-4385	103	39	[	[	X
ejpam-4385	103	40	(	(	PUNCT
ejpam-4385	103	41	xt	xt	ADP
ejpam-4385	103	42	−k)+|ft	−k)+|ft	PROPN
ejpam-4385	103	43	]	]	X
ejpam-4385	103	44	=	=	SYM
ejpam-4385	103	45	gµc(t	gµc(t	PROPN
ejpam-4385	103	46	,	,	PUNCT
ejpam-4385	103	47	xt	xt	NUM
ejpam-4385	103	48	)	)	PUNCT
ejpam-4385	103	49	(	(	PUNCT
ejpam-4385	103	50	16	16	NUM
ejpam-4385	103	51	)	)	PUNCT
ejpam-4385	103	52	where	where	SCONJ
ejpam-4385	103	53	gµc	gµc	NOUN
ejpam-4385	103	54	is	be	AUX
ejpam-4385	103	55	the	the	DET
ejpam-4385	103	56	payoff	payoff	NOUN
ejpam-4385	103	57	function	function	NOUN
ejpam-4385	103	58	given	give	VERB
ejpam-4385	103	59	by	by	ADP
ejpam-4385	103	60	gµc(t	gµc(t	PROPN
ejpam-4385	103	61	,	,	PUNCT
ejpam-4385	103	62	x	x	NOUN
ejpam-4385	103	63	)	)	PUNCT
ejpam-4385	103	64	=	=	SYM
ejpam-4385	103	65	e(xzµc	e(xzµc	NOUN
ejpam-4385	103	66	t−t	t−t	PROPN
ejpam-4385	103	67	−k)+	−k)+	PROPN
ejpam-4385	103	68	(	(	PUNCT
ejpam-4385	103	69	see	see	VERB
ejpam-4385	103	70	[	[	X
ejpam-4385	103	71	11	11	NUM
ejpam-4385	103	72	]	]	SYM
ejpam-4385	103	73	)	)	PUNCT
ejpam-4385	103	74	(	(	PUNCT
ejpam-4385	103	75	17	17	NUM
ejpam-4385	103	76	)	)	PUNCT
ejpam-4385	103	77	for	for	ADP
ejpam-4385	103	78	t	t	PROPN
ejpam-4385	103	79	∈	∈	PROPN
ejpam-4385	104	1	[	[	X
ejpam-4385	104	2	0	0	NUM
ejpam-4385	104	3	,	,	PUNCT
ejpam-4385	104	4	t	t	NOUN
ejpam-4385	104	5	]	]	PUNCT
ejpam-4385	104	6	and	and	CCONJ
ejpam-4385	104	7	x	x	X
ejpam-4385	104	8	>	>	X
ejpam-4385	104	9	0	0	NUM
ejpam-4385	104	10	where	where	SCONJ
ejpam-4385	104	11	gµc(t	gµc(t	NOUN
ejpam-4385	104	12	,	,	PUNCT
ejpam-4385	104	13	x	x	NOUN
ejpam-4385	104	14	)	)	PUNCT
ejpam-4385	104	15	represents	represent	VERB
ejpam-4385	104	16	the	the	DET
ejpam-4385	104	17	value	value	NOUN
ejpam-4385	104	18	of	of	ADP
ejpam-4385	104	19	the	the	DET
ejpam-4385	104	20	investment	investment	NOUN
ejpam-4385	104	21	and	and	CCONJ
ejpam-4385	104	22	e(xzµc	e(xzµc	VERB
ejpam-4385	104	23	t−t	t−t	PROPN
ejpam-4385	104	24	−k)+	−k)+	PROPN
ejpam-4385	104	25	represents	represent	VERB
ejpam-4385	104	26	the	the	DET
ejpam-4385	104	27	expected	expect	VERB
ejpam-4385	104	28	value	value	NOUN
ejpam-4385	104	29	of	of	ADP
ejpam-4385	104	30	its	its	PRON
ejpam-4385	104	31	payoff	payoff	NOUN
ejpam-4385	104	32	,	,	PUNCT
ejpam-4385	104	33	and	and	CCONJ
ejpam-4385	104	34	zµc	zµc	NOUN
ejpam-4385	104	35	t−t	t−t	PROPN
ejpam-4385	104	36	is	be	AUX
ejpam-4385	104	37	given	give	VERB
ejpam-4385	104	38	by	by	ADP
ejpam-4385	104	39	zµc	zµc	NOUN
ejpam-4385	104	40	t−t	t−t	PROPN
ejpam-4385	104	41	=	=	SYM
ejpam-4385	104	42	exp	exp	NOUN
ejpam-4385	104	43	[	[	PUNCT
ejpam-4385	104	44	(	(	PUNCT
ejpam-4385	104	45	µc	µc	INTJ
ejpam-4385	104	46	−	−	PROPN
ejpam-4385	104	47	σ2	σ2	NOUN
ejpam-4385	104	48	1	1	NUM
ejpam-4385	104	49	2	2	NUM
ejpam-4385	104	50	)	)	PUNCT
ejpam-4385	104	51	(	(	PUNCT
ejpam-4385	104	52	t	t	PROPN
ejpam-4385	104	53	−	−	PROPN
ejpam-4385	104	54	t	t	PROPN
ejpam-4385	104	55	)	)	PUNCT
ejpam-4385	105	1	+	+	CCONJ
ejpam-4385	105	2	σ1wt−t	σ1wt−t	ADV
ejpam-4385	105	3	]	]	PUNCT
ejpam-4385	105	4	(	(	PUNCT
ejpam-4385	105	5	18	18	NUM
ejpam-4385	105	6	)	)	PUNCT
ejpam-4385	105	7	for	for	ADP
ejpam-4385	105	8	t	t	PROPN
ejpam-4385	105	9	∈	∈	PROPN
ejpam-4385	106	1	[	[	X
ejpam-4385	106	2	0	0	NUM
ejpam-4385	106	3	,	,	PUNCT
ejpam-4385	106	4	t	t	NOUN
ejpam-4385	106	5	]	]	PUNCT
ejpam-4385	106	6	and	and	CCONJ
ejpam-4385	106	7	x	x	PUNCT
ejpam-4385	106	8	∈	∈	PROPN
ejpam-4385	106	9	(	(	PUNCT
ejpam-4385	106	10	0,∞	0,∞	NOUN
ejpam-4385	106	11	)	)	PUNCT
ejpam-4385	106	12	.	.	PUNCT
ejpam-4385	107	1	it	it	PRON
ejpam-4385	107	2	can	can	AUX
ejpam-4385	107	3	be	be	AUX
ejpam-4385	107	4	verified	verify	VERB
ejpam-4385	107	5	that	that	SCONJ
ejpam-4385	107	6	(	(	PUNCT
ejpam-4385	107	7	17	17	NUM
ejpam-4385	107	8	)	)	PUNCT
ejpam-4385	107	9	can	can	AUX
ejpam-4385	107	10	be	be	AUX
ejpam-4385	107	11	expressed	express	VERB
ejpam-4385	107	12	as	as	SCONJ
ejpam-4385	107	13	follows	follow	VERB
ejpam-4385	107	14	k.	k.	PROPN
ejpam-4385	107	15	falcasantos	falcasantos	PROPN
ejpam-4385	107	16	,	,	PUNCT
ejpam-4385	107	17	f.	f.	PROPN
ejpam-4385	107	18	sumalpong	sumalpong	PROPN
ejpam-4385	107	19	/	/	SYM
ejpam-4385	107	20	eur	eur	PROPN
ejpam-4385	107	21	.	.	PUNCT
ejpam-4385	108	1	j.	j.	PROPN
ejpam-4385	108	2	pure	pure	PROPN
ejpam-4385	108	3	appl	appl	PROPN
ejpam-4385	108	4	.	.	PROPN
ejpam-4385	108	5	math	math	PROPN
ejpam-4385	108	6	,	,	PUNCT
ejpam-4385	108	7	15	15	NUM
ejpam-4385	108	8	(	(	PUNCT
ejpam-4385	108	9	3	3	NUM
ejpam-4385	108	10	)	)	PUNCT
ejpam-4385	108	11	(	(	PUNCT
ejpam-4385	108	12	2022	2022	NUM
ejpam-4385	108	13	)	)	PUNCT
ejpam-4385	108	14	,	,	PUNCT
ejpam-4385	108	15	948	948	NUM
ejpam-4385	108	16	-	-	SYM
ejpam-4385	108	17	970	970	NUM
ejpam-4385	108	18	953	953	NUM
ejpam-4385	108	19	gµc(t	gµc(t	PROPN
ejpam-4385	108	20	,	,	PUNCT
ejpam-4385	108	21	x	x	NOUN
ejpam-4385	108	22	)	)	PUNCT
ejpam-4385	108	23	=	=	SYM
ejpam-4385	108	24	xeµc(t−t)φ(d1)−kφ(d2	xeµc(t−t)φ(d1)−kφ(d2	PROPN
ejpam-4385	108	25	)	)	PUNCT
ejpam-4385	108	26	where	where	SCONJ
ejpam-4385	108	27	d1	d1	NOUN
ejpam-4385	108	28	=	=	PUNCT
ejpam-4385	109	1	ln	ln	NOUN
ejpam-4385	109	2	x	x	X
ejpam-4385	110	1	k	k	X
ejpam-4385	110	2	+	+	CCONJ
ejpam-4385	110	3	(	(	PUNCT
ejpam-4385	110	4	µc	µc	INTJ
ejpam-4385	110	5	+	+	NUM
ejpam-4385	110	6	1	1	NUM
ejpam-4385	110	7	2σ	2σ	NUM
ejpam-4385	110	8	2	2	NUM
ejpam-4385	110	9	1)(t	1)(t	NUM
ejpam-4385	110	10	−	−	PROPN
ejpam-4385	110	11	t	t	PROPN
ejpam-4385	110	12	)	)	PUNCT
ejpam-4385	110	13	σ1	σ1	PROPN
ejpam-4385	110	14	√	√	PROPN
ejpam-4385	110	15	t	t	PROPN
ejpam-4385	110	16	−	−	PROPN
ejpam-4385	110	17	t	t	PROPN
ejpam-4385	110	18	,	,	PUNCT
ejpam-4385	110	19	d2	d2	PROPN
ejpam-4385	110	20	=	=	SYM
ejpam-4385	110	21	d1	d1	PROPN
ejpam-4385	110	22	−	−	PROPN
ejpam-4385	110	23	σ1	σ1	PROPN
ejpam-4385	110	24	√	√	PROPN
ejpam-4385	110	25	t	t	PROPN
ejpam-4385	110	26	−	−	PROPN
ejpam-4385	110	27	t	t	PROPN
ejpam-4385	110	28	for	for	ADP
ejpam-4385	110	29	t	t	PROPN
ejpam-4385	110	30	∈	∈	PROPN
ejpam-4385	111	1	[	[	X
ejpam-4385	111	2	0	0	NUM
ejpam-4385	111	3	,	,	PUNCT
ejpam-4385	111	4	t	t	X
ejpam-4385	111	5	]	]	PUNCT
ejpam-4385	111	6	,	,	PUNCT
ejpam-4385	111	7	x	x	X
ejpam-4385	111	8	>	>	X
ejpam-4385	111	9	0	0	NUM
ejpam-4385	111	10	and	and	CCONJ
ejpam-4385	111	11	φ	φ	NUM
ejpam-4385	111	12	(	(	PUNCT
ejpam-4385	111	13	·	·	PUNCT
ejpam-4385	111	14	)	)	PUNCT
ejpam-4385	111	15	is	be	AUX
ejpam-4385	111	16	the	the	DET
ejpam-4385	111	17	standard	standard	ADJ
ejpam-4385	111	18	normal	normal	ADJ
ejpam-4385	111	19	cumulative	cumulative	ADJ
ejpam-4385	111	20	distribution	distribution	NOUN
ejpam-4385	111	21	function	function	NOUN
ejpam-4385	111	22	.	.	PUNCT
ejpam-4385	112	1	by	by	ADP
ejpam-4385	112	2	applying	apply	VERB
ejpam-4385	112	3	the	the	DET
ejpam-4385	112	4	standard	standard	ADJ
ejpam-4385	112	5	hegding	hegde	VERB
ejpam-4385	112	6	scheme	scheme	NOUN
ejpam-4385	112	7	based	base	VERB
ejpam-4385	112	8	on	on	ADP
ejpam-4385	112	9	self	self	NOUN
ejpam-4385	112	10	-	-	PUNCT
ejpam-4385	112	11	financing	finance	VERB
ejpam-4385	112	12	portfolios	portfolio	NOUN
ejpam-4385	112	13	(	(	PUNCT
ejpam-4385	112	14	with	with	ADP
ejpam-4385	112	15	consumption	consumption	NOUN
ejpam-4385	112	16	)	)	PUNCT
ejpam-4385	112	17	,	,	PUNCT
ejpam-4385	112	18	the	the	DET
ejpam-4385	112	19	arbitrage	arbitrage	NOUN
ejpam-4385	112	20	-	-	PUNCT
ejpam-4385	112	21	free	free	ADJ
ejpam-4385	112	22	price	price	NOUN
ejpam-4385	112	23	of	of	ADP
ejpam-4385	112	24	the	the	DET
ejpam-4385	112	25	british	british	ADJ
ejpam-4385	112	26	call	call	NOUN
ejpam-4385	112	27	option	option	NOUN
ejpam-4385	112	28	at	at	ADP
ejpam-4385	112	29	deal	deal	NOUN
ejpam-4385	112	30	time	time	NOUN
ejpam-4385	112	31	(	(	PUNCT
ejpam-4385	112	32	time	time	NOUN
ejpam-4385	112	33	0	0	NUM
ejpam-4385	112	34	)	)	PUNCT
ejpam-4385	112	35	is	be	AUX
ejpam-4385	112	36	given	give	VERB
ejpam-4385	112	37	by	by	ADP
ejpam-4385	112	38	v	v	NOUN
ejpam-4385	112	39	=	=	SYM
ejpam-4385	112	40	sup	sup	NOUN
ejpam-4385	112	41	0≤τ≤t	0≤τ≤t	NUM
ejpam-4385	112	42	ẽ	ẽ	PROPN
ejpam-4385	112	43	[	[	PUNCT
ejpam-4385	112	44	e−	e−	PROPN
ejpam-4385	112	45	∫	∫	PROPN
ejpam-4385	112	46	τ	τ	PROPN
ejpam-4385	112	47	0	0	NUM
ejpam-4385	112	48	rudueµc	rudueµc	NOUN
ejpam-4385	112	49	[	[	PUNCT
ejpam-4385	112	50	(	(	PUNCT
ejpam-4385	112	51	xt	xt	X
ejpam-4385	112	52	−k)+|fτ	−k)+|fτ	PROPN
ejpam-4385	112	53	]	]	X
ejpam-4385	112	54	]	]	X
ejpam-4385	112	55	,	,	PUNCT
ejpam-4385	112	56	(	(	PUNCT
ejpam-4385	112	57	19	19	NUM
ejpam-4385	112	58	)	)	PUNCT
ejpam-4385	112	59	where	where	SCONJ
ejpam-4385	112	60	the	the	DET
ejpam-4385	112	61	supremum	supremum	NOUN
ejpam-4385	112	62	is	be	AUX
ejpam-4385	112	63	taken	take	VERB
ejpam-4385	112	64	over	over	ADP
ejpam-4385	112	65	all	all	DET
ejpam-4385	112	66	stopping	stop	VERB
ejpam-4385	112	67	time	time	NOUN
ejpam-4385	112	68	τ	τ	X
ejpam-4385	112	69	∈	∈	PROPN
ejpam-4385	113	1	[	[	X
ejpam-4385	113	2	0	0	NUM
ejpam-4385	113	3	,	,	PUNCT
ejpam-4385	113	4	t	t	NOUN
ejpam-4385	113	5	]	]	PUNCT
ejpam-4385	113	6	of	of	ADP
ejpam-4385	113	7	x	x	X
ejpam-4385	113	8	and	and	CCONJ
ejpam-4385	113	9	ẽ	ẽ	PROPN
ejpam-4385	113	10	is	be	AUX
ejpam-4385	113	11	taken	take	VERB
ejpam-4385	113	12	with	with	ADP
ejpam-4385	113	13	respect	respect	NOUN
ejpam-4385	113	14	to	to	ADP
ejpam-4385	113	15	the	the	DET
ejpam-4385	113	16	(	(	PUNCT
ejpam-4385	113	17	unique	unique	ADJ
ejpam-4385	113	18	)	)	PUNCT
ejpam-4385	113	19	equivalent	equivalent	ADJ
ejpam-4385	113	20	martingale	martingale	NOUN
ejpam-4385	113	21	measure	measure	NOUN
ejpam-4385	113	22	p̃	p̃	PROPN
ejpam-4385	113	23	under	under	ADP
ejpam-4385	113	24	which	which	PRON
ejpam-4385	113	25	the	the	DET
ejpam-4385	113	26	stock	stock	NOUN
ejpam-4385	113	27	price	price	NOUN
ejpam-4385	113	28	process	process	NOUN
ejpam-4385	113	29	evolve	evolve	VERB
ejpam-4385	113	30	as	as	ADP
ejpam-4385	113	31	dxs	dxs	PROPN
ejpam-4385	113	32	=	=	PROPN
ejpam-4385	113	33	rsxsds+	rsxsds+	PROPN
ejpam-4385	113	34	σ1xsdw	σ1xsdw	NOUN
ejpam-4385	113	35	p̃	p̃	PROPN
ejpam-4385	113	36	s	s	PROPN
ejpam-4385	113	37	,	,	PUNCT
ejpam-4385	113	38	(	(	PUNCT
ejpam-4385	113	39	20	20	NUM
ejpam-4385	113	40	)	)	PUNCT
ejpam-4385	113	41	s	s	PART
ejpam-4385	113	42	≥	≥	PROPN
ejpam-4385	113	43	t	t	PROPN
ejpam-4385	113	44	,	,	PUNCT
ejpam-4385	113	45	with	with	ADP
ejpam-4385	113	46	xt	xt	PROPN
ejpam-4385	114	1	=	=	PUNCT
ejpam-4385	114	2	x	x	X
ejpam-4385	114	3	>	>	X
ejpam-4385	114	4	0	0	PUNCT
ejpam-4385	114	5	and	and	CCONJ
ejpam-4385	114	6	w	w	PROPN
ejpam-4385	114	7	p̃	p̃	PROPN
ejpam-4385	114	8	t	t	PROPN
ejpam-4385	114	9	is	be	AUX
ejpam-4385	114	10	a	a	DET
ejpam-4385	114	11	brownian	brownian	ADJ
ejpam-4385	114	12	motion	motion	NOUN
ejpam-4385	114	13	under	under	ADP
ejpam-4385	114	14	p̃.	p̃.	NOUN
ejpam-4385	114	15	since	since	SCONJ
ejpam-4385	114	16	the	the	DET
ejpam-4385	114	17	price	price	NOUN
ejpam-4385	114	18	is	be	AUX
ejpam-4385	114	19	given	give	VERB
ejpam-4385	114	20	by	by	ADP
ejpam-4385	114	21	xs	xs	PROPN
ejpam-4385	114	22	=	=	SYM
ejpam-4385	114	23	xe	xe	PROPN
ejpam-4385	114	24	(	(	PUNCT
ejpam-4385	114	25	∫	∫	PROPN
ejpam-4385	114	26	s	s	PROPN
ejpam-4385	114	27	t	t	PROPN
ejpam-4385	114	28	rudu−	rudu−	VERB
ejpam-4385	114	29	1	1	NUM
ejpam-4385	114	30	2	2	NUM
ejpam-4385	114	31	σ2	σ2	NOUN
ejpam-4385	114	32	1(s−t)+σ1w	1(s−t)+σ1w	NUM
ejpam-4385	114	33	p̃	p̃	PROPN
ejpam-4385	114	34	s−t	s−t	NOUN
ejpam-4385	114	35	)	)	PUNCT
ejpam-4385	114	36	,	,	PUNCT
ejpam-4385	114	37	then	then	ADV
ejpam-4385	114	38	the	the	DET
ejpam-4385	114	39	discounted	discount	VERB
ejpam-4385	114	40	price	price	NOUN
ejpam-4385	114	41	given	give	VERB
ejpam-4385	114	42	by	by	ADP
ejpam-4385	114	43	e	e	PROPN
ejpam-4385	114	44	(	(	PUNCT
ejpam-4385	114	45	∫	∫	PROPN
ejpam-4385	114	46	s	s	PROPN
ejpam-4385	114	47	t	t	NOUN
ejpam-4385	114	48	rudu)xs	rudu)xs	NOUN
ejpam-4385	115	1	=	=	PROPN
ejpam-4385	115	2	xe	xe	PROPN
ejpam-4385	115	3	(	(	PUNCT
ejpam-4385	115	4	−	−	PROPN
ejpam-4385	115	5	1	1	NUM
ejpam-4385	115	6	2	2	NUM
ejpam-4385	115	7	σ2	σ2	NOUN
ejpam-4385	115	8	1(s−t)+σ1w	1(s−t)+σ1w	NUM
ejpam-4385	115	9	p̃	p̃	PROPN
ejpam-4385	115	10	s−t	s−t	NOUN
ejpam-4385	115	11	)	)	PUNCT
ejpam-4385	115	12	is	be	AUX
ejpam-4385	115	13	a	a	DET
ejpam-4385	115	14	martingale	martingale	NOUN
ejpam-4385	115	15	.	.	PUNCT
ejpam-4385	116	1	note	note	VERB
ejpam-4385	116	2	that	that	SCONJ
ejpam-4385	116	3	in	in	ADP
ejpam-4385	116	4	(	(	PUNCT
ejpam-4385	116	5	19	19	NUM
ejpam-4385	116	6	)	)	PUNCT
ejpam-4385	116	7	,	,	PUNCT
ejpam-4385	116	8	e	e	X
ejpam-4385	116	9	[	[	PUNCT
ejpam-4385	116	10	e−	e−	PROPN
ejpam-4385	116	11	∫	∫	PROPN
ejpam-4385	116	12	τ	τ	PROPN
ejpam-4385	116	13	0	0	PROPN
ejpam-4385	116	14	rudu	rudu	NOUN
ejpam-4385	116	15	]	]	PUNCT
ejpam-4385	116	16	is	be	AUX
ejpam-4385	116	17	the	the	DET
ejpam-4385	116	18	discounting	discount	VERB
ejpam-4385	116	19	factor	factor	NOUN
ejpam-4385	116	20	which	which	PRON
ejpam-4385	116	21	brings	bring	VERB
ejpam-4385	116	22	the	the	DET
ejpam-4385	116	23	payoff	payoff	NOUN
ejpam-4385	117	1	[	[	X
ejpam-4385	117	2	eµc(xt	eµc(xt	NOUN
ejpam-4385	117	3	−k)+|fτ	−k)+|fτ	PROPN
ejpam-4385	117	4	]	]	PUNCT
ejpam-4385	117	5	from	from	ADP
ejpam-4385	117	6	exercise	exercise	NOUN
ejpam-4385	117	7	date	date	NOUN
ejpam-4385	117	8	τ	τ	PROPN
ejpam-4385	117	9	to	to	ADP
ejpam-4385	117	10	time	time	NOUN
ejpam-4385	117	11	0	0	NUM
ejpam-4385	117	12	.	.	PUNCT
ejpam-4385	118	1	now	now	ADV
ejpam-4385	118	2	,	,	PUNCT
ejpam-4385	118	3	we	we	PRON
ejpam-4385	118	4	fix	fix	VERB
ejpam-4385	118	5	t	t	X
ejpam-4385	118	6	∈	∈	PROPN
ejpam-4385	119	1	[	[	X
ejpam-4385	119	2	0	0	NUM
ejpam-4385	119	3	,	,	PUNCT
ejpam-4385	119	4	t	t	X
ejpam-4385	119	5	]	]	PUNCT
ejpam-4385	119	6	.	.	PUNCT
ejpam-4385	120	1	we	we	PRON
ejpam-4385	120	2	want	want	VERB
ejpam-4385	120	3	to	to	PART
ejpam-4385	120	4	solve	solve	VERB
ejpam-4385	120	5	for	for	ADP
ejpam-4385	120	6	a	a	DET
ejpam-4385	120	7	general	general	ADJ
ejpam-4385	120	8	expression	expression	NOUN
ejpam-4385	120	9	for	for	ADP
ejpam-4385	120	10	the	the	DET
ejpam-4385	120	11	price	price	NOUN
ejpam-4385	120	12	of	of	ADP
ejpam-4385	120	13	the	the	DET
ejpam-4385	120	14	british	british	ADJ
ejpam-4385	120	15	call	call	NOUN
ejpam-4385	120	16	option	option	NOUN
ejpam-4385	120	17	at	at	ADP
ejpam-4385	120	18	any	any	DET
ejpam-4385	120	19	time	time	NOUN
ejpam-4385	120	20	t	t	NOUN
ejpam-4385	120	21	with	with	ADP
ejpam-4385	120	22	stock	stock	NOUN
ejpam-4385	120	23	price	price	NOUN
ejpam-4385	120	24	xt	xt	PUNCT
ejpam-4385	121	1	=	=	SYM
ejpam-4385	121	2	x	x	PUNCT
ejpam-4385	121	3	and	and	CCONJ
ejpam-4385	121	4	short	short	ADJ
ejpam-4385	121	5	rate	rate	NOUN
ejpam-4385	121	6	rt	rt	PROPN
ejpam-4385	121	7	=	=	PUNCT
ejpam-4385	121	8	r.	r.	PROPN
ejpam-4385	121	9	we	we	PRON
ejpam-4385	121	10	denote	denote	VERB
ejpam-4385	121	11	this	this	PRON
ejpam-4385	121	12	by	by	ADP
ejpam-4385	121	13	v	v	NOUN
ejpam-4385	121	14	(	(	PUNCT
ejpam-4385	121	15	t	t	PROPN
ejpam-4385	121	16	,	,	PUNCT
ejpam-4385	121	17	r	r	NOUN
ejpam-4385	121	18	,	,	PUNCT
ejpam-4385	121	19	x	x	NOUN
ejpam-4385	121	20	)	)	PUNCT
ejpam-4385	121	21	.	.	PUNCT
ejpam-4385	122	1	extending	extend	VERB
ejpam-4385	122	2	the	the	DET
ejpam-4385	122	3	argument	argument	NOUN
ejpam-4385	122	4	in	in	ADP
ejpam-4385	122	5	(	(	PUNCT
ejpam-4385	122	6	19	19	NUM
ejpam-4385	122	7	)	)	PUNCT
ejpam-4385	122	8	,	,	PUNCT
ejpam-4385	122	9	if	if	SCONJ
ejpam-4385	122	10	the	the	DET
ejpam-4385	122	11	exercise	exercise	NOUN
ejpam-4385	122	12	date	date	NOUN
ejpam-4385	122	13	is	be	AUX
ejpam-4385	122	14	at	at	ADP
ejpam-4385	122	15	any	any	DET
ejpam-4385	122	16	time	time	NOUN
ejpam-4385	122	17	t	t	X
ejpam-4385	122	18	∈	∈	PROPN
ejpam-4385	123	1	[	[	X
ejpam-4385	123	2	0	0	NUM
ejpam-4385	123	3	,	,	PUNCT
ejpam-4385	123	4	t	t	X
ejpam-4385	123	5	]	]	PUNCT
ejpam-4385	123	6	,	,	PUNCT
ejpam-4385	123	7	then	then	ADV
ejpam-4385	123	8	using	use	VERB
ejpam-4385	123	9	(	(	PUNCT
ejpam-4385	123	10	16	16	NUM
ejpam-4385	123	11	)	)	PUNCT
ejpam-4385	123	12	and	and	CCONJ
ejpam-4385	123	13	the	the	DET
ejpam-4385	123	14	optimal	optimal	ADJ
ejpam-4385	123	15	sampling	sampling	NOUN
ejpam-4385	123	16	theorem	theorem	NOUN
ejpam-4385	123	17	,	,	PUNCT
ejpam-4385	123	18	we	we	PRON
ejpam-4385	123	19	have	have	VERB
ejpam-4385	123	20	v	v	NUM
ejpam-4385	123	21	(	(	PUNCT
ejpam-4385	123	22	t	t	PROPN
ejpam-4385	123	23	,	,	PUNCT
ejpam-4385	123	24	r	r	NOUN
ejpam-4385	123	25	,	,	PUNCT
ejpam-4385	123	26	xt	xt	ADJ
ejpam-4385	123	27	)	)	PUNCT
ejpam-4385	124	1	=	=	SYM
ejpam-4385	124	2	sup	sup	NOUN
ejpam-4385	124	3	0≤τ≤t−t	0≤τ≤t−t	NUM
ejpam-4385	124	4	ẽt	ẽt	NOUN
ejpam-4385	124	5	,	,	PUNCT
ejpam-4385	124	6	x	x	X
ejpam-4385	124	7	[	[	PUNCT
ejpam-4385	124	8	e−	e−	X
ejpam-4385	124	9	∫	∫	PROPN
ejpam-4385	124	10	t+τ	t+τ	NUM
ejpam-4385	124	11	t	t	PROPN
ejpam-4385	124	12	rudugµc(t+	rudugµc(t+	VERB
ejpam-4385	124	13	τ	τ	PROPN
ejpam-4385	124	14	,	,	PUNCT
ejpam-4385	124	15	xt+τ	xt+τ	PROPN
ejpam-4385	124	16	)	)	PUNCT
ejpam-4385	124	17	|fτ	|fτ	NUM
ejpam-4385	124	18	]	]	PUNCT
ejpam-4385	124	19	,	,	PUNCT
ejpam-4385	124	20	(	(	PUNCT
ejpam-4385	124	21	21	21	NUM
ejpam-4385	124	22	)	)	PUNCT
ejpam-4385	124	23	where	where	SCONJ
ejpam-4385	124	24	the	the	DET
ejpam-4385	124	25	supremum	supremum	NOUN
ejpam-4385	124	26	is	be	AUX
ejpam-4385	124	27	taken	take	VERB
ejpam-4385	124	28	over	over	ADP
ejpam-4385	124	29	all	all	PRON
ejpam-4385	124	30	stopping	stop	VERB
ejpam-4385	124	31	times	time	NOUN
ejpam-4385	124	32	τ	τ	PROPN
ejpam-4385	124	33	∈	∈	PROPN
ejpam-4385	125	1	[	[	X
ejpam-4385	125	2	0	0	NUM
ejpam-4385	125	3	,	,	PUNCT
ejpam-4385	125	4	t	t	PROPN
ejpam-4385	125	5	−	−	PROPN
ejpam-4385	125	6	t	t	PROPN
ejpam-4385	125	7	]	]	PUNCT
ejpam-4385	125	8	of	of	ADP
ejpam-4385	125	9	x	x	X
ejpam-4385	125	10	and	and	CCONJ
ejpam-4385	125	11	ẽt	ẽt	NOUN
ejpam-4385	125	12	,	,	PUNCT
ejpam-4385	125	13	x	x	PRON
ejpam-4385	125	14	is	be	AUX
ejpam-4385	125	15	taken	take	VERB
ejpam-4385	125	16	with	with	ADP
ejpam-4385	125	17	respect	respect	NOUN
ejpam-4385	125	18	to	to	ADP
ejpam-4385	125	19	the	the	DET
ejpam-4385	125	20	(	(	PUNCT
ejpam-4385	125	21	unique	unique	ADJ
ejpam-4385	125	22	)	)	PUNCT
ejpam-4385	125	23	equivalent	equivalent	ADJ
ejpam-4385	125	24	martingale	martingale	NOUN
ejpam-4385	125	25	measure	measure	NOUN
ejpam-4385	125	26	p̃t	p̃t	NOUN
ejpam-4385	125	27	,	,	PUNCT
ejpam-4385	125	28	x	x	VERB
ejpam-4385	125	29	under	under	ADP
ejpam-4385	125	30	which	which	PRON
ejpam-4385	125	31	xt	xt	ADP
ejpam-4385	125	32	=	=	SYM
ejpam-4385	125	33	x	x	X
ejpam-4385	125	34	and	and	CCONJ
ejpam-4385	125	35	rt	rt	PROPN
ejpam-4385	125	36	∈	∈	PROPN
ejpam-4385	125	37	r.	r.	PROPN
ejpam-4385	125	38	note	note	VERB
ejpam-4385	126	1	that	that	SCONJ
ejpam-4385	126	2	v	v	X
ejpam-4385	126	3	(	(	PUNCT
ejpam-4385	126	4	0	0	NUM
ejpam-4385	126	5	,	,	PUNCT
ejpam-4385	126	6	r0	r0	NOUN
ejpam-4385	126	7	,	,	PUNCT
ejpam-4385	126	8	x	x	NOUN
ejpam-4385	126	9	)	)	PUNCT
ejpam-4385	126	10	=	=	SYM
ejpam-4385	126	11	v	v	NOUN
ejpam-4385	126	12	.	.	PUNCT
ejpam-4385	127	1	since	since	SCONJ
ejpam-4385	127	2	the	the	DET
ejpam-4385	127	3	supremum	supremum	NOUN
ejpam-4385	127	4	in	in	ADP
ejpam-4385	127	5	(	(	PUNCT
ejpam-4385	127	6	21	21	NUM
ejpam-4385	127	7	)	)	PUNCT
ejpam-4385	127	8	is	be	AUX
ejpam-4385	127	9	attained	attain	VERB
ejpam-4385	127	10	in	in	ADP
ejpam-4385	127	11	the	the	DET
ejpam-4385	127	12	first	first	ADJ
ejpam-4385	127	13	entry	entry	NOUN
ejpam-4385	127	14	time	time	NOUN
ejpam-4385	127	15	of	of	ADP
ejpam-4385	127	16	x	x	PUNCT
ejpam-4385	127	17	to	to	ADP
ejpam-4385	127	18	the	the	DET
ejpam-4385	127	19	closed	closed	ADJ
ejpam-4385	127	20	set	set	NOUN
ejpam-4385	127	21	where	where	SCONJ
ejpam-4385	127	22	v	v	NOUN
ejpam-4385	127	23	=	=	SYM
ejpam-4385	127	24	gµc	gµc	NOUN
ejpam-4385	127	25	and	and	CCONJ
ejpam-4385	127	26	law(x(µ)|p	law(x(µ)|p	PROPN
ejpam-4385	127	27	)	)	PUNCT
ejpam-4385	127	28	is	be	AUX
ejpam-4385	127	29	the	the	DET
ejpam-4385	127	30	same	same	ADJ
ejpam-4385	127	31	as	as	ADP
ejpam-4385	127	32	law(x(rt)|p̃	law(x(rt)|p̃	PROPN
ejpam-4385	127	33	)	)	PUNCT
ejpam-4385	127	34	,	,	PUNCT
ejpam-4385	127	35	then	then	ADV
ejpam-4385	127	36	from	from	ADP
ejpam-4385	127	37	the	the	DET
ejpam-4385	127	38	well	well	ADV
ejpam-4385	127	39	-	-	PUNCT
ejpam-4385	127	40	known	know	VERB
ejpam-4385	127	41	structure	structure	NOUN
ejpam-4385	127	42	of	of	ADP
ejpam-4385	127	43	the	the	DET
ejpam-4385	127	44	geometric	geometric	ADJ
ejpam-4385	127	45	brownian	brownian	ADJ
ejpam-4385	127	46	motion	motion	NOUN
ejpam-4385	127	47	x	x	NOUN
ejpam-4385	127	48	,	,	PUNCT
ejpam-4385	127	49	v	v	PROPN
ejpam-4385	127	50	(	(	PUNCT
ejpam-4385	127	51	t	t	PROPN
ejpam-4385	127	52	,	,	PUNCT
ejpam-4385	127	53	r	r	NOUN
ejpam-4385	127	54	,	,	PUNCT
ejpam-4385	127	55	x	x	NOUN
ejpam-4385	127	56	)	)	PUNCT
ejpam-4385	128	1	=	=	SYM
ejpam-4385	128	2	sup	sup	NOUN
ejpam-4385	128	3	0≤τ≤t−t	0≤τ≤t−t	PROPN
ejpam-4385	128	4	e	e	NOUN
ejpam-4385	128	5	[	[	PUNCT
ejpam-4385	128	6	e−	e−	PROPN
ejpam-4385	128	7	∫	∫	PROPN
ejpam-4385	128	8	t+τ	t+τ	NUM
ejpam-4385	128	9	t	t	PROPN
ejpam-4385	128	10	rudugµc(t+	rudugµc(t+	VERB
ejpam-4385	128	11	τ	τ	PROPN
ejpam-4385	128	12	,	,	PUNCT
ejpam-4385	128	13	xxτ	xxτ	PROPN
ejpam-4385	128	14	)	)	PUNCT
ejpam-4385	128	15	|xt	|xt	X
ejpam-4385	128	16	=	=	SYM
ejpam-4385	128	17	x	x	NOUN
ejpam-4385	128	18	,	,	PUNCT
ejpam-4385	128	19	rt	rt	PROPN
ejpam-4385	128	20	=	=	SYM
ejpam-4385	128	21	r	r	NOUN
ejpam-4385	128	22	]	]	PUNCT
ejpam-4385	128	23	,	,	PUNCT
ejpam-4385	128	24	(	(	PUNCT
ejpam-4385	128	25	22	22	NUM
ejpam-4385	128	26	)	)	PUNCT
ejpam-4385	128	27	k.	k.	NOUN
ejpam-4385	128	28	falcasantos	falcasantos	PROPN
ejpam-4385	128	29	,	,	PUNCT
ejpam-4385	128	30	f.	f.	PROPN
ejpam-4385	128	31	sumalpong	sumalpong	PROPN
ejpam-4385	128	32	/	/	SYM
ejpam-4385	128	33	eur	eur	PROPN
ejpam-4385	128	34	.	.	PUNCT
ejpam-4385	129	1	j.	j.	PROPN
ejpam-4385	129	2	pure	pure	PROPN
ejpam-4385	129	3	appl	appl	PROPN
ejpam-4385	129	4	.	.	PROPN
ejpam-4385	129	5	math	math	PROPN
ejpam-4385	129	6	,	,	PUNCT
ejpam-4385	129	7	15	15	NUM
ejpam-4385	129	8	(	(	PUNCT
ejpam-4385	129	9	3	3	NUM
ejpam-4385	129	10	)	)	PUNCT
ejpam-4385	129	11	(	(	PUNCT
ejpam-4385	129	12	2022	2022	NUM
ejpam-4385	129	13	)	)	PUNCT
ejpam-4385	129	14	,	,	PUNCT
ejpam-4385	129	15	948	948	NUM
ejpam-4385	129	16	-	-	SYM
ejpam-4385	129	17	970	970	NUM
ejpam-4385	129	18	954	954	NUM
ejpam-4385	129	19	where	where	SCONJ
ejpam-4385	129	20	the	the	DET
ejpam-4385	129	21	process	process	NOUN
ejpam-4385	129	22	x	x	X
ejpam-4385	129	23	=	=	SYM
ejpam-4385	129	24	(	(	PUNCT
ejpam-4385	129	25	xt(t	xt(t	PROPN
ejpam-4385	129	26	,	,	PUNCT
ejpam-4385	129	27	rt))t∈[0,t	rt))t∈[0,t	PROPN
ejpam-4385	129	28	]	]	PUNCT
ejpam-4385	129	29	under	under	ADP
ejpam-4385	129	30	p	p	PROPN
ejpam-4385	129	31	evolves	evolve	NOUN
ejpam-4385	129	32	as	as	ADP
ejpam-4385	129	33	dxt	dxt	PROPN
ejpam-4385	129	34	=	=	PROPN
ejpam-4385	129	35	rtxtdt+	rtxtdt+	X
ejpam-4385	129	36	σ1xtdwt	σ1xtdwt	PROPN
ejpam-4385	129	37	(	(	PUNCT
ejpam-4385	129	38	x0	x0	PROPN
ejpam-4385	129	39	=	=	SYM
ejpam-4385	129	40	1	1	NUM
ejpam-4385	129	41	)	)	PUNCT
ejpam-4385	129	42	.	.	PUNCT
ejpam-4385	130	1	(	(	PUNCT
ejpam-4385	130	2	23	23	NUM
ejpam-4385	130	3	)	)	PUNCT
ejpam-4385	130	4	moreover	moreover	ADV
ejpam-4385	130	5	,	,	PUNCT
ejpam-4385	130	6	the	the	DET
ejpam-4385	130	7	british	british	ADJ
ejpam-4385	130	8	call	call	NOUN
ejpam-4385	130	9	option	option	NOUN
ejpam-4385	130	10	at	at	ADP
ejpam-4385	130	11	maturity	maturity	NOUN
ejpam-4385	130	12	time	time	NOUN
ejpam-4385	130	13	t	t	PROPN
ejpam-4385	130	14	is	be	AUX
ejpam-4385	130	15	given	give	VERB
ejpam-4385	130	16	by	by	ADP
ejpam-4385	130	17	v	v	PROPN
ejpam-4385	130	18	(	(	PUNCT
ejpam-4385	130	19	t	t	PROPN
ejpam-4385	130	20	,	,	PUNCT
ejpam-4385	130	21	rt	rt	PROPN
ejpam-4385	130	22	,	,	PUNCT
ejpam-4385	130	23	xt	xt	PROPN
ejpam-4385	130	24	)	)	PUNCT
ejpam-4385	131	1	=	=	PUNCT
ejpam-4385	131	2	gµc(t	gµc(t	PROPN
ejpam-4385	131	3	,	,	PUNCT
ejpam-4385	131	4	xt	xt	X
ejpam-4385	131	5	)	)	PUNCT
ejpam-4385	132	1	=	=	PUNCT
ejpam-4385	132	2	e(xt	e(xt	PROPN
ejpam-4385	132	3	−k)+	−k)+	NUM
ejpam-4385	132	4	.	.	PUNCT
ejpam-4385	133	1	(	(	PUNCT
ejpam-4385	133	2	24	24	NUM
ejpam-4385	133	3	)	)	PUNCT
ejpam-4385	133	4	this	this	PRON
ejpam-4385	133	5	implies	imply	VERB
ejpam-4385	133	6	that	that	SCONJ
ejpam-4385	133	7	the	the	DET
ejpam-4385	133	8	price	price	NOUN
ejpam-4385	133	9	of	of	ADP
ejpam-4385	133	10	the	the	DET
ejpam-4385	133	11	british	british	ADJ
ejpam-4385	133	12	call	call	NOUN
ejpam-4385	133	13	option	option	NOUN
ejpam-4385	133	14	at	at	ADP
ejpam-4385	133	15	maturity	maturity	NOUN
ejpam-4385	133	16	time	time	NOUN
ejpam-4385	133	17	t	t	PROPN
ejpam-4385	133	18	coincides	coincide	VERB
ejpam-4385	133	19	with	with	ADP
ejpam-4385	133	20	the	the	DET
ejpam-4385	133	21	payoff	payoff	NOUN
ejpam-4385	133	22	of	of	ADP
ejpam-4385	133	23	the	the	DET
ejpam-4385	133	24	european	european	ADJ
ejpam-4385	133	25	call	call	NOUN
ejpam-4385	133	26	option	option	NOUN
ejpam-4385	133	27	whose	whose	DET
ejpam-4385	133	28	stock	stock	NOUN
ejpam-4385	133	29	dynamics	dynamic	NOUN
ejpam-4385	133	30	follows	follow	VERB
ejpam-4385	133	31	the	the	DET
ejpam-4385	133	32	stochastic	stochastic	ADJ
ejpam-4385	133	33	differential	differential	ADJ
ejpam-4385	133	34	equation	equation	NOUN
ejpam-4385	133	35	(	(	PUNCT
ejpam-4385	133	36	20	20	NUM
ejpam-4385	133	37	)	)	PUNCT
ejpam-4385	133	38	above	above	ADV
ejpam-4385	133	39	.	.	PUNCT
ejpam-4385	134	1	let	let	VERB
ejpam-4385	134	2	grt(t	grt(t	NOUN
ejpam-4385	134	3	,	,	PUNCT
ejpam-4385	134	4	x	x	NOUN
ejpam-4385	134	5	)	)	PUNCT
ejpam-4385	134	6	=	=	NUM
ejpam-4385	134	7	e(xt	e(xt	PROPN
ejpam-4385	134	8	−k)+	−k)+	NOUN
ejpam-4385	134	9	,	,	PUNCT
ejpam-4385	134	10	where	where	SCONJ
ejpam-4385	134	11	x	x	PRON
ejpam-4385	134	12	follows	follow	VERB
ejpam-4385	134	13	(	(	PUNCT
ejpam-4385	134	14	20	20	NUM
ejpam-4385	134	15	)	)	PUNCT
ejpam-4385	134	16	with	with	ADP
ejpam-4385	134	17	xt	xt	PROPN
ejpam-4385	135	1	=	=	PUNCT
ejpam-4385	135	2	x.	x.	NOUN
ejpam-4385	135	3	thus	thus	ADV
ejpam-4385	135	4	v	v	X
ejpam-4385	135	5	(	(	PUNCT
ejpam-4385	135	6	t	t	PROPN
ejpam-4385	135	7	,	,	PUNCT
ejpam-4385	135	8	rt	rt	PROPN
ejpam-4385	135	9	,	,	PUNCT
ejpam-4385	135	10	xt	xt	PROPN
ejpam-4385	135	11	)	)	PUNCT
ejpam-4385	136	1	=	=	PUNCT
ejpam-4385	136	2	grt(t	grt(t	PROPN
ejpam-4385	136	3	,	,	PUNCT
ejpam-4385	136	4	x	x	NOUN
ejpam-4385	136	5	)	)	PUNCT
ejpam-4385	136	6	.	.	PUNCT
ejpam-4385	137	1	note	note	VERB
ejpam-4385	137	2	that	that	SCONJ
ejpam-4385	137	3	when	when	SCONJ
ejpam-4385	137	4	the	the	DET
ejpam-4385	137	5	interest	interest	NOUN
ejpam-4385	137	6	rate	rate	NOUN
ejpam-4385	137	7	is	be	AUX
ejpam-4385	137	8	constant	constant	ADJ
ejpam-4385	137	9	(	(	PUNCT
ejpam-4385	137	10	rt	rt	NOUN
ejpam-4385	137	11	=	=	SYM
ejpam-4385	137	12	r	r	NOUN
ejpam-4385	137	13	for	for	ADP
ejpam-4385	137	14	all	all	DET
ejpam-4385	137	15	t	t	NOUN
ejpam-4385	137	16	∈	∈	PROPN
ejpam-4385	138	1	[	[	X
ejpam-4385	138	2	0	0	NUM
ejpam-4385	138	3	,	,	PUNCT
ejpam-4385	138	4	t	t	X
ejpam-4385	138	5	]	]	PUNCT
ejpam-4385	138	6	)	)	PUNCT
ejpam-4385	138	7	,	,	PUNCT
ejpam-4385	138	8	i.e.	i.e.	X
ejpam-4385	138	9	,	,	PUNCT
ejpam-4385	138	10	the	the	DET
ejpam-4385	138	11	coefficients	coefficient	NOUN
ejpam-4385	138	12	a	a	PRON
ejpam-4385	138	13	and	and	CCONJ
ejpam-4385	138	14	σ2	σ2	NOUN
ejpam-4385	138	15	in	in	ADP
ejpam-4385	138	16	equation	equation	NOUN
ejpam-4385	138	17	(	(	PUNCT
ejpam-4385	138	18	3	3	X
ejpam-4385	138	19	)	)	PUNCT
ejpam-4385	138	20	are	be	AUX
ejpam-4385	138	21	all	all	ADV
ejpam-4385	138	22	equal	equal	ADJ
ejpam-4385	138	23	to	to	ADP
ejpam-4385	138	24	zero	zero	NUM
ejpam-4385	138	25	,	,	PUNCT
ejpam-4385	138	26	then	then	ADV
ejpam-4385	138	27	the	the	DET
ejpam-4385	138	28	expression	expression	NOUN
ejpam-4385	138	29	for	for	ADP
ejpam-4385	138	30	grt(t	grt(t	PROPN
ejpam-4385	138	31	,	,	PUNCT
ejpam-4385	138	32	x	x	NOUN
ejpam-4385	138	33	)	)	PUNCT
ejpam-4385	138	34	multiplied	multiply	VERB
ejpam-4385	138	35	by	by	ADP
ejpam-4385	138	36	e−r(t−t	e−r(t−t	NOUN
ejpam-4385	138	37	)	)	PUNCT
ejpam-4385	138	38	coincides	coincide	VERB
ejpam-4385	138	39	with	with	ADP
ejpam-4385	138	40	the	the	DET
ejpam-4385	138	41	black	black	ADJ
ejpam-4385	138	42	-	-	PUNCT
ejpam-4385	138	43	scholes	schole	NOUN
ejpam-4385	138	44	formula	formula	NOUN
ejpam-4385	138	45	for	for	ADP
ejpam-4385	138	46	the	the	DET
ejpam-4385	138	47	arbitrage	arbitrage	NOUN
ejpam-4385	138	48	-	-	PUNCT
ejpam-4385	138	49	free	free	ADJ
ejpam-4385	138	50	price	price	NOUN
ejpam-4385	138	51	of	of	ADP
ejpam-4385	138	52	the	the	DET
ejpam-4385	138	53	european	european	ADJ
ejpam-4385	138	54	call	call	NOUN
ejpam-4385	138	55	option	option	NOUN
ejpam-4385	138	56	at	at	ADP
ejpam-4385	138	57	time	time	NOUN
ejpam-4385	138	58	t	t	NOUN
ejpam-4385	138	59	with	with	ADP
ejpam-4385	138	60	maturity	maturity	NOUN
ejpam-4385	138	61	time	time	NOUN
ejpam-4385	138	62	t	t	PROPN
ejpam-4385	138	63	.	.	PUNCT
ejpam-4385	139	1	we	we	PRON
ejpam-4385	139	2	can	can	AUX
ejpam-4385	139	3	directly	directly	ADV
ejpam-4385	139	4	see	see	VERB
ejpam-4385	139	5	from	from	ADP
ejpam-4385	139	6	(	(	PUNCT
ejpam-4385	139	7	17	17	NUM
ejpam-4385	139	8	)	)	PUNCT
ejpam-4385	139	9	that	that	SCONJ
ejpam-4385	139	10	x	x	X
ejpam-4385	139	11	7→	7→	NUM
ejpam-4385	139	12	gµc(t	gµc(t	NOUN
ejpam-4385	139	13	,	,	PUNCT
ejpam-4385	139	14	x	x	PRON
ejpam-4385	139	15	)	)	PUNCT
ejpam-4385	139	16	is	be	AUX
ejpam-4385	139	17	convex	convex	ADJ
ejpam-4385	139	18	.	.	PUNCT
ejpam-4385	140	1	to	to	PART
ejpam-4385	140	2	clearly	clearly	ADV
ejpam-4385	140	3	verify	verify	VERB
ejpam-4385	140	4	this	this	PRON
ejpam-4385	140	5	,	,	PUNCT
ejpam-4385	140	6	we	we	PRON
ejpam-4385	140	7	present	present	VERB
ejpam-4385	140	8	the	the	DET
ejpam-4385	140	9	proposition	proposition	NOUN
ejpam-4385	140	10	below	below	ADV
ejpam-4385	140	11	.	.	PUNCT
ejpam-4385	141	1	proposition	proposition	NOUN
ejpam-4385	141	2	1	1	NUM
ejpam-4385	141	3	.	.	X
ejpam-4385	142	1	for	for	ADP
ejpam-4385	142	2	any	any	DET
ejpam-4385	142	3	t	t	NOUN
ejpam-4385	142	4	∈	∈	PROPN
ejpam-4385	143	1	[	[	X
ejpam-4385	143	2	0	0	NUM
ejpam-4385	143	3	,	,	PUNCT
ejpam-4385	143	4	t	t	NOUN
ejpam-4385	143	5	]	]	PUNCT
ejpam-4385	143	6	given	give	VERB
ejpam-4385	143	7	and	and	CCONJ
ejpam-4385	143	8	fixed	fix	VERB
ejpam-4385	143	9	,	,	PUNCT
ejpam-4385	143	10	the	the	DET
ejpam-4385	143	11	mapping	mapping	NOUN
ejpam-4385	143	12	x	x	SYM
ejpam-4385	143	13	7→	7→	NUM
ejpam-4385	143	14	gµc(t	gµc(t	NOUN
ejpam-4385	143	15	,	,	PUNCT
ejpam-4385	143	16	x	x	NOUN
ejpam-4385	143	17	)	)	PUNCT
ejpam-4385	143	18	(	(	PUNCT
ejpam-4385	143	19	25	25	NUM
ejpam-4385	143	20	)	)	PUNCT
ejpam-4385	143	21	is	be	AUX
ejpam-4385	143	22	convex	convex	ADJ
ejpam-4385	143	23	on	on	ADP
ejpam-4385	143	24	(	(	PUNCT
ejpam-4385	143	25	0,∞	0,∞	NUM
ejpam-4385	143	26	)	)	PUNCT
ejpam-4385	143	27	.	.	PUNCT
ejpam-4385	144	1	proof	proof	NOUN
ejpam-4385	144	2	.	.	PUNCT
ejpam-4385	145	1	let	let	VERB
ejpam-4385	145	2	t	t	PROPN
ejpam-4385	145	3	∈	∈	PROPN
ejpam-4385	146	1	[	[	X
ejpam-4385	146	2	0	0	NUM
ejpam-4385	146	3	,	,	PUNCT
ejpam-4385	146	4	t	t	PROPN
ejpam-4385	146	5	]	]	PUNCT
ejpam-4385	146	6	be	be	AUX
ejpam-4385	146	7	given	give	VERB
ejpam-4385	146	8	and	and	CCONJ
ejpam-4385	146	9	fixed	fix	VERB
ejpam-4385	146	10	.	.	PUNCT
ejpam-4385	147	1	moreover	moreover	ADV
ejpam-4385	147	2	,	,	PUNCT
ejpam-4385	147	3	let	let	VERB
ejpam-4385	147	4	0	0	NUM
ejpam-4385	147	5	≤	≤	NUM
ejpam-4385	148	1	λ	λ	X
ejpam-4385	148	2	≤	≤	NUM
ejpam-4385	148	3	1	1	NUM
ejpam-4385	148	4	and	and	CCONJ
ejpam-4385	148	5	x2	x2	PRON
ejpam-4385	148	6	=	=	PUNCT
ejpam-4385	149	1	λx1	λx1	X
ejpam-4385	150	1	+	+	PUNCT
ejpam-4385	151	1	(	(	PUNCT
ejpam-4385	151	2	1−	1−	NUM
ejpam-4385	151	3	λ)x3	λ)x3	PROPN
ejpam-4385	151	4	for	for	ADP
ejpam-4385	151	5	some	some	DET
ejpam-4385	151	6	x1	x1	PROPN
ejpam-4385	151	7	,	,	PUNCT
ejpam-4385	151	8	x2	x2	PROPN
ejpam-4385	151	9	,	,	PUNCT
ejpam-4385	151	10	x3	x3	PROPN
ejpam-4385	151	11	∈	∈	PROPN
ejpam-4385	151	12	(	(	PUNCT
ejpam-4385	151	13	0,∞	0,∞	NOUN
ejpam-4385	151	14	)	)	PUNCT
ejpam-4385	151	15	with	with	ADP
ejpam-4385	151	16	x1	x1	PROPN
ejpam-4385	151	17	<	<	X
ejpam-4385	151	18	x3	x3	PROPN
ejpam-4385	151	19	.	.	PUNCT
ejpam-4385	152	1	then	then	ADV
ejpam-4385	152	2	,	,	PUNCT
ejpam-4385	152	3	we	we	PRON
ejpam-4385	152	4	have	have	VERB
ejpam-4385	152	5	gµc(t	gµc(t	PROPN
ejpam-4385	152	6	,	,	PUNCT
ejpam-4385	152	7	x2	x2	PROPN
ejpam-4385	152	8	)	)	PUNCT
ejpam-4385	153	1	=	=	SYM
ejpam-4385	153	2	gµc(t	gµc(t	NOUN
ejpam-4385	153	3	,	,	PUNCT
ejpam-4385	153	4	λx1	λx1	X
ejpam-4385	153	5	+	+	CCONJ
ejpam-4385	153	6	(	(	PUNCT
ejpam-4385	153	7	1−	1−	NUM
ejpam-4385	153	8	λ)x3	λ)x3	PROPN
ejpam-4385	153	9	)	)	PUNCT
ejpam-4385	153	10	=	=	SYM
ejpam-4385	154	1	eµc	eµc	PROPN
ejpam-4385	155	1	[	[	X
ejpam-4385	155	2	(	(	PUNCT
ejpam-4385	155	3	λx1z	λx1z	X
ejpam-4385	155	4	µc	µc	INTJ
ejpam-4385	155	5	t	t	PROPN
ejpam-4385	155	6	,	,	PUNCT
ejpam-4385	155	7	t	t	PROPN
ejpam-4385	155	8	+	+	CCONJ
ejpam-4385	155	9	(	(	PUNCT
ejpam-4385	155	10	1−	1−	NUM
ejpam-4385	155	11	λ)x3z	λ)x3z	PROPN
ejpam-4385	155	12	µc	µc	PROPN
ejpam-4385	155	13	t	t	PROPN
ejpam-4385	155	14	,	,	PUNCT
ejpam-4385	155	15	t	t	PROPN
ejpam-4385	155	16	−k	−k	PROPN
ejpam-4385	155	17	)	)	PUNCT
ejpam-4385	156	1	+	+	CCONJ
ejpam-4385	156	2	|	|	ADV
ejpam-4385	156	3	xt	xt	X
ejpam-4385	156	4	=	=	SYM
ejpam-4385	156	5	x2	x2	PROPN
ejpam-4385	156	6	]	]	PUNCT
ejpam-4385	157	1	=	=	PUNCT
ejpam-4385	157	2	eµc	eµc	PROPN
ejpam-4385	157	3	[	[	PUNCT
ejpam-4385	157	4	(	(	PUNCT
ejpam-4385	157	5	λx1z	λx1z	X
ejpam-4385	157	6	µc	µc	INTJ
ejpam-4385	157	7	t	t	PROPN
ejpam-4385	157	8	,	,	PUNCT
ejpam-4385	157	9	t	t	PROPN
ejpam-4385	157	10	+	+	CCONJ
ejpam-4385	157	11	(	(	PUNCT
ejpam-4385	157	12	1−	1−	NUM
ejpam-4385	157	13	λ)x3z	λ)x3z	PROPN
ejpam-4385	157	14	µc	µc	PROPN
ejpam-4385	157	15	t	t	PROPN
ejpam-4385	157	16	,	,	PUNCT
ejpam-4385	157	17	t	t	PROPN
ejpam-4385	157	18	−	−	PROPN
ejpam-4385	157	19	(	(	PUNCT
ejpam-4385	157	20	λk	λk	X
ejpam-4385	157	21	+	+	CCONJ
ejpam-4385	157	22	(	(	PUNCT
ejpam-4385	157	23	1−	1−	NUM
ejpam-4385	157	24	λ)k	λ)k	NUM
ejpam-4385	157	25	)	)	PUNCT
ejpam-4385	157	26	)	)	PUNCT
ejpam-4385	158	1	+	+	CCONJ
ejpam-4385	158	2	|	|	ADV
ejpam-4385	158	3	xt	xt	X
ejpam-4385	158	4	=	=	SYM
ejpam-4385	158	5	x2	x2	PROPN
ejpam-4385	158	6	]	]	PUNCT
ejpam-4385	159	1	=	=	PUNCT
ejpam-4385	159	2	eµc	eµc	PROPN
ejpam-4385	159	3	[	[	PUNCT
ejpam-4385	159	4	(	(	PUNCT
ejpam-4385	159	5	λx1z	λx1z	X
ejpam-4385	159	6	µc	µc	INTJ
ejpam-4385	159	7	t	t	PROPN
ejpam-4385	159	8	,	,	PUNCT
ejpam-4385	159	9	t	t	PROPN
ejpam-4385	159	10	+	+	CCONJ
ejpam-4385	159	11	(	(	PUNCT
ejpam-4385	159	12	1−	1−	NUM
ejpam-4385	159	13	λ)x3z	λ)x3z	PROPN
ejpam-4385	159	14	µc	µc	PROPN
ejpam-4385	159	15	t	t	PROPN
ejpam-4385	159	16	,	,	PUNCT
ejpam-4385	159	17	t	t	PROPN
ejpam-4385	159	18	−	−	PROPN
ejpam-4385	159	19	λk	λk	INTJ
ejpam-4385	159	20	−	−	PROPN
ejpam-4385	159	21	(	(	PUNCT
ejpam-4385	159	22	1−	1−	NUM
ejpam-4385	159	23	λ)k	λ)k	PUNCT
ejpam-4385	159	24	)	)	PUNCT
ejpam-4385	160	1	+	+	CCONJ
ejpam-4385	160	2	|	|	ADV
ejpam-4385	160	3	xt	xt	X
ejpam-4385	160	4	=	=	SYM
ejpam-4385	160	5	x2	x2	PROPN
ejpam-4385	160	6	]	]	PUNCT
ejpam-4385	161	1	=	=	PUNCT
ejpam-4385	161	2	eµc	eµc	PROPN
ejpam-4385	161	3	[	[	PUNCT
ejpam-4385	161	4	(	(	PUNCT
ejpam-4385	161	5	λx1z	λx1z	X
ejpam-4385	161	6	µc	µc	INTJ
ejpam-4385	161	7	t	t	PROPN
ejpam-4385	161	8	,	,	PUNCT
ejpam-4385	161	9	t	t	NOUN
ejpam-4385	161	10	−	−	PROPN
ejpam-4385	161	11	λk	λk	X
ejpam-4385	162	1	+	+	CCONJ
ejpam-4385	162	2	(	(	PUNCT
ejpam-4385	162	3	1−	1−	NUM
ejpam-4385	162	4	λ)x3z	λ)x3z	PROPN
ejpam-4385	162	5	µc	µc	PROPN
ejpam-4385	162	6	t	t	PROPN
ejpam-4385	162	7	,	,	PUNCT
ejpam-4385	162	8	t	t	NOUN
ejpam-4385	162	9	−	−	PROPN
ejpam-4385	162	10	(	(	PUNCT
ejpam-4385	162	11	1−	1−	NUM
ejpam-4385	162	12	λ)k	λ)k	PUNCT
ejpam-4385	162	13	)	)	PUNCT
ejpam-4385	163	1	+	+	CCONJ
ejpam-4385	163	2	|	|	ADV
ejpam-4385	163	3	xt	xt	X
ejpam-4385	163	4	=	=	SYM
ejpam-4385	163	5	x2	x2	PROPN
ejpam-4385	163	6	]	]	PUNCT
ejpam-4385	164	1	=	=	PUNCT
ejpam-4385	164	2	eµc	eµc	PROPN
ejpam-4385	164	3	[	[	X
ejpam-4385	164	4	(	(	PUNCT
ejpam-4385	164	5	(	(	PUNCT
ejpam-4385	164	6	λx1z	λx1z	X
ejpam-4385	164	7	µc	µc	INTJ
ejpam-4385	164	8	t	t	PROPN
ejpam-4385	164	9	,	,	PUNCT
ejpam-4385	164	10	t	t	PROPN
ejpam-4385	164	11	−	−	PROPN
ejpam-4385	164	12	λk	λk	NOUN
ejpam-4385	164	13	)	)	PUNCT
ejpam-4385	164	14	+	+	CCONJ
ejpam-4385	164	15	(	(	PUNCT
ejpam-4385	164	16	(	(	PUNCT
ejpam-4385	164	17	1−	1−	NUM
ejpam-4385	164	18	λ)x3z	λ)x3z	PROPN
ejpam-4385	164	19	µc	µc	PROPN
ejpam-4385	164	20	t	t	PROPN
ejpam-4385	164	21	,	,	PUNCT
ejpam-4385	164	22	t	t	NOUN
ejpam-4385	164	23	−	−	PROPN
ejpam-4385	164	24	(	(	PUNCT
ejpam-4385	164	25	1−	1−	NUM
ejpam-4385	164	26	λ)k	λ)k	NUM
ejpam-4385	164	27	)	)	PUNCT
ejpam-4385	164	28	)	)	PUNCT
ejpam-4385	165	1	+	+	CCONJ
ejpam-4385	166	1	|xt	|xt	NUM
ejpam-4385	166	2	=	=	SYM
ejpam-4385	166	3	x2	x2	PROPN
ejpam-4385	166	4	]	]	PUNCT
ejpam-4385	166	5	≤	≤	NUM
ejpam-4385	166	6	λeµc	λeµc	NOUN
ejpam-4385	166	7	[	[	X
ejpam-4385	166	8	(	(	PUNCT
ejpam-4385	166	9	x1z	x1z	PROPN
ejpam-4385	166	10	µc	µc	PROPN
ejpam-4385	166	11	t	t	PROPN
ejpam-4385	166	12	,	,	PUNCT
ejpam-4385	166	13	tk	tk	PROPN
ejpam-4385	166	14	)	)	PUNCT
ejpam-4385	167	1	+	+	CCONJ
ejpam-4385	167	2	|xt	|xt	X
ejpam-4385	167	3	=	=	SYM
ejpam-4385	167	4	x1	x1	PRON
ejpam-4385	167	5	]	]	PUNCT
ejpam-4385	168	1	+	+	CCONJ
ejpam-4385	168	2	(	(	PUNCT
ejpam-4385	168	3	1−	1−	NUM
ejpam-4385	168	4	λ)eµc	λ)eµc	X
ejpam-4385	168	5	[	[	X
ejpam-4385	168	6	(	(	PUNCT
ejpam-4385	168	7	x3z	x3z	PROPN
ejpam-4385	168	8	µc	µc	PROPN
ejpam-4385	168	9	t	t	PROPN
ejpam-4385	168	10	,	,	PUNCT
ejpam-4385	168	11	t	t	PROPN
ejpam-4385	168	12	−k	−k	PROPN
ejpam-4385	168	13	)	)	PUNCT
ejpam-4385	169	1	+	+	CCONJ
ejpam-4385	169	2	|xt	|xt	NUM
ejpam-4385	169	3	=	=	SYM
ejpam-4385	169	4	x3	x3	ADJ
ejpam-4385	169	5	]	]	PUNCT
ejpam-4385	169	6	=	=	SYM
ejpam-4385	169	7	λgµc(t	λgµc(t	PROPN
ejpam-4385	169	8	,	,	PUNCT
ejpam-4385	169	9	x1	x1	PROPN
ejpam-4385	169	10	)	)	PUNCT
ejpam-4385	170	1	+	+	CCONJ
ejpam-4385	170	2	(	(	PUNCT
ejpam-4385	170	3	1−	1−	NUM
ejpam-4385	170	4	λ)gµc(t	λ)gµc(t	NOUN
ejpam-4385	170	5	,	,	PUNCT
ejpam-4385	170	6	x3	x3	ADJ
ejpam-4385	170	7	)	)	PUNCT
ejpam-4385	170	8	.	.	PUNCT
ejpam-4385	171	1	therefore	therefore	ADV
ejpam-4385	171	2	,	,	PUNCT
ejpam-4385	171	3	the	the	DET
ejpam-4385	171	4	mapping	mapping	NOUN
ejpam-4385	171	5	x	x	SYM
ejpam-4385	171	6	7→	7→	NUM
ejpam-4385	171	7	gµc(t	gµc(t	NOUN
ejpam-4385	171	8	,	,	PUNCT
ejpam-4385	171	9	x	x	PRON
ejpam-4385	171	10	)	)	PUNCT
ejpam-4385	171	11	is	be	AUX
ejpam-4385	171	12	convex	convex	ADJ
ejpam-4385	171	13	on	on	ADP
ejpam-4385	171	14	(	(	PUNCT
ejpam-4385	171	15	0,∞	0,∞	NOUN
ejpam-4385	171	16	)	)	PUNCT
ejpam-4385	171	17	.	.	PUNCT
ejpam-4385	172	1	k.	k.	PROPN
ejpam-4385	172	2	falcasantos	falcasantos	PROPN
ejpam-4385	172	3	,	,	PUNCT
ejpam-4385	172	4	f.	f.	PROPN
ejpam-4385	172	5	sumalpong	sumalpong	PROPN
ejpam-4385	172	6	/	/	SYM
ejpam-4385	172	7	eur	eur	PROPN
ejpam-4385	172	8	.	.	PUNCT
ejpam-4385	173	1	j.	j.	PROPN
ejpam-4385	173	2	pure	pure	PROPN
ejpam-4385	173	3	appl	appl	PROPN
ejpam-4385	173	4	.	.	PROPN
ejpam-4385	173	5	math	math	PROPN
ejpam-4385	173	6	,	,	PUNCT
ejpam-4385	173	7	15	15	NUM
ejpam-4385	173	8	(	(	PUNCT
ejpam-4385	173	9	3	3	NUM
ejpam-4385	173	10	)	)	PUNCT
ejpam-4385	173	11	(	(	PUNCT
ejpam-4385	173	12	2022	2022	NUM
ejpam-4385	173	13	)	)	PUNCT
ejpam-4385	173	14	,	,	PUNCT
ejpam-4385	173	15	948	948	NUM
ejpam-4385	173	16	-	-	SYM
ejpam-4385	173	17	970	970	NUM
ejpam-4385	173	18	955	955	NUM
ejpam-4385	173	19	it	it	PRON
ejpam-4385	173	20	can	can	AUX
ejpam-4385	173	21	also	also	ADV
ejpam-4385	173	22	be	be	AUX
ejpam-4385	173	23	verified	verify	VERB
ejpam-4385	173	24	that	that	SCONJ
ejpam-4385	173	25	the	the	DET
ejpam-4385	173	26	mapping	mapping	NOUN
ejpam-4385	173	27	in	in	ADP
ejpam-4385	173	28	(	(	PUNCT
ejpam-4385	173	29	25	25	NUM
ejpam-4385	173	30	)	)	PUNCT
ejpam-4385	173	31	is	be	AUX
ejpam-4385	173	32	strictly	strictly	ADV
ejpam-4385	173	33	increasing	increase	VERB
ejpam-4385	173	34	on	on	ADP
ejpam-4385	173	35	(	(	PUNCT
ejpam-4385	173	36	0,∞	0,∞	NOUN
ejpam-4385	173	37	)	)	PUNCT
ejpam-4385	173	38	with	with	ADP
ejpam-4385	173	39	gµc(t	gµc(t	PROPN
ejpam-4385	173	40	,	,	PUNCT
ejpam-4385	173	41	0	0	NUM
ejpam-4385	173	42	)	)	PUNCT
ejpam-4385	173	43	=	=	SYM
ejpam-4385	173	44	0	0	NUM
ejpam-4385	173	45	and	and	CCONJ
ejpam-4385	173	46	gµc(t,∞	gµc(t,∞	PROPN
ejpam-4385	173	47	)	)	PUNCT
ejpam-4385	174	1	=	=	SYM
ejpam-4385	174	2	∞	∞	PROPN
ejpam-4385	174	3	for	for	ADP
ejpam-4385	174	4	any	any	DET
ejpam-4385	174	5	t	t	NOUN
ejpam-4385	174	6	∈	∈	PROPN
ejpam-4385	175	1	[	[	X
ejpam-4385	175	2	0	0	NUM
ejpam-4385	175	3	,	,	PUNCT
ejpam-4385	175	4	t	t	NOUN
ejpam-4385	175	5	]	]	PUNCT
ejpam-4385	175	6	given	give	VERB
ejpam-4385	175	7	and	and	CCONJ
ejpam-4385	175	8	fixed	fix	VERB
ejpam-4385	175	9	.	.	PUNCT
ejpam-4385	176	1	define	define	VERB
ejpam-4385	176	2	the	the	DET
ejpam-4385	176	3	set	set	NOUN
ejpam-4385	176	4	d	d	NOUN
ejpam-4385	176	5	:	:	PUNCT
ejpam-4385	177	1	=	=	SYM
ejpam-4385	177	2	{	{	PUNCT
ejpam-4385	177	3	(	(	PUNCT
ejpam-4385	177	4	t	t	PROPN
ejpam-4385	177	5	,	,	PUNCT
ejpam-4385	177	6	rt	rt	PROPN
ejpam-4385	177	7	,	,	PUNCT
ejpam-4385	177	8	xt	xt	X
ejpam-4385	177	9	)	)	PUNCT
ejpam-4385	177	10	∈	∈	PROPN
ejpam-4385	178	1	[	[	X
ejpam-4385	178	2	0	0	NUM
ejpam-4385	178	3	,	,	PUNCT
ejpam-4385	178	4	t	t	X
ejpam-4385	178	5	]	]	X
ejpam-4385	178	6	×	×	X
ejpam-4385	178	7	r×	r×	NOUN
ejpam-4385	178	8	(	(	PUNCT
ejpam-4385	178	9	0,∞)|v	0,∞)|v	NUM
ejpam-4385	178	10	(	(	PUNCT
ejpam-4385	178	11	t	t	PROPN
ejpam-4385	178	12	,	,	PUNCT
ejpam-4385	178	13	rt	rt	PROPN
ejpam-4385	178	14	,	,	PUNCT
ejpam-4385	178	15	xt	xt	X
ejpam-4385	178	16	)	)	PUNCT
ejpam-4385	178	17	=	=	SYM
ejpam-4385	178	18	gµc(t	gµc(t	PROPN
ejpam-4385	178	19	,	,	PUNCT
ejpam-4385	178	20	xt	xt	NUM
ejpam-4385	178	21	)	)	PUNCT
ejpam-4385	178	22	}	}	PUNCT
ejpam-4385	178	23	.	.	PUNCT
ejpam-4385	179	1	(	(	PUNCT
ejpam-4385	179	2	26	26	NUM
ejpam-4385	179	3	)	)	PUNCT
ejpam-4385	179	4	by	by	ADP
ejpam-4385	179	5	(	(	PUNCT
ejpam-4385	179	6	20	20	NUM
ejpam-4385	179	7	)	)	PUNCT
ejpam-4385	179	8	,	,	PUNCT
ejpam-4385	179	9	we	we	PRON
ejpam-4385	179	10	say	say	VERB
ejpam-4385	179	11	that	that	SCONJ
ejpam-4385	179	12	{	{	PUNCT
ejpam-4385	179	13	t	t	NOUN
ejpam-4385	179	14	}	}	PUNCT
ejpam-4385	179	15	×	×	PROPN
ejpam-4385	179	16	{	{	PUNCT
ejpam-4385	179	17	rt	rt	PROPN
ejpam-4385	179	18	}	}	PUNCT
ejpam-4385	179	19	×	×	PROPN
ejpam-4385	179	20	(	(	PUNCT
ejpam-4385	179	21	0,∞	0,∞	NOUN
ejpam-4385	179	22	)	)	PUNCT
ejpam-4385	180	1	⊂	⊂	PROPN
ejpam-4385	181	1	d	d	X
ejpam-4385	181	2	,	,	PUNCT
ejpam-4385	181	3	which	which	PRON
ejpam-4385	181	4	is	be	AUX
ejpam-4385	181	5	consistent	consistent	ADJ
ejpam-4385	181	6	with	with	ADP
ejpam-4385	181	7	the	the	DET
ejpam-4385	181	8	fact	fact	NOUN
ejpam-4385	181	9	that	that	SCONJ
ejpam-4385	181	10	the	the	DET
ejpam-4385	181	11	supremum	supremum	NOUN
ejpam-4385	181	12	in	in	ADP
ejpam-4385	181	13	(	(	PUNCT
ejpam-4385	181	14	17	17	NUM
ejpam-4385	181	15	)	)	PUNCT
ejpam-4385	181	16	is	be	AUX
ejpam-4385	181	17	taken	take	VERB
ejpam-4385	181	18	over	over	ADP
ejpam-4385	181	19	(	(	PUNCT
ejpam-4385	181	20	f)t∈[0,t	f)t∈[0,t	NOUN
ejpam-4385	181	21	]	]	PUNCT
ejpam-4385	181	22	stopping	stop	VERB
ejpam-4385	181	23	times	time	NOUN
ejpam-4385	181	24	τ	τ	PROPN
ejpam-4385	181	25	∈	∈	PROPN
ejpam-4385	182	1	[	[	X
ejpam-4385	182	2	t	t	PROPN
ejpam-4385	182	3	,	,	PUNCT
ejpam-4385	182	4	t	t	X
ejpam-4385	182	5	]	]	PUNCT
ejpam-4385	182	6	.	.	PUNCT
ejpam-4385	183	1	furthermore	furthermore	ADV
ejpam-4385	183	2	,	,	PUNCT
ejpam-4385	183	3	by	by	ADP
ejpam-4385	183	4	a	a	DET
ejpam-4385	183	5	corollary	corollary	NOUN
ejpam-4385	183	6	in	in	ADP
ejpam-4385	183	7	[	[	X
ejpam-4385	183	8	12	12	NUM
ejpam-4385	183	9	]	]	PUNCT
ejpam-4385	183	10	,	,	PUNCT
ejpam-4385	183	11	the	the	DET
ejpam-4385	183	12	(	(	PUNCT
ejpam-4385	183	13	f)t∈[0,t	f)t∈[0,t	NOUN
ejpam-4385	183	14	]	]	PUNCT
ejpam-4385	183	15	stopping	stop	VERB
ejpam-4385	183	16	time	time	NOUN
ejpam-4385	183	17	defined	define	VERB
ejpam-4385	183	18	by	by	ADP
ejpam-4385	183	19	τd(t	τd(t	NOUN
ejpam-4385	183	20	,	,	PUNCT
ejpam-4385	183	21	rt	rt	PROPN
ejpam-4385	183	22	,	,	PUNCT
ejpam-4385	183	23	x	x	NOUN
ejpam-4385	183	24	)	)	PUNCT
ejpam-4385	183	25	:	:	PUNCT
ejpam-4385	183	26	=	=	SYM
ejpam-4385	183	27	inf	inf	PROPN
ejpam-4385	183	28	{	{	PUNCT
ejpam-4385	183	29	s	s	NOUN
ejpam-4385	183	30	∈	∈	X
ejpam-4385	184	1	[	[	X
ejpam-4385	184	2	0	0	NUM
ejpam-4385	184	3	,	,	PUNCT
ejpam-4385	184	4	t	t	PROPN
ejpam-4385	184	5	−	−	PROPN
ejpam-4385	184	6	t	t	PROPN
ejpam-4385	184	7	]	]	PUNCT
ejpam-4385	184	8	:	:	PUNCT
ejpam-4385	184	9	(	(	PUNCT
ejpam-4385	184	10	t+	t+	NOUN
ejpam-4385	184	11	s	s	NOUN
ejpam-4385	184	12	,	,	PUNCT
ejpam-4385	184	13	rt+s	rt+s	PROPN
ejpam-4385	184	14	,	,	PUNCT
ejpam-4385	184	15	xt+s	xt+s	NUM
ejpam-4385	184	16	)	)	PUNCT
ejpam-4385	184	17	∈	∈	PROPN
ejpam-4385	185	1	d	d	NOUN
ejpam-4385	185	2	}	}	PUNCT
ejpam-4385	185	3	,	,	PUNCT
ejpam-4385	185	4	(	(	PUNCT
ejpam-4385	185	5	27	27	NUM
ejpam-4385	185	6	)	)	PUNCT
ejpam-4385	185	7	with	with	ADP
ejpam-4385	185	8	xt+s	xt+s	PROPN
ejpam-4385	185	9	=	=	PUNCT
ejpam-4385	185	10	x	x	SYM
ejpam-4385	185	11	∈	∈	PROPN
ejpam-4385	185	12	(	(	PUNCT
ejpam-4385	185	13	0,∞	0,∞	NOUN
ejpam-4385	185	14	)	)	PUNCT
ejpam-4385	185	15	and	and	CCONJ
ejpam-4385	185	16	rt+s	rt+s	NUM
ejpam-4385	185	17	∈	∈	PROPN
ejpam-4385	185	18	r	r	NOUN
ejpam-4385	185	19	,	,	PUNCT
ejpam-4385	185	20	is	be	AUX
ejpam-4385	185	21	an	an	DET
ejpam-4385	185	22	optimal	optimal	ADJ
ejpam-4385	185	23	stopping	stopping	NOUN
ejpam-4385	185	24	time	time	NOUN
ejpam-4385	185	25	for	for	ADP
ejpam-4385	185	26	the	the	DET
ejpam-4385	185	27	option	option	NOUN
ejpam-4385	185	28	price	price	NOUN
ejpam-4385	185	29	in	in	ADP
ejpam-4385	185	30	(	(	PUNCT
ejpam-4385	185	31	17	17	NUM
ejpam-4385	185	32	)	)	PUNCT
ejpam-4385	185	33	since	since	SCONJ
ejpam-4385	185	34	both	both	DET
ejpam-4385	185	35	x	x	SYM
ejpam-4385	185	36	7→	7→	NUM
ejpam-4385	185	37	v	v	NOUN
ejpam-4385	185	38	(	(	PUNCT
ejpam-4385	185	39	t	t	PROPN
ejpam-4385	185	40	,	,	PUNCT
ejpam-4385	185	41	rt	rt	PROPN
ejpam-4385	185	42	,	,	PUNCT
ejpam-4385	185	43	x	x	NOUN
ejpam-4385	185	44	)	)	PUNCT
ejpam-4385	185	45	and	and	CCONJ
ejpam-4385	185	46	x	x	SYM
ejpam-4385	185	47	7→	7→	NUM
ejpam-4385	185	48	gµc(t	gµc(t	NOUN
ejpam-4385	185	49	,	,	PUNCT
ejpam-4385	185	50	x	x	PRON
ejpam-4385	185	51	)	)	PUNCT
ejpam-4385	185	52	are	be	AUX
ejpam-4385	185	53	continuous	continuous	ADJ
ejpam-4385	185	54	on	on	ADP
ejpam-4385	185	55	(	(	PUNCT
ejpam-4385	185	56	0,∞	0,∞	NOUN
ejpam-4385	185	57	)	)	PUNCT
ejpam-4385	185	58	and	and	CCONJ
ejpam-4385	186	1	gµc(t	gµc(t	NOUN
ejpam-4385	186	2	,	,	PUNCT
ejpam-4385	186	3	x	x	NOUN
ejpam-4385	186	4	)	)	PUNCT
ejpam-4385	186	5	≤	≤	NOUN
ejpam-4385	186	6	k	k	NOUN
ejpam-4385	186	7	for	for	ADP
ejpam-4385	186	8	all	all	DET
ejpam-4385	186	9	t	t	NOUN
ejpam-4385	186	10	∈	∈	PROPN
ejpam-4385	187	1	[	[	X
ejpam-4385	187	2	0	0	NUM
ejpam-4385	187	3	,	,	PUNCT
ejpam-4385	187	4	t	t	NOUN
ejpam-4385	187	5	]	]	PUNCT
ejpam-4385	187	6	and	and	CCONJ
ejpam-4385	187	7	rt	rt	PROPN
ejpam-4385	187	8	∈	∈	PROPN
ejpam-4385	187	9	r.	r.	PROPN
ejpam-4385	187	10	consequently	consequently	ADV
ejpam-4385	187	11	,	,	PUNCT
ejpam-4385	187	12	we	we	PRON
ejpam-4385	187	13	call	call	VERB
ejpam-4385	187	14	the	the	DET
ejpam-4385	187	15	set	set	NOUN
ejpam-4385	187	16	d	d	NOUN
ejpam-4385	187	17	as	as	ADP
ejpam-4385	187	18	stopping	stop	VERB
ejpam-4385	187	19	set	set	NOUN
ejpam-4385	187	20	.	.	PUNCT
ejpam-4385	188	1	thus	thus	ADV
ejpam-4385	188	2	,	,	PUNCT
ejpam-4385	188	3	we	we	PRON
ejpam-4385	188	4	can	can	AUX
ejpam-4385	188	5	define	define	VERB
ejpam-4385	188	6	the	the	DET
ejpam-4385	188	7	continuation	continuation	NOUN
ejpam-4385	188	8	set	set	NOUN
ejpam-4385	188	9	c	c	NOUN
ejpam-4385	188	10	=	=	SYM
ejpam-4385	188	11	dc	dc	PROPN
ejpam-4385	188	12	as	as	ADP
ejpam-4385	188	13	c	c	PROPN
ejpam-4385	188	14	=	=	SYM
ejpam-4385	188	15	{	{	PUNCT
ejpam-4385	188	16	(	(	PUNCT
ejpam-4385	188	17	t	t	PROPN
ejpam-4385	188	18	,	,	PUNCT
ejpam-4385	188	19	rt	rt	PROPN
ejpam-4385	188	20	,	,	PUNCT
ejpam-4385	188	21	x	x	NOUN
ejpam-4385	188	22	)	)	PUNCT
ejpam-4385	188	23	∈	∈	PROPN
ejpam-4385	189	1	[	[	X
ejpam-4385	189	2	0	0	NUM
ejpam-4385	189	3	,	,	PUNCT
ejpam-4385	189	4	t	t	X
ejpam-4385	189	5	]	]	X
ejpam-4385	189	6	×	×	X
ejpam-4385	189	7	r×	r×	NOUN
ejpam-4385	189	8	(	(	PUNCT
ejpam-4385	189	9	0,∞)|v	0,∞)|v	NUM
ejpam-4385	189	10	(	(	PUNCT
ejpam-4385	189	11	t	t	PROPN
ejpam-4385	189	12	,	,	PUNCT
ejpam-4385	189	13	rt	rt	PROPN
ejpam-4385	189	14	,	,	PUNCT
ejpam-4385	189	15	x	x	NOUN
ejpam-4385	189	16	)	)	PUNCT
ejpam-4385	189	17	>	>	X
ejpam-4385	190	1	gµc(t	gµc(t	PROPN
ejpam-4385	190	2	,	,	PUNCT
ejpam-4385	190	3	x	x	NOUN
ejpam-4385	190	4	)	)	PUNCT
ejpam-4385	190	5	}	}	PUNCT
ejpam-4385	190	6	.	.	PUNCT
ejpam-4385	191	1	(	(	PUNCT
ejpam-4385	191	2	28	28	NUM
ejpam-4385	191	3	)	)	PUNCT
ejpam-4385	191	4	4	4	NUM
ejpam-4385	191	5	.	.	PUNCT
ejpam-4385	192	1	stopping	stop	VERB
ejpam-4385	192	2	set	set	VERB
ejpam-4385	192	3	and	and	CCONJ
ejpam-4385	192	4	boundary	boundary	ADJ
ejpam-4385	192	5	function	function	NOUN
ejpam-4385	192	6	in	in	ADP
ejpam-4385	192	7	order	order	NOUN
ejpam-4385	192	8	to	to	PART
ejpam-4385	192	9	deal	deal	VERB
ejpam-4385	192	10	with	with	ADP
ejpam-4385	192	11	the	the	DET
ejpam-4385	192	12	existence	existence	NOUN
ejpam-4385	192	13	of	of	ADP
ejpam-4385	192	14	an	an	DET
ejpam-4385	192	15	optimal	optimal	ADJ
ejpam-4385	192	16	stopping	stopping	NOUN
ejpam-4385	192	17	time	time	NOUN
ejpam-4385	192	18	for	for	ADP
ejpam-4385	192	19	(	(	PUNCT
ejpam-4385	192	20	26	26	NUM
ejpam-4385	192	21	)	)	PUNCT
ejpam-4385	192	22	above	above	ADV
ejpam-4385	192	23	,	,	PUNCT
ejpam-4385	192	24	we	we	PRON
ejpam-4385	192	25	define	define	VERB
ejpam-4385	192	26	f	f	PROPN
ejpam-4385	192	27	(	(	PUNCT
ejpam-4385	192	28	t	t	PROPN
ejpam-4385	192	29	,	,	PUNCT
ejpam-4385	192	30	rt	rt	PROPN
ejpam-4385	192	31	,	,	PUNCT
ejpam-4385	192	32	x	x	NOUN
ejpam-4385	192	33	)	)	PUNCT
ejpam-4385	192	34	=	=	SYM
ejpam-4385	192	35	v	v	NOUN
ejpam-4385	192	36	(	(	PUNCT
ejpam-4385	192	37	t	t	PROPN
ejpam-4385	192	38	,	,	PUNCT
ejpam-4385	192	39	rt	rt	PROPN
ejpam-4385	192	40	,	,	PUNCT
ejpam-4385	192	41	x)−gµc(t	x)−gµc(t	PROPN
ejpam-4385	192	42	,	,	PUNCT
ejpam-4385	192	43	x	x	X
ejpam-4385	192	44	)	)	PUNCT
ejpam-4385	192	45	≥	≥	NOUN
ejpam-4385	192	46	0	0	NUM
ejpam-4385	192	47	,	,	PUNCT
ejpam-4385	192	48	which	which	PRON
ejpam-4385	192	49	is	be	AUX
ejpam-4385	192	50	nonnegative	nonnegative	ADJ
ejpam-4385	192	51	for	for	ADP
ejpam-4385	192	52	t	t	PROPN
ejpam-4385	192	53	∈	∈	PROPN
ejpam-4385	193	1	[	[	X
ejpam-4385	193	2	0	0	NUM
ejpam-4385	193	3	,	,	PUNCT
ejpam-4385	193	4	t	t	X
ejpam-4385	193	5	]	]	PUNCT
ejpam-4385	193	6	,	,	PUNCT
ejpam-4385	193	7	rt	rt	PROPN
ejpam-4385	193	8	∈	∈	PROPN
ejpam-4385	193	9	r	r	NOUN
ejpam-4385	193	10	and	and	CCONJ
ejpam-4385	193	11	x	x	PROPN
ejpam-4385	193	12	∈	∈	PROPN
ejpam-4385	193	13	(	(	PUNCT
ejpam-4385	193	14	0,∞	0,∞	NOUN
ejpam-4385	193	15	)	)	PUNCT
ejpam-4385	193	16	,	,	PUNCT
ejpam-4385	193	17	so	so	SCONJ
ejpam-4385	193	18	that	that	SCONJ
ejpam-4385	193	19	we	we	PRON
ejpam-4385	193	20	define	define	VERB
ejpam-4385	193	21	the	the	DET
ejpam-4385	193	22	stopping	stopping	NOUN
ejpam-4385	193	23	set	set	VERB
ejpam-4385	193	24	d	d	NOUN
ejpam-4385	193	25	=	=	SYM
ejpam-4385	193	26	{	{	PUNCT
ejpam-4385	193	27	(	(	PUNCT
ejpam-4385	193	28	t	t	PROPN
ejpam-4385	193	29	,	,	PUNCT
ejpam-4385	193	30	rt	rt	PROPN
ejpam-4385	193	31	,	,	PUNCT
ejpam-4385	193	32	x	x	NOUN
ejpam-4385	193	33	)	)	PUNCT
ejpam-4385	193	34	∈	∈	PROPN
ejpam-4385	194	1	[	[	X
ejpam-4385	194	2	0	0	NUM
ejpam-4385	194	3	,	,	PUNCT
ejpam-4385	194	4	t	t	X
ejpam-4385	194	5	]	]	X
ejpam-4385	194	6	×	×	X
ejpam-4385	194	7	r×	r×	NOUN
ejpam-4385	194	8	(	(	PUNCT
ejpam-4385	194	9	0,∞)|f	0,∞)|f	NUM
ejpam-4385	194	10	(	(	PUNCT
ejpam-4385	194	11	t	t	PROPN
ejpam-4385	194	12	,	,	PUNCT
ejpam-4385	194	13	rt	rt	PROPN
ejpam-4385	194	14	,	,	PUNCT
ejpam-4385	194	15	x	x	NOUN
ejpam-4385	194	16	)	)	PUNCT
ejpam-4385	194	17	=	=	SYM
ejpam-4385	194	18	0	0	NUM
ejpam-4385	194	19	}	}	PUNCT
ejpam-4385	194	20	.	.	PUNCT
ejpam-4385	195	1	by	by	ADP
ejpam-4385	195	2	lemmas	lemmas	PROPN
ejpam-4385	195	3	2	2	NUM
ejpam-4385	195	4	and	and	CCONJ
ejpam-4385	195	5	3	3	NUM
ejpam-4385	195	6	,	,	PUNCT
ejpam-4385	195	7	we	we	PRON
ejpam-4385	195	8	say	say	VERB
ejpam-4385	195	9	that	that	SCONJ
ejpam-4385	195	10	the	the	DET
ejpam-4385	195	11	set	set	NOUN
ejpam-4385	195	12	d	d	PROPN
ejpam-4385	195	13	is	be	AUX
ejpam-4385	195	14	closed	closed	ADJ
ejpam-4385	195	15	.	.	PUNCT
ejpam-4385	196	1	thus	thus	ADV
ejpam-4385	196	2	,	,	PUNCT
ejpam-4385	196	3	the	the	DET
ejpam-4385	196	4	continuation	continuation	NOUN
ejpam-4385	196	5	set	set	NOUN
ejpam-4385	196	6	defined	define	VERB
ejpam-4385	196	7	by	by	ADP
ejpam-4385	196	8	c	c	NOUN
ejpam-4385	196	9	:	:	PUNCT
ejpam-4385	197	1	=	=	SYM
ejpam-4385	197	2	dc	dc	PROPN
ejpam-4385	197	3	=	=	SYM
ejpam-4385	197	4	{	{	PUNCT
ejpam-4385	197	5	(	(	PUNCT
ejpam-4385	197	6	t	t	PROPN
ejpam-4385	197	7	,	,	PUNCT
ejpam-4385	197	8	rt	rt	PROPN
ejpam-4385	197	9	,	,	PUNCT
ejpam-4385	197	10	x	x	NOUN
ejpam-4385	197	11	)	)	PUNCT
ejpam-4385	197	12	∈	∈	PROPN
ejpam-4385	198	1	[	[	X
ejpam-4385	198	2	0	0	NUM
ejpam-4385	198	3	,	,	PUNCT
ejpam-4385	198	4	t	t	X
ejpam-4385	198	5	]	]	X
ejpam-4385	198	6	×	×	X
ejpam-4385	198	7	r×	r×	NOUN
ejpam-4385	198	8	(	(	PUNCT
ejpam-4385	198	9	0,∞)|f	0,∞)|f	NUM
ejpam-4385	198	10	(	(	PUNCT
ejpam-4385	198	11	t	t	PROPN
ejpam-4385	198	12	,	,	PUNCT
ejpam-4385	198	13	rt	rt	PROPN
ejpam-4385	198	14	,	,	PUNCT
ejpam-4385	198	15	x	x	NOUN
ejpam-4385	198	16	)	)	PUNCT
ejpam-4385	198	17	>	>	X
ejpam-4385	198	18	0	0	NUM
ejpam-4385	198	19	}	}	PUNCT
ejpam-4385	198	20	is	be	AUX
ejpam-4385	198	21	open	open	ADJ
ejpam-4385	198	22	.	.	PUNCT
ejpam-4385	199	1	let	let	VERB
ejpam-4385	199	2	(	(	PUNCT
ejpam-4385	199	3	t	t	PROPN
ejpam-4385	199	4	,	,	PUNCT
ejpam-4385	199	5	rt	rt	PROPN
ejpam-4385	199	6	,	,	PUNCT
ejpam-4385	199	7	x	x	NOUN
ejpam-4385	199	8	)	)	PUNCT
ejpam-4385	199	9	∈	∈	PROPN
ejpam-4385	199	10	{	{	PUNCT
ejpam-4385	199	11	t	t	PROPN
ejpam-4385	199	12	}	}	PUNCT
ejpam-4385	199	13	×	×	PROPN
ejpam-4385	199	14	{	{	PUNCT
ejpam-4385	199	15	rt	rt	PROPN
ejpam-4385	199	16	}	}	PUNCT
ejpam-4385	199	17	×	×	PROPN
ejpam-4385	199	18	(	(	PUNCT
ejpam-4385	199	19	0,∞	0,∞	NOUN
ejpam-4385	199	20	)	)	PUNCT
ejpam-4385	200	1	⊂	⊂	PROPN
ejpam-4385	201	1	d	d	X
ejpam-4385	201	2	,	,	PUNCT
ejpam-4385	201	3	which	which	PRON
ejpam-4385	201	4	is	be	AUX
ejpam-4385	201	5	consistent	consistent	ADJ
ejpam-4385	201	6	with	with	ADP
ejpam-4385	201	7	the	the	DET
ejpam-4385	201	8	fact	fact	NOUN
ejpam-4385	201	9	that	that	SCONJ
ejpam-4385	201	10	the	the	DET
ejpam-4385	201	11	supremum	supremum	NOUN
ejpam-4385	201	12	in	in	ADP
ejpam-4385	201	13	(	(	PUNCT
ejpam-4385	201	14	21	21	NUM
ejpam-4385	201	15	)	)	PUNCT
ejpam-4385	201	16	is	be	AUX
ejpam-4385	201	17	taken	take	VERB
ejpam-4385	201	18	over	over	ADP
ejpam-4385	201	19	(	(	PUNCT
ejpam-4385	201	20	f)t∈[0,t	f)t∈[0,t	NOUN
ejpam-4385	201	21	]	]	PUNCT
ejpam-4385	201	22	stopping	stop	VERB
ejpam-4385	201	23	times	time	NOUN
ejpam-4385	201	24	τ	τ	PROPN
ejpam-4385	201	25	∈	∈	PROPN
ejpam-4385	202	1	[	[	X
ejpam-4385	202	2	t	t	PROPN
ejpam-4385	202	3	,	,	PUNCT
ejpam-4385	202	4	t	t	X
ejpam-4385	202	5	]	]	PUNCT
ejpam-4385	202	6	.	.	PUNCT
ejpam-4385	203	1	furthermore	furthermore	ADV
ejpam-4385	203	2	,	,	PUNCT
ejpam-4385	203	3	by	by	ADP
ejpam-4385	203	4	a	a	DET
ejpam-4385	203	5	corollary	corollary	NOUN
ejpam-4385	203	6	in	in	ADP
ejpam-4385	203	7	[	[	X
ejpam-4385	203	8	12	12	NUM
ejpam-4385	203	9	]	]	PUNCT
ejpam-4385	203	10	,	,	PUNCT
ejpam-4385	203	11	the	the	DET
ejpam-4385	203	12	(	(	PUNCT
ejpam-4385	203	13	f)t∈[0,t	f)t∈[0,t	NOUN
ejpam-4385	203	14	]	]	PUNCT
ejpam-4385	203	15	stopping	stop	VERB
ejpam-4385	203	16	time	time	NOUN
ejpam-4385	203	17	defined	define	VERB
ejpam-4385	203	18	by	by	ADP
ejpam-4385	203	19	τd(t	τd(t	NOUN
ejpam-4385	203	20	,	,	PUNCT
ejpam-4385	203	21	rt	rt	PROPN
ejpam-4385	203	22	,	,	PUNCT
ejpam-4385	203	23	x	x	NOUN
ejpam-4385	203	24	)	)	PUNCT
ejpam-4385	203	25	:	:	PUNCT
ejpam-4385	203	26	=	=	SYM
ejpam-4385	203	27	inf	inf	PROPN
ejpam-4385	203	28	{	{	PUNCT
ejpam-4385	203	29	s	s	NOUN
ejpam-4385	203	30	∈	∈	X
ejpam-4385	204	1	[	[	X
ejpam-4385	204	2	0	0	NUM
ejpam-4385	204	3	,	,	PUNCT
ejpam-4385	204	4	t	t	PROPN
ejpam-4385	204	5	−	−	PROPN
ejpam-4385	204	6	t	t	PROPN
ejpam-4385	204	7	]	]	PUNCT
ejpam-4385	204	8	:	:	PUNCT
ejpam-4385	204	9	(	(	PUNCT
ejpam-4385	204	10	t+	t+	NOUN
ejpam-4385	204	11	s	s	NOUN
ejpam-4385	204	12	,	,	PUNCT
ejpam-4385	204	13	rt+s	rt+s	PROPN
ejpam-4385	204	14	,	,	PUNCT
ejpam-4385	204	15	xt+s	xt+s	NUM
ejpam-4385	204	16	)	)	PUNCT
ejpam-4385	204	17	∈	∈	PROPN
ejpam-4385	205	1	d	d	NOUN
ejpam-4385	205	2	}	}	PUNCT
ejpam-4385	205	3	(	(	PUNCT
ejpam-4385	205	4	29	29	NUM
ejpam-4385	205	5	)	)	PUNCT
ejpam-4385	205	6	with	with	ADP
ejpam-4385	205	7	xt+s	xt+s	PROPN
ejpam-4385	205	8	=	=	PUNCT
ejpam-4385	205	9	x	x	SYM
ejpam-4385	205	10	∈	∈	PROPN
ejpam-4385	205	11	(	(	PUNCT
ejpam-4385	205	12	0,∞	0,∞	NOUN
ejpam-4385	205	13	)	)	PUNCT
ejpam-4385	205	14	and	and	CCONJ
ejpam-4385	205	15	rt+s	rt+s	NUM
ejpam-4385	205	16	∈	∈	PROPN
ejpam-4385	205	17	r	r	NOUN
ejpam-4385	205	18	,	,	PUNCT
ejpam-4385	205	19	is	be	AUX
ejpam-4385	205	20	an	an	DET
ejpam-4385	205	21	optimal	optimal	ADJ
ejpam-4385	205	22	stopping	stopping	NOUN
ejpam-4385	205	23	time	time	NOUN
ejpam-4385	205	24	for	for	ADP
ejpam-4385	205	25	the	the	DET
ejpam-4385	205	26	option	option	NOUN
ejpam-4385	205	27	price	price	NOUN
ejpam-4385	205	28	in	in	ADP
ejpam-4385	205	29	(	(	PUNCT
ejpam-4385	205	30	21	21	NUM
ejpam-4385	205	31	)	)	PUNCT
ejpam-4385	205	32	since	since	SCONJ
ejpam-4385	205	33	both	both	DET
ejpam-4385	205	34	x	x	SYM
ejpam-4385	205	35	7→	7→	NUM
ejpam-4385	205	36	v	v	NOUN
ejpam-4385	205	37	(	(	PUNCT
ejpam-4385	205	38	t	t	PROPN
ejpam-4385	205	39	,	,	PUNCT
ejpam-4385	205	40	rt	rt	PROPN
ejpam-4385	205	41	,	,	PUNCT
ejpam-4385	205	42	x	x	NOUN
ejpam-4385	205	43	)	)	PUNCT
ejpam-4385	205	44	and	and	CCONJ
ejpam-4385	205	45	x	x	SYM
ejpam-4385	205	46	7→	7→	NUM
ejpam-4385	205	47	gµc(t	gµc(t	NOUN
ejpam-4385	205	48	,	,	PUNCT
ejpam-4385	205	49	x	x	PRON
ejpam-4385	205	50	)	)	PUNCT
ejpam-4385	205	51	are	be	AUX
ejpam-4385	205	52	continuous	continuous	ADJ
ejpam-4385	205	53	on	on	ADP
ejpam-4385	205	54	(	(	PUNCT
ejpam-4385	205	55	0,∞	0,∞	NOUN
ejpam-4385	205	56	)	)	PUNCT
ejpam-4385	205	57	and	and	CCONJ
ejpam-4385	206	1	gµc(t	gµc(t	NOUN
ejpam-4385	206	2	,	,	PUNCT
ejpam-4385	206	3	x	x	NOUN
ejpam-4385	206	4	)	)	PUNCT
ejpam-4385	206	5	≤	≤	NOUN
ejpam-4385	206	6	k	k	NOUN
ejpam-4385	206	7	for	for	ADP
ejpam-4385	206	8	all	all	DET
ejpam-4385	206	9	t	t	NOUN
ejpam-4385	206	10	∈	∈	PROPN
ejpam-4385	207	1	[	[	X
ejpam-4385	207	2	0	0	NUM
ejpam-4385	207	3	,	,	PUNCT
ejpam-4385	207	4	t	t	NOUN
ejpam-4385	207	5	]	]	PUNCT
ejpam-4385	207	6	and	and	CCONJ
ejpam-4385	207	7	rt	rt	PROPN
ejpam-4385	207	8	∈	∈	PROPN
ejpam-4385	207	9	r.	r.	PROPN
ejpam-4385	207	10	lemma	lemma	PROPN
ejpam-4385	208	1	1	1	NUM
ejpam-4385	208	2	.	.	PUNCT
ejpam-4385	209	1	for	for	ADP
ejpam-4385	209	2	any	any	DET
ejpam-4385	209	3	(	(	PUNCT
ejpam-4385	209	4	t	t	PROPN
ejpam-4385	209	5	,	,	PUNCT
ejpam-4385	209	6	rt	rt	PROPN
ejpam-4385	209	7	,	,	PUNCT
ejpam-4385	209	8	x	x	NOUN
ejpam-4385	209	9	)	)	PUNCT
ejpam-4385	209	10	∈	∈	PROPN
ejpam-4385	210	1	d	d	NOUN
ejpam-4385	210	2	,	,	PUNCT
ejpam-4385	210	3	we	we	PRON
ejpam-4385	210	4	have	have	VERB
ejpam-4385	210	5	lim	lim	PROPN
ejpam-4385	210	6	sup	sup	PROPN
ejpam-4385	210	7	ϵ	ϵ	PROPN
ejpam-4385	210	8	↘	↘	PROPN
ejpam-4385	210	9	0	0	PROPN
ejpam-4385	210	10	f	f	PROPN
ejpam-4385	210	11	(	(	PUNCT
ejpam-4385	210	12	t	t	PROPN
ejpam-4385	210	13	,	,	PUNCT
ejpam-4385	210	14	rt	rt	PROPN
ejpam-4385	210	15	,	,	PUNCT
ejpam-4385	210	16	x+	x+	PROPN
ejpam-4385	211	1	ϵ)−	ϵ)−	ADJ
ejpam-4385	211	2	f	f	X
ejpam-4385	211	3	(	(	PUNCT
ejpam-4385	211	4	t	t	PROPN
ejpam-4385	211	5	,	,	PUNCT
ejpam-4385	211	6	rt	rt	PROPN
ejpam-4385	211	7	,	,	PUNCT
ejpam-4385	211	8	x	x	X
ejpam-4385	211	9	)	)	PUNCT
ejpam-4385	211	10	ϵ	ϵ	ADP
ejpam-4385	211	11	≤	≤	NUM
ejpam-4385	211	12	0	0	NUM
ejpam-4385	211	13	.	.	PUNCT
ejpam-4385	212	1	k.	k.	PROPN
ejpam-4385	212	2	falcasantos	falcasantos	PROPN
ejpam-4385	212	3	,	,	PUNCT
ejpam-4385	212	4	f.	f.	PROPN
ejpam-4385	212	5	sumalpong	sumalpong	PROPN
ejpam-4385	212	6	/	/	SYM
ejpam-4385	212	7	eur	eur	PROPN
ejpam-4385	212	8	.	.	PUNCT
ejpam-4385	213	1	j.	j.	PROPN
ejpam-4385	213	2	pure	pure	PROPN
ejpam-4385	213	3	appl	appl	PROPN
ejpam-4385	213	4	.	.	PROPN
ejpam-4385	213	5	math	math	PROPN
ejpam-4385	213	6	,	,	PUNCT
ejpam-4385	213	7	15	15	NUM
ejpam-4385	213	8	(	(	PUNCT
ejpam-4385	213	9	3	3	NUM
ejpam-4385	213	10	)	)	PUNCT
ejpam-4385	213	11	(	(	PUNCT
ejpam-4385	213	12	2022	2022	NUM
ejpam-4385	213	13	)	)	PUNCT
ejpam-4385	213	14	,	,	PUNCT
ejpam-4385	213	15	948	948	NUM
ejpam-4385	213	16	-	-	SYM
ejpam-4385	213	17	970	970	NUM
ejpam-4385	213	18	956	956	NUM
ejpam-4385	213	19	proof	proof	NOUN
ejpam-4385	213	20	.	.	PUNCT
ejpam-4385	214	1	for	for	ADP
ejpam-4385	214	2	all	all	DET
ejpam-4385	214	3	x	x	SYM
ejpam-4385	214	4	∈	∈	PROPN
ejpam-4385	214	5	(	(	PUNCT
ejpam-4385	214	6	0,∞	0,∞	NOUN
ejpam-4385	214	7	)	)	PUNCT
ejpam-4385	214	8	and	and	CCONJ
ejpam-4385	214	9	ϵ	ϵ	X
ejpam-4385	214	10	>	>	X
ejpam-4385	214	11	0	0	NUM
ejpam-4385	214	12	,	,	PUNCT
ejpam-4385	214	13	consider	consider	VERB
ejpam-4385	214	14	the	the	DET
ejpam-4385	214	15	(	(	PUNCT
ejpam-4385	214	16	fs)s∈[t	fs)s∈[t	PROPN
ejpam-4385	214	17	,	,	PUNCT
ejpam-4385	214	18	t	t	NOUN
ejpam-4385	214	19	]	]	PUNCT
ejpam-4385	214	20	-stopping	-stopping	NOUN
ejpam-4385	214	21	time	time	NOUN
ejpam-4385	214	22	τ+ϵ	τ+ϵ	X
ejpam-4385	214	23	=	=	SYM
ejpam-4385	214	24	τd(t	τd(t	X
ejpam-4385	214	25	,	,	PUNCT
ejpam-4385	214	26	rt	rt	PROPN
ejpam-4385	214	27	,	,	PUNCT
ejpam-4385	214	28	x+	x+	ADJ
ejpam-4385	214	29	ϵ	ϵ	X
ejpam-4385	214	30	)	)	PUNCT
ejpam-4385	214	31	∈	∈	PROPN
ejpam-4385	215	1	[	[	X
ejpam-4385	215	2	0	0	NUM
ejpam-4385	215	3	,	,	PUNCT
ejpam-4385	215	4	t	t	PROPN
ejpam-4385	215	5	−	−	PROPN
ejpam-4385	215	6	t	t	PROPN
ejpam-4385	215	7	]	]	PUNCT
ejpam-4385	215	8	(	(	PUNCT
ejpam-4385	215	9	30	30	NUM
ejpam-4385	215	10	)	)	PUNCT
ejpam-4385	215	11	defined	define	VERB
ejpam-4385	215	12	by	by	ADP
ejpam-4385	215	13	τd(t	τd(t	NOUN
ejpam-4385	215	14	,	,	PUNCT
ejpam-4385	215	15	rt	rt	PROPN
ejpam-4385	215	16	,	,	PUNCT
ejpam-4385	215	17	x	x	NOUN
ejpam-4385	215	18	)	)	PUNCT
ejpam-4385	215	19	:	:	PUNCT
ejpam-4385	215	20	=	=	SYM
ejpam-4385	215	21	inf	inf	PROPN
ejpam-4385	215	22	{	{	PUNCT
ejpam-4385	215	23	s	s	NOUN
ejpam-4385	215	24	∈	∈	X
ejpam-4385	216	1	[	[	X
ejpam-4385	216	2	0	0	NUM
ejpam-4385	216	3	,	,	PUNCT
ejpam-4385	216	4	t	t	PROPN
ejpam-4385	216	5	−	−	PROPN
ejpam-4385	216	6	t	t	PROPN
ejpam-4385	216	7	]	]	PUNCT
ejpam-4385	216	8	:	:	PUNCT
ejpam-4385	216	9	(	(	PUNCT
ejpam-4385	216	10	t+	t+	NOUN
ejpam-4385	216	11	s	s	NOUN
ejpam-4385	216	12	,	,	PUNCT
ejpam-4385	216	13	rt+s	rt+s	PROPN
ejpam-4385	216	14	,	,	PUNCT
ejpam-4385	216	15	xt+s	xt+s	NUM
ejpam-4385	216	16	)	)	PUNCT
ejpam-4385	216	17	∈	∈	PROPN
ejpam-4385	217	1	d	d	NOUN
ejpam-4385	217	2	}	}	PUNCT
ejpam-4385	217	3	.	.	PUNCT
ejpam-4385	218	1	note	note	VERB
ejpam-4385	218	2	that	that	SCONJ
ejpam-4385	218	3	τd(t	τd(t	VERB
ejpam-4385	218	4	,	,	PUNCT
ejpam-4385	218	5	rt	rt	PROPN
ejpam-4385	218	6	,	,	PUNCT
ejpam-4385	218	7	x	x	NOUN
ejpam-4385	218	8	)	)	PUNCT
ejpam-4385	218	9	solves	solve	VERB
ejpam-4385	218	10	the	the	DET
ejpam-4385	218	11	optimal	optimal	ADJ
ejpam-4385	218	12	stopping	stopping	NOUN
ejpam-4385	218	13	problem	problem	NOUN
ejpam-4385	218	14	given	give	VERB
ejpam-4385	218	15	by	by	ADP
ejpam-4385	218	16	v	v	PROPN
ejpam-4385	218	17	(	(	PUNCT
ejpam-4385	218	18	t	t	PROPN
ejpam-4385	218	19	,	,	PUNCT
ejpam-4385	218	20	rt	rt	PROPN
ejpam-4385	218	21	,	,	PUNCT
ejpam-4385	218	22	x+	x+	PROPN
ejpam-4385	218	23	ϵ	ϵ	X
ejpam-4385	218	24	)	)	PUNCT
ejpam-4385	218	25	=	=	PUNCT
ejpam-4385	219	1	sup	sup	NOUN
ejpam-4385	219	2	0≤τ≤t−t	0≤τ≤t−t	PROPN
ejpam-4385	219	3	ẽ	ẽ	PROPN
ejpam-4385	219	4	[	[	PUNCT
ejpam-4385	219	5	e−	e−	PROPN
ejpam-4385	219	6	∫	∫	PROPN
ejpam-4385	219	7	t+τ	t+τ	NUM
ejpam-4385	219	8	t	t	PROPN
ejpam-4385	219	9	rudugµc(t+	rudugµc(t+	VERB
ejpam-4385	219	10	τ	τ	PROPN
ejpam-4385	219	11	,	,	PUNCT
ejpam-4385	219	12	xt+τ	xt+τ	PROPN
ejpam-4385	219	13	)	)	PUNCT
ejpam-4385	219	14	]	]	PUNCT
ejpam-4385	220	1	=	=	PUNCT
ejpam-4385	220	2	ẽ	ẽ	PROPN
ejpam-4385	220	3	[	[	PUNCT
ejpam-4385	220	4	e−	e−	PROPN
ejpam-4385	220	5	∫	∫	PROPN
ejpam-4385	220	6	t+τ	t+τ	NUM
ejpam-4385	220	7	t	t	PROPN
ejpam-4385	220	8	rudugµc(t+	rudugµc(t+	PRON
ejpam-4385	220	9	τ+ϵ	τ+ϵ	PUNCT
ejpam-4385	220	10	,	,	PUNCT
ejpam-4385	220	11	xt+τ+ϵ	xt+τ+ϵ	PROPN
ejpam-4385	220	12	)	)	PUNCT
ejpam-4385	220	13	]	]	PUNCT
ejpam-4385	220	14	(	(	PUNCT
ejpam-4385	220	15	31	31	NUM
ejpam-4385	220	16	)	)	PUNCT
ejpam-4385	220	17	claim	claim	NOUN
ejpam-4385	220	18	:	:	PUNCT
ejpam-4385	220	19	τ+ϵ	τ+ϵ	PUNCT
ejpam-4385	220	20	→	→	SYM
ejpam-4385	220	21	0	0	PUNCT
ejpam-4385	220	22	as	as	ADP
ejpam-4385	220	23	ϵ	ϵ	PROPN
ejpam-4385	220	24	→	→	SYM
ejpam-4385	220	25	0	0	NUM
ejpam-4385	220	26	.	.	PUNCT
ejpam-4385	220	27	from	from	ADP
ejpam-4385	220	28	the	the	DET
ejpam-4385	220	29	definition	definition	NOUN
ejpam-4385	220	30	τd(t	τd(t	ADP
ejpam-4385	220	31	,	,	PUNCT
ejpam-4385	220	32	rt	rt	PROPN
ejpam-4385	220	33	,	,	PUNCT
ejpam-4385	220	34	x	x	NOUN
ejpam-4385	220	35	)	)	PUNCT
ejpam-4385	220	36	of	of	ADP
ejpam-4385	220	37	τd(t	τd(t	ADP
ejpam-4385	220	38	,	,	PUNCT
ejpam-4385	220	39	rt	rt	PROPN
ejpam-4385	220	40	,	,	PUNCT
ejpam-4385	220	41	x+	x+	ADJ
ejpam-4385	220	42	ϵ	ϵ	X
ejpam-4385	220	43	)	)	PUNCT
ejpam-4385	220	44	,	,	PUNCT
ejpam-4385	220	45	τd(t	τd(t	ADJ
ejpam-4385	220	46	,	,	PUNCT
ejpam-4385	220	47	rt	rt	INTJ
ejpam-4385	220	48	,	,	PUNCT
ejpam-4385	220	49	x+	x+	ADJ
ejpam-4385	220	50	ϵ	ϵ	X
ejpam-4385	220	51	)	)	PUNCT
ejpam-4385	220	52	=	=	SYM
ejpam-4385	220	53	inf	inf	NOUN
ejpam-4385	220	54	{	{	PUNCT
ejpam-4385	220	55	s	s	NOUN
ejpam-4385	220	56	∈	∈	X
ejpam-4385	220	57	[	[	X
ejpam-4385	220	58	0	0	NUM
ejpam-4385	220	59	,	,	PUNCT
ejpam-4385	220	60	t	t	PROPN
ejpam-4385	220	61	−	−	PROPN
ejpam-4385	220	62	t	t	PROPN
ejpam-4385	220	63	]	]	PUNCT
ejpam-4385	220	64	:	:	PUNCT
ejpam-4385	220	65	(	(	PUNCT
ejpam-4385	220	66	t+	t+	NOUN
ejpam-4385	220	67	s	s	NOUN
ejpam-4385	220	68	,	,	PUNCT
ejpam-4385	220	69	rt+s	rt+s	PROPN
ejpam-4385	220	70	,	,	PUNCT
ejpam-4385	220	71	xt+s	xt+s	NUM
ejpam-4385	220	72	)	)	PUNCT
ejpam-4385	220	73	∈	∈	PROPN
ejpam-4385	221	1	d	d	NOUN
ejpam-4385	221	2	}	}	PUNCT
ejpam-4385	221	3	=	=	SYM
ejpam-4385	221	4	inf	inf	NOUN
ejpam-4385	221	5	{	{	PUNCT
ejpam-4385	221	6	s	s	PROPN
ejpam-4385	221	7	∈	∈	PROPN
ejpam-4385	222	1	[	[	X
ejpam-4385	222	2	0	0	NUM
ejpam-4385	222	3	,	,	PUNCT
ejpam-4385	222	4	t	t	PROPN
ejpam-4385	222	5	−	−	PROPN
ejpam-4385	222	6	t	t	PROPN
ejpam-4385	222	7	]	]	PUNCT
ejpam-4385	222	8	:	:	PUNCT
ejpam-4385	222	9	sup	sup	NOUN
ejpam-4385	222	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	223	1	ẽ	ẽ	PROPN
ejpam-4385	223	2	[	[	PUNCT
ejpam-4385	223	3	e−	e−	PROPN
ejpam-4385	223	4	∫	∫	PROPN
ejpam-4385	223	5	t+τ	t+τ	NUM
ejpam-4385	223	6	t	t	NOUN
ejpam-4385	223	7	rudueµc	rudueµc	NOUN
ejpam-4385	223	8	[	[	X
ejpam-4385	223	9	(	(	PUNCT
ejpam-4385	223	10	(	(	PUNCT
ejpam-4385	223	11	x+	x+	PROPN
ejpam-4385	223	12	ϵ)xtz	ϵ)xtz	PROPN
ejpam-4385	223	13	µc	µc	INTJ
ejpam-4385	223	14	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	223	15	)	)	PUNCT
ejpam-4385	223	16	−k	−k	PROPN
ejpam-4385	223	17	)	)	PUNCT
ejpam-4385	224	1	+	+	NUM
ejpam-4385	224	2	|ft+τ	|ft+τ	X
ejpam-4385	224	3	]	]	PUNCT
ejpam-4385	225	1	|fr	|fr	X
ejpam-4385	225	2	]	]	PUNCT
ejpam-4385	225	3	=	=	SYM
ejpam-4385	225	4	eµc	eµc	PROPN
ejpam-4385	225	5	[	[	X
ejpam-4385	225	6	(	(	PUNCT
ejpam-4385	225	7	(	(	PUNCT
ejpam-4385	225	8	x+	x+	PROPN
ejpam-4385	225	9	ϵ)xtz	ϵ)xtz	PROPN
ejpam-4385	225	10	µc	µc	INTJ
ejpam-4385	225	11	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	225	12	)	)	PUNCT
ejpam-4385	225	13	−k	−k	PROPN
ejpam-4385	225	14	)	)	PUNCT
ejpam-4385	226	1	+	+	NUM
ejpam-4385	226	2	|ft+τ	|ft+τ	NOUN
ejpam-4385	226	3	]	]	X
ejpam-4385	226	4	}	}	PUNCT
ejpam-4385	226	5	≤	≤	NUM
ejpam-4385	226	6	inf	inf	NOUN
ejpam-4385	226	7	{	{	PUNCT
ejpam-4385	226	8	s	s	PROPN
ejpam-4385	226	9	∈	∈	PROPN
ejpam-4385	227	1	[	[	X
ejpam-4385	227	2	0	0	NUM
ejpam-4385	227	3	,	,	PUNCT
ejpam-4385	227	4	t	t	PROPN
ejpam-4385	227	5	−	−	PROPN
ejpam-4385	227	6	t	t	PROPN
ejpam-4385	227	7	]	]	PUNCT
ejpam-4385	227	8	:	:	PUNCT
ejpam-4385	227	9	sup	sup	NOUN
ejpam-4385	227	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	228	1	ẽ	ẽ	PROPN
ejpam-4385	228	2	[	[	PUNCT
ejpam-4385	228	3	e−	e−	PROPN
ejpam-4385	228	4	∫	∫	PROPN
ejpam-4385	228	5	t+τ	t+τ	NUM
ejpam-4385	228	6	t	t	NOUN
ejpam-4385	228	7	rudueµc	rudueµc	NOUN
ejpam-4385	228	8	[	[	X
ejpam-4385	228	9	(	(	PUNCT
ejpam-4385	228	10	xxtz	xxtz	PROPN
ejpam-4385	228	11	µc	µc	INTJ
ejpam-4385	228	12	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	228	13	)	)	PUNCT
ejpam-4385	228	14	−k	−k	PROPN
ejpam-4385	228	15	)	)	PUNCT
ejpam-4385	229	1	+	+	NUM
ejpam-4385	229	2	|ft+τ	|ft+τ	X
ejpam-4385	229	3	]	]	PUNCT
ejpam-4385	229	4	|fr	|fr	X
ejpam-4385	229	5	]	]	PUNCT
ejpam-4385	229	6	≥	≥	X
ejpam-4385	229	7	eµc	eµc	PROPN
ejpam-4385	229	8	[	[	X
ejpam-4385	229	9	(	(	PUNCT
ejpam-4385	229	10	(	(	PUNCT
ejpam-4385	229	11	x+	x+	PROPN
ejpam-4385	229	12	ϵ)xtz	ϵ)xtz	PROPN
ejpam-4385	229	13	µc	µc	INTJ
ejpam-4385	229	14	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	229	15	)	)	PUNCT
ejpam-4385	229	16	−k	−k	PROPN
ejpam-4385	229	17	)	)	PUNCT
ejpam-4385	230	1	+	+	NUM
ejpam-4385	230	2	|ft+τ	|ft+τ	NOUN
ejpam-4385	230	3	]	]	X
ejpam-4385	230	4	}	}	PUNCT
ejpam-4385	230	5	≤	≤	NUM
ejpam-4385	230	6	inf	inf	NOUN
ejpam-4385	230	7	{	{	PUNCT
ejpam-4385	230	8	s	s	PROPN
ejpam-4385	230	9	∈	∈	PROPN
ejpam-4385	231	1	[	[	X
ejpam-4385	231	2	0	0	NUM
ejpam-4385	231	3	,	,	PUNCT
ejpam-4385	231	4	t	t	PROPN
ejpam-4385	231	5	−	−	PROPN
ejpam-4385	231	6	t	t	PROPN
ejpam-4385	231	7	]	]	PUNCT
ejpam-4385	231	8	:	:	PUNCT
ejpam-4385	231	9	sup	sup	NOUN
ejpam-4385	231	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	232	1	ẽ	ẽ	PROPN
ejpam-4385	232	2	[	[	PUNCT
ejpam-4385	232	3	e−	e−	PROPN
ejpam-4385	232	4	∫	∫	PROPN
ejpam-4385	232	5	t+τ	t+τ	NUM
ejpam-4385	232	6	t	t	NOUN
ejpam-4385	232	7	rudueµc	rudueµc	NOUN
ejpam-4385	232	8	[	[	X
ejpam-4385	232	9	(	(	PUNCT
ejpam-4385	232	10	(	(	PUNCT
ejpam-4385	232	11	x+	x+	PROPN
ejpam-4385	232	12	ϵ)xtz	ϵ)xtz	PROPN
ejpam-4385	232	13	µc	µc	INTJ
ejpam-4385	232	14	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	232	15	)	)	PUNCT
ejpam-4385	232	16	−k	−k	PROPN
ejpam-4385	232	17	)	)	PUNCT
ejpam-4385	233	1	+	+	NUM
ejpam-4385	233	2	|ft+τ	|ft+τ	X
ejpam-4385	233	3	]	]	PUNCT
ejpam-4385	233	4	|fr	|fr	X
ejpam-4385	233	5	]	]	PUNCT
ejpam-4385	233	6	≥	≥	X
ejpam-4385	233	7	eµc	eµc	PROPN
ejpam-4385	233	8	[	[	PUNCT
ejpam-4385	233	9	1	1	NUM
ejpam-4385	233	10	2	2	NUM
ejpam-4385	233	11	(	(	PUNCT
ejpam-4385	233	12	xzµc	xzµc	PROPN
ejpam-4385	233	13	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	233	14	)	)	PUNCT
ejpam-4385	234	1	+	+	CCONJ
ejpam-4385	234	2	ϵzµc	ϵzµc	PROPN
ejpam-4385	234	3	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	234	4	)	)	PUNCT
ejpam-4385	234	5	−k	−k	VERB
ejpam-4385	234	6	+	+	CCONJ
ejpam-4385	234	7	|xzµc	|xzµc	ADP
ejpam-4385	234	8	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	234	9	)	)	PUNCT
ejpam-4385	235	1	+	+	CCONJ
ejpam-4385	235	2	ϵzµc	ϵzµc	PROPN
ejpam-4385	235	3	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	235	4	)	)	PUNCT
ejpam-4385	235	5	−k|	−k|	NOUN
ejpam-4385	235	6	)	)	PUNCT
ejpam-4385	236	1	+	+	NUM
ejpam-4385	236	2	|ft+τ	|ft+τ	NOUN
ejpam-4385	236	3	]	]	X
ejpam-4385	236	4	}	}	PUNCT
ejpam-4385	236	5	.	.	PUNCT
ejpam-4385	237	1	this	this	PRON
ejpam-4385	237	2	implies	imply	VERB
ejpam-4385	237	3	that	that	SCONJ
ejpam-4385	237	4	lim	lim	PROPN
ejpam-4385	237	5	ϵ→0	ϵ→0	X
ejpam-4385	237	6	τd(t	τd(t	PROPN
ejpam-4385	237	7	,	,	PUNCT
ejpam-4385	237	8	rt	rt	PROPN
ejpam-4385	237	9	,	,	PUNCT
ejpam-4385	237	10	x+	x+	ADJ
ejpam-4385	237	11	ϵ	ϵ	X
ejpam-4385	237	12	)	)	PUNCT
ejpam-4385	237	13	≤	≤	NOUN
ejpam-4385	237	14	lim	lim	PROPN
ejpam-4385	237	15	ϵ→0	ϵ→0	PROPN
ejpam-4385	237	16	inf	inf	PROPN
ejpam-4385	237	17	{	{	PUNCT
ejpam-4385	237	18	s	s	PROPN
ejpam-4385	237	19	∈	∈	PROPN
ejpam-4385	238	1	[	[	X
ejpam-4385	238	2	0	0	NUM
ejpam-4385	238	3	,	,	PUNCT
ejpam-4385	238	4	t	t	PROPN
ejpam-4385	238	5	−	−	PROPN
ejpam-4385	238	6	t	t	PROPN
ejpam-4385	238	7	]	]	PUNCT
ejpam-4385	238	8	:	:	PUNCT
ejpam-4385	238	9	sup	sup	NOUN
ejpam-4385	238	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	239	1	ẽ	ẽ	PROPN
ejpam-4385	239	2	[	[	PUNCT
ejpam-4385	239	3	e−	e−	PROPN
ejpam-4385	239	4	∫	∫	PROPN
ejpam-4385	239	5	t+τ	t+τ	NUM
ejpam-4385	239	6	t	t	NOUN
ejpam-4385	239	7	rudueµc	rudueµc	NOUN
ejpam-4385	239	8	[	[	X
ejpam-4385	239	9	(	(	PUNCT
ejpam-4385	239	10	(	(	PUNCT
ejpam-4385	239	11	x+	x+	PROPN
ejpam-4385	239	12	ϵ)xtz	ϵ)xtz	PROPN
ejpam-4385	239	13	µc	µc	INTJ
ejpam-4385	239	14	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	239	15	)	)	PUNCT
ejpam-4385	239	16	−k	−k	PROPN
ejpam-4385	239	17	)	)	PUNCT
ejpam-4385	240	1	+	+	NUM
ejpam-4385	240	2	|ft+τ	|ft+τ	X
ejpam-4385	240	3	]	]	PUNCT
ejpam-4385	240	4	|fr	|fr	X
ejpam-4385	240	5	]	]	PUNCT
ejpam-4385	240	6	≥	≥	X
ejpam-4385	240	7	eµc	eµc	PROPN
ejpam-4385	240	8	[	[	PUNCT
ejpam-4385	240	9	1	1	NUM
ejpam-4385	240	10	2	2	NUM
ejpam-4385	240	11	(	(	PUNCT
ejpam-4385	240	12	xzµc	xzµc	PROPN
ejpam-4385	240	13	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	240	14	)	)	PUNCT
ejpam-4385	241	1	+	+	CCONJ
ejpam-4385	241	2	ϵzµc	ϵzµc	PROPN
ejpam-4385	241	3	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	241	4	)	)	PUNCT
ejpam-4385	241	5	−k	−k	PROPN
ejpam-4385	241	6	k.	k.	PROPN
ejpam-4385	241	7	falcasantos	falcasantos	PROPN
ejpam-4385	241	8	,	,	PUNCT
ejpam-4385	241	9	f.	f.	PROPN
ejpam-4385	241	10	sumalpong	sumalpong	PROPN
ejpam-4385	241	11	/	/	SYM
ejpam-4385	241	12	eur	eur	PROPN
ejpam-4385	241	13	.	.	PUNCT
ejpam-4385	242	1	j.	j.	PROPN
ejpam-4385	242	2	pure	pure	PROPN
ejpam-4385	242	3	appl	appl	PROPN
ejpam-4385	242	4	.	.	PROPN
ejpam-4385	242	5	math	math	PROPN
ejpam-4385	242	6	,	,	PUNCT
ejpam-4385	242	7	15	15	NUM
ejpam-4385	242	8	(	(	PUNCT
ejpam-4385	242	9	3	3	NUM
ejpam-4385	242	10	)	)	PUNCT
ejpam-4385	242	11	(	(	PUNCT
ejpam-4385	242	12	2022	2022	NUM
ejpam-4385	242	13	)	)	PUNCT
ejpam-4385	242	14	,	,	PUNCT
ejpam-4385	242	15	948	948	NUM
ejpam-4385	242	16	-	-	SYM
ejpam-4385	242	17	970	970	NUM
ejpam-4385	242	18	957	957	NUM
ejpam-4385	242	19	+	+	CCONJ
ejpam-4385	242	20	|xzµc	|xzµc	ADP
ejpam-4385	242	21	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	242	22	)	)	PUNCT
ejpam-4385	243	1	+	+	CCONJ
ejpam-4385	243	2	ϵzµc	ϵzµc	PROPN
ejpam-4385	243	3	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	243	4	)	)	PUNCT
ejpam-4385	243	5	−k|	−k|	NOUN
ejpam-4385	243	6	)	)	PUNCT
ejpam-4385	244	1	+	+	NUM
ejpam-4385	244	2	|ft+τ	|ft+τ	NOUN
ejpam-4385	244	3	]	]	X
ejpam-4385	244	4	}	}	PUNCT
ejpam-4385	244	5	=	=	SYM
ejpam-4385	244	6	inf	inf	NOUN
ejpam-4385	244	7	{	{	PUNCT
ejpam-4385	244	8	s	s	PROPN
ejpam-4385	244	9	∈	∈	PROPN
ejpam-4385	245	1	[	[	X
ejpam-4385	245	2	0	0	NUM
ejpam-4385	245	3	,	,	PUNCT
ejpam-4385	245	4	t	t	PROPN
ejpam-4385	245	5	−	−	PROPN
ejpam-4385	245	6	t	t	PROPN
ejpam-4385	245	7	]	]	PUNCT
ejpam-4385	245	8	:	:	PUNCT
ejpam-4385	245	9	sup	sup	NOUN
ejpam-4385	245	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	246	1	ẽ	ẽ	PROPN
ejpam-4385	246	2	[	[	PUNCT
ejpam-4385	246	3	e−	e−	PROPN
ejpam-4385	246	4	∫	∫	PROPN
ejpam-4385	246	5	t+τ	t+τ	NUM
ejpam-4385	246	6	t	t	NOUN
ejpam-4385	246	7	rudueµc	rudueµc	NOUN
ejpam-4385	246	8	[	[	X
ejpam-4385	246	9	(	(	PUNCT
ejpam-4385	246	10	xxtz	xxtz	PROPN
ejpam-4385	246	11	µc	µc	INTJ
ejpam-4385	246	12	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	246	13	)	)	PUNCT
ejpam-4385	246	14	−k	−k	PROPN
ejpam-4385	246	15	)	)	PUNCT
ejpam-4385	247	1	+	+	NUM
ejpam-4385	247	2	|ft+τ	|ft+τ	X
ejpam-4385	247	3	]	]	PUNCT
ejpam-4385	247	4	|fr	|fr	X
ejpam-4385	247	5	]	]	PUNCT
ejpam-4385	247	6	≥	≥	X
ejpam-4385	247	7	eµc	eµc	PROPN
ejpam-4385	247	8	[	[	PUNCT
ejpam-4385	247	9	1	1	NUM
ejpam-4385	247	10	2	2	NUM
ejpam-4385	247	11	(	(	PUNCT
ejpam-4385	247	12	xzµc	xzµc	PROPN
ejpam-4385	247	13	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	247	14	)	)	PUNCT
ejpam-4385	247	15	−k	−k	VERB
ejpam-4385	247	16	+	+	CCONJ
ejpam-4385	247	17	|xzµc	|xzµc	ADP
ejpam-4385	247	18	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	247	19	)	)	PUNCT
ejpam-4385	247	20	−k|	−k|	NOUN
ejpam-4385	247	21	)	)	PUNCT
ejpam-4385	248	1	+	+	NUM
ejpam-4385	248	2	|ft+τ	|ft+τ	NOUN
ejpam-4385	248	3	]	]	X
ejpam-4385	248	4	}	}	PUNCT
ejpam-4385	248	5	=	=	SYM
ejpam-4385	248	6	inf	inf	NOUN
ejpam-4385	248	7	{	{	PUNCT
ejpam-4385	248	8	s	s	PROPN
ejpam-4385	248	9	∈	∈	PROPN
ejpam-4385	249	1	[	[	X
ejpam-4385	249	2	0	0	NUM
ejpam-4385	249	3	,	,	PUNCT
ejpam-4385	249	4	t	t	PROPN
ejpam-4385	249	5	−	−	PROPN
ejpam-4385	249	6	t	t	PROPN
ejpam-4385	249	7	]	]	PUNCT
ejpam-4385	249	8	:	:	PUNCT
ejpam-4385	249	9	sup	sup	NOUN
ejpam-4385	249	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	250	1	ẽ	ẽ	PROPN
ejpam-4385	250	2	[	[	PUNCT
ejpam-4385	250	3	e−	e−	PROPN
ejpam-4385	250	4	∫	∫	PROPN
ejpam-4385	250	5	t+τ	t+τ	NUM
ejpam-4385	250	6	t	t	NOUN
ejpam-4385	250	7	rudueµc	rudueµc	NOUN
ejpam-4385	250	8	[	[	X
ejpam-4385	250	9	(	(	PUNCT
ejpam-4385	250	10	xxtz	xxtz	PROPN
ejpam-4385	250	11	µc	µc	INTJ
ejpam-4385	250	12	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	250	13	)	)	PUNCT
ejpam-4385	250	14	−k	−k	PROPN
ejpam-4385	250	15	)	)	PUNCT
ejpam-4385	251	1	+	+	NUM
ejpam-4385	251	2	|ft+τ	|ft+τ	X
ejpam-4385	251	3	]	]	PUNCT
ejpam-4385	251	4	|fr	|fr	X
ejpam-4385	251	5	]	]	PUNCT
ejpam-4385	251	6	≥	≥	X
ejpam-4385	251	7	eµc	eµc	PROPN
ejpam-4385	251	8	[	[	PUNCT
ejpam-4385	251	9	1	1	NUM
ejpam-4385	251	10	2	2	NUM
ejpam-4385	251	11	(	(	PUNCT
ejpam-4385	251	12	(	(	PUNCT
ejpam-4385	251	13	xzµc	xzµc	PROPN
ejpam-4385	251	14	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	251	15	)	)	PUNCT
ejpam-4385	251	16	−k)+	−k)+	X
ejpam-4385	251	17	]	]	PUNCT
ejpam-4385	251	18	}	}	PUNCT
ejpam-4385	251	19	=	=	SYM
ejpam-4385	251	20	inf	inf	NOUN
ejpam-4385	251	21	{	{	PUNCT
ejpam-4385	251	22	s	s	PROPN
ejpam-4385	251	23	∈	∈	PROPN
ejpam-4385	252	1	[	[	X
ejpam-4385	252	2	0	0	NUM
ejpam-4385	252	3	,	,	PUNCT
ejpam-4385	252	4	t	t	PROPN
ejpam-4385	252	5	−	−	PROPN
ejpam-4385	252	6	t	t	PROPN
ejpam-4385	252	7	]	]	PUNCT
ejpam-4385	252	8	:	:	PUNCT
ejpam-4385	252	9	sup	sup	NOUN
ejpam-4385	252	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	253	1	ẽ	ẽ	PROPN
ejpam-4385	253	2	[	[	PUNCT
ejpam-4385	253	3	e−	e−	PROPN
ejpam-4385	253	4	∫	∫	PROPN
ejpam-4385	253	5	t+τ	t+τ	NUM
ejpam-4385	253	6	t	t	NOUN
ejpam-4385	253	7	rudueµc	rudueµc	NOUN
ejpam-4385	253	8	[	[	X
ejpam-4385	253	9	(	(	PUNCT
ejpam-4385	253	10	xxtz	xxtz	PROPN
ejpam-4385	253	11	µc	µc	INTJ
ejpam-4385	253	12	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	253	13	)	)	PUNCT
ejpam-4385	253	14	−k	−k	PROPN
ejpam-4385	253	15	)	)	PUNCT
ejpam-4385	254	1	+	+	PUNCT
ejpam-4385	254	2	=	=	PUNCT
ejpam-4385	254	3	inf	inf	NOUN
ejpam-4385	254	4	{	{	PUNCT
ejpam-4385	254	5	s	s	PROPN
ejpam-4385	254	6	∈	∈	PROPN
ejpam-4385	255	1	[	[	X
ejpam-4385	255	2	0	0	NUM
ejpam-4385	255	3	,	,	PUNCT
ejpam-4385	255	4	t	t	PROPN
ejpam-4385	255	5	−	−	PROPN
ejpam-4385	255	6	t	t	PROPN
ejpam-4385	255	7	]	]	PUNCT
ejpam-4385	255	8	:	:	PUNCT
ejpam-4385	255	9	sup	sup	NOUN
ejpam-4385	255	10	0≤τ≤t−s	0≤τ≤t−s	X
ejpam-4385	256	1	ẽ	ẽ	PROPN
ejpam-4385	256	2	[	[	PUNCT
ejpam-4385	256	3	e−	e−	PROPN
ejpam-4385	256	4	∫	∫	PROPN
ejpam-4385	256	5	t+τ	t+τ	NUM
ejpam-4385	256	6	t	t	NOUN
ejpam-4385	256	7	rudueµc	rudueµc	NOUN
ejpam-4385	256	8	[	[	X
ejpam-4385	256	9	(	(	PUNCT
ejpam-4385	256	10	xxtz	xxtz	PROPN
ejpam-4385	256	11	µc	µc	INTJ
ejpam-4385	256	12	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	256	13	)	)	PUNCT
ejpam-4385	256	14	−k	−k	PROPN
ejpam-4385	256	15	)	)	PUNCT
ejpam-4385	257	1	+	+	NUM
ejpam-4385	257	2	|ft+τ	|ft+τ	X
ejpam-4385	257	3	]	]	PUNCT
ejpam-4385	257	4	|fr	|fr	X
ejpam-4385	257	5	]	]	PUNCT
ejpam-4385	257	6	=	=	SYM
ejpam-4385	257	7	eµc	eµc	PROPN
ejpam-4385	257	8	[	[	PUNCT
ejpam-4385	257	9	1	1	NUM
ejpam-4385	257	10	2	2	NUM
ejpam-4385	257	11	(	(	PUNCT
ejpam-4385	257	12	(	(	PUNCT
ejpam-4385	257	13	xzµc	xzµc	PROPN
ejpam-4385	257	14	t−(t+τ	t−(t+τ	PROPN
ejpam-4385	257	15	)	)	PUNCT
ejpam-4385	257	16	−k)+	−k)+	X
ejpam-4385	257	17	]	]	PUNCT
ejpam-4385	257	18	}	}	PUNCT
ejpam-4385	257	19	=	=	SYM
ejpam-4385	257	20	inf	inf	NOUN
ejpam-4385	257	21	{	{	PUNCT
ejpam-4385	257	22	s	s	PROPN
ejpam-4385	257	23	∈	∈	PROPN
ejpam-4385	258	1	[	[	X
ejpam-4385	258	2	0	0	NUM
ejpam-4385	258	3	,	,	PUNCT
ejpam-4385	258	4	t	t	PROPN
ejpam-4385	258	5	−	−	PROPN
ejpam-4385	258	6	t	t	PROPN
ejpam-4385	258	7	]	]	PUNCT
ejpam-4385	258	8	:	:	PUNCT
ejpam-4385	258	9	(	(	PUNCT
ejpam-4385	258	10	t	t	PROPN
ejpam-4385	258	11	,	,	PUNCT
ejpam-4385	258	12	rt	rt	PROPN
ejpam-4385	258	13	,	,	PUNCT
ejpam-4385	258	14	x	x	NOUN
ejpam-4385	258	15	)	)	PUNCT
ejpam-4385	258	16	∈	∈	PROPN
ejpam-4385	259	1	d	d	NOUN
ejpam-4385	259	2	}	}	PUNCT
ejpam-4385	259	3	.	.	PUNCT
ejpam-4385	260	1	now	now	ADV
ejpam-4385	260	2	to	to	PART
ejpam-4385	260	3	show	show	VERB
ejpam-4385	260	4	that	that	SCONJ
ejpam-4385	260	5	lim	lim	PROPN
ejpam-4385	260	6	sup	sup	PROPN
ejpam-4385	260	7	ϵ	ϵ	PROPN
ejpam-4385	260	8	↘	↘	PROPN
ejpam-4385	260	9	0	0	PROPN
ejpam-4385	260	10	f	f	PROPN
ejpam-4385	260	11	(	(	PUNCT
ejpam-4385	260	12	t	t	PROPN
ejpam-4385	260	13	,	,	PUNCT
ejpam-4385	260	14	rt	rt	PROPN
ejpam-4385	260	15	,	,	PUNCT
ejpam-4385	260	16	x+ϵ)−f	x+ϵ)−f	PROPN
ejpam-4385	260	17	(	(	PUNCT
ejpam-4385	260	18	t	t	PROPN
ejpam-4385	260	19	,	,	PUNCT
ejpam-4385	260	20	rt	rt	PROPN
ejpam-4385	260	21	,	,	PUNCT
ejpam-4385	260	22	x	x	X
ejpam-4385	260	23	)	)	PUNCT
ejpam-4385	260	24	ϵ	ϵ	ADP
ejpam-4385	260	25	≤	≤	NUM
ejpam-4385	260	26	0	0	NUM
ejpam-4385	260	27	,	,	PUNCT
ejpam-4385	260	28	we	we	PRON
ejpam-4385	260	29	use	use	VERB
ejpam-4385	260	30	the	the	DET
ejpam-4385	260	31	optimal	optimal	ADJ
ejpam-4385	260	32	stopping	stopping	NOUN
ejpam-4385	260	33	problem	problem	NOUN
ejpam-4385	260	34	.	.	PUNCT
ejpam-4385	261	1	hence	hence	ADV
ejpam-4385	261	2	,	,	PUNCT
ejpam-4385	261	3	we	we	PRON
ejpam-4385	261	4	have	have	VERB
ejpam-4385	261	5	lim	lim	PROPN
ejpam-4385	261	6	sup	sup	PROPN
ejpam-4385	261	7	ϵ	ϵ	PROPN
ejpam-4385	261	8	↘	↘	PROPN
ejpam-4385	261	9	0	0	PROPN
ejpam-4385	261	10	v	v	PROPN
ejpam-4385	261	11	(	(	PUNCT
ejpam-4385	261	12	t	t	PROPN
ejpam-4385	261	13	,	,	PUNCT
ejpam-4385	261	14	rt	rt	PROPN
ejpam-4385	261	15	,	,	PUNCT
ejpam-4385	261	16	x+	x+	PROPN
ejpam-4385	262	1	ϵ)−	ϵ)−	ADJ
ejpam-4385	262	2	v	v	NOUN
ejpam-4385	262	3	(	(	PUNCT
ejpam-4385	262	4	t	t	PROPN
ejpam-4385	262	5	,	,	PUNCT
ejpam-4385	262	6	rt	rt	PROPN
ejpam-4385	262	7	,	,	PUNCT
ejpam-4385	262	8	x	x	NOUN
ejpam-4385	262	9	)	)	PUNCT
ejpam-4385	262	10	ϵ	ϵ	X
ejpam-4385	262	11	=	=	SYM
ejpam-4385	262	12	lim	lim	PROPN
ejpam-4385	262	13	sup	sup	PROPN
ejpam-4385	262	14	ϵ	ϵ	PROPN
ejpam-4385	262	15	↘	↘	PROPN
ejpam-4385	262	16	0	0	NUM
ejpam-4385	262	17	1	1	NUM
ejpam-4385	262	18	ϵ	ϵ	NOUN
ejpam-4385	262	19	{	{	PUNCT
ejpam-4385	262	20	ẽ	ẽ	PROPN
ejpam-4385	262	21	[	[	PUNCT
ejpam-4385	262	22	e−	e−	PROPN
ejpam-4385	262	23	∫	∫	PROPN
ejpam-4385	262	24	t+τ	t+τ	NUM
ejpam-4385	262	25	t	t	PROPN
ejpam-4385	262	26	rudugµc(t+	rudugµc(t+	PRON
ejpam-4385	262	27	τ+ϵ	τ+ϵ	PUNCT
ejpam-4385	262	28	,	,	PUNCT
ejpam-4385	262	29	x+	x+	ADJ
ejpam-4385	262	30	ϵ)|ft	ϵ)|ft	NOUN
ejpam-4385	262	31	]	]	PUNCT
ejpam-4385	262	32	−	−	PROPN
ejpam-4385	262	33	sup	sup	NOUN
ejpam-4385	262	34	0≤τ≤t−t	0≤τ≤t−t	PROPN
ejpam-4385	262	35	ẽ	ẽ	PROPN
ejpam-4385	262	36	[	[	PUNCT
ejpam-4385	262	37	e−	e−	PROPN
ejpam-4385	262	38	∫	∫	PROPN
ejpam-4385	262	39	t+τ	t+τ	NUM
ejpam-4385	262	40	t	t	PROPN
ejpam-4385	262	41	rudugµc(t+	rudugµc(t+	VERB
ejpam-4385	262	42	τ	τ	PROPN
ejpam-4385	262	43	,	,	PUNCT
ejpam-4385	262	44	x	x	X
ejpam-4385	262	45	)	)	PUNCT
ejpam-4385	262	46	]	]	PUNCT
ejpam-4385	262	47	}	}	PUNCT
ejpam-4385	262	48	≤	≤	NUM
ejpam-4385	263	1	lim	lim	PROPN
ejpam-4385	263	2	sup	sup	PROPN
ejpam-4385	263	3	ϵ	ϵ	PROPN
ejpam-4385	263	4	↘	↘	PROPN
ejpam-4385	263	5	0	0	NUM
ejpam-4385	263	6	1	1	NUM
ejpam-4385	263	7	ϵ	ϵ	NOUN
ejpam-4385	263	8	{	{	PUNCT
ejpam-4385	263	9	ẽ	ẽ	PROPN
ejpam-4385	263	10	[	[	PUNCT
ejpam-4385	263	11	e−	e−	PROPN
ejpam-4385	263	12	∫	∫	PROPN
ejpam-4385	263	13	t+τ	t+τ	NUM
ejpam-4385	263	14	t	t	PROPN
ejpam-4385	263	15	rudugµc(t+	rudugµc(t+	PRON
ejpam-4385	263	16	τ+ϵ	τ+ϵ	PUNCT
ejpam-4385	263	17	,	,	PUNCT
ejpam-4385	263	18	x+	x+	ADJ
ejpam-4385	263	19	ϵ)|ft	ϵ)|ft	NOUN
ejpam-4385	263	20	]	]	PUNCT
ejpam-4385	263	21	−	−	PROPN
ejpam-4385	264	1	ẽ	ẽ	PROPN
ejpam-4385	264	2	[	[	PUNCT
ejpam-4385	264	3	e−	e−	PROPN
ejpam-4385	264	4	∫	∫	PROPN
ejpam-4385	264	5	t+τ	t+τ	NUM
ejpam-4385	264	6	t	t	PROPN
ejpam-4385	264	7	rudugµc(t+	rudugµc(t+	VERB
ejpam-4385	264	8	τ	τ	PROPN
ejpam-4385	264	9	,	,	PUNCT
ejpam-4385	264	10	x	x	X
ejpam-4385	264	11	)	)	PUNCT
ejpam-4385	264	12	]	]	PUNCT
ejpam-4385	264	13	}	}	PUNCT
ejpam-4385	264	14	≤	≤	NUM
ejpam-4385	264	15	lim	lim	PROPN
ejpam-4385	264	16	sup	sup	PROPN
ejpam-4385	264	17	ϵ	ϵ	PROPN
ejpam-4385	264	18	↘	↘	PROPN
ejpam-4385	264	19	0	0	NUM
ejpam-4385	264	20	1	1	NUM
ejpam-4385	264	21	ϵ	ϵ	NOUN
ejpam-4385	264	22	{	{	PUNCT
ejpam-4385	264	23	gµc(t+	gµc(t+	PROPN
ejpam-4385	264	24	τ+ϵ	τ+ϵ	PUNCT
ejpam-4385	264	25	,	,	PUNCT
ejpam-4385	264	26	x+	x+	X
ejpam-4385	264	27	ϵ)−gµc(t+	ϵ)−gµc(t+	NUM
ejpam-4385	264	28	τ+ϵ	τ+ϵ	PUNCT
ejpam-4385	264	29	,	,	PUNCT
ejpam-4385	264	30	x	x	X
ejpam-4385	264	31	)	)	PUNCT
ejpam-4385	264	32	}	}	PUNCT
ejpam-4385	264	33	k.	k.	PROPN
ejpam-4385	264	34	falcasantos	falcasantos	PROPN
ejpam-4385	264	35	,	,	PUNCT
ejpam-4385	264	36	f.	f.	PROPN
ejpam-4385	264	37	sumalpong	sumalpong	PROPN
ejpam-4385	264	38	/	/	SYM
ejpam-4385	264	39	eur	eur	PROPN
ejpam-4385	264	40	.	.	PUNCT
ejpam-4385	265	1	j.	j.	PROPN
ejpam-4385	265	2	pure	pure	PROPN
ejpam-4385	265	3	appl	appl	PROPN
ejpam-4385	265	4	.	.	PROPN
ejpam-4385	265	5	math	math	PROPN
ejpam-4385	265	6	,	,	PUNCT
ejpam-4385	265	7	15	15	NUM
ejpam-4385	265	8	(	(	PUNCT
ejpam-4385	265	9	3	3	NUM
ejpam-4385	265	10	)	)	PUNCT
ejpam-4385	265	11	(	(	PUNCT
ejpam-4385	265	12	2022	2022	NUM
ejpam-4385	265	13	)	)	PUNCT
ejpam-4385	265	14	,	,	PUNCT
ejpam-4385	265	15	948	948	NUM
ejpam-4385	265	16	-	-	SYM
ejpam-4385	265	17	970	970	NUM
ejpam-4385	265	18	958	958	NUM
ejpam-4385	265	19	=	=	SYM
ejpam-4385	265	20	∂gµc	∂gµc	NOUN
ejpam-4385	265	21	∂x	∂x	PROPN
ejpam-4385	265	22	(	(	PUNCT
ejpam-4385	265	23	t	t	PROPN
ejpam-4385	265	24	,	,	PUNCT
ejpam-4385	265	25	x	x	NOUN
ejpam-4385	265	26	)	)	PUNCT
ejpam-4385	265	27	.	.	PUNCT
ejpam-4385	266	1	therefore	therefore	ADV
ejpam-4385	266	2	,	,	PUNCT
ejpam-4385	266	3	lim	lim	PROPN
ejpam-4385	266	4	sup	sup	PROPN
ejpam-4385	266	5	ϵ	ϵ	PROPN
ejpam-4385	266	6	↘	↘	PROPN
ejpam-4385	266	7	0	0	PROPN
ejpam-4385	266	8	f	f	PROPN
ejpam-4385	266	9	(	(	PUNCT
ejpam-4385	266	10	t	t	PROPN
ejpam-4385	266	11	,	,	PUNCT
ejpam-4385	266	12	rt	rt	PROPN
ejpam-4385	266	13	,	,	PUNCT
ejpam-4385	266	14	x+ϵ)−f	x+ϵ)−f	PROPN
ejpam-4385	266	15	(	(	PUNCT
ejpam-4385	266	16	t	t	PROPN
ejpam-4385	266	17	,	,	PUNCT
ejpam-4385	266	18	rt	rt	PROPN
ejpam-4385	266	19	,	,	PUNCT
ejpam-4385	266	20	x	x	X
ejpam-4385	266	21	)	)	PUNCT
ejpam-4385	266	22	ϵ	ϵ	ADP
ejpam-4385	266	23	≤	≤	NUM
ejpam-4385	266	24	0	0	NUM
ejpam-4385	266	25	.	.	PUNCT
ejpam-4385	267	1	now	now	ADV
ejpam-4385	267	2	,	,	PUNCT
ejpam-4385	267	3	we	we	PRON
ejpam-4385	267	4	characterize	characterize	VERB
ejpam-4385	267	5	the	the	DET
ejpam-4385	267	6	stopping	stopping	NOUN
ejpam-4385	267	7	set	set	NOUN
ejpam-4385	267	8	defined	define	VERB
ejpam-4385	267	9	above	above	ADP
ejpam-4385	267	10	in	in	ADP
ejpam-4385	267	11	terms	term	NOUN
ejpam-4385	267	12	of	of	ADP
ejpam-4385	267	13	the	the	DET
ejpam-4385	267	14	boundary	boundary	ADJ
ejpam-4385	267	15	function	function	NOUN
ejpam-4385	267	16	bd(t	bd(t	PROPN
ejpam-4385	267	17	,	,	PUNCT
ejpam-4385	267	18	rt	rt	PROPN
ejpam-4385	267	19	)	)	PUNCT
ejpam-4385	267	20	.	.	PUNCT
ejpam-4385	268	1	proposition	proposition	NOUN
ejpam-4385	268	2	2	2	NUM
ejpam-4385	268	3	.	.	X
ejpam-4385	269	1	for	for	ADP
ejpam-4385	269	2	any	any	DET
ejpam-4385	269	3	(	(	PUNCT
ejpam-4385	269	4	t	t	PROPN
ejpam-4385	269	5	,	,	PUNCT
ejpam-4385	269	6	rt	rt	PROPN
ejpam-4385	269	7	,	,	PUNCT
ejpam-4385	269	8	x	x	NOUN
ejpam-4385	269	9	)	)	PUNCT
ejpam-4385	269	10	∈	∈	PROPN
ejpam-4385	270	1	[	[	X
ejpam-4385	270	2	0	0	NUM
ejpam-4385	270	3	,	,	PUNCT
ejpam-4385	270	4	t	t	X
ejpam-4385	270	5	]	]	X
ejpam-4385	270	6	×	×	X
ejpam-4385	270	7	r×	r×	NOUN
ejpam-4385	270	8	(	(	PUNCT
ejpam-4385	270	9	0,∞	0,∞	NOUN
ejpam-4385	270	10	)	)	PUNCT
ejpam-4385	270	11	such	such	ADJ
ejpam-4385	270	12	that	that	SCONJ
ejpam-4385	270	13	(	(	PUNCT
ejpam-4385	270	14	t	t	PROPN
ejpam-4385	270	15	,	,	PUNCT
ejpam-4385	270	16	rt	rt	PROPN
ejpam-4385	270	17	,	,	PUNCT
ejpam-4385	270	18	x	x	NOUN
ejpam-4385	270	19	)	)	PUNCT
ejpam-4385	270	20	∈	∈	PROPN
ejpam-4385	271	1	d	d	NOUN
ejpam-4385	271	2	we	we	PRON
ejpam-4385	271	3	have	have	VERB
ejpam-4385	271	4	{	{	PUNCT
ejpam-4385	271	5	t	t	PROPN
ejpam-4385	271	6	}	}	PUNCT
ejpam-4385	271	7	×	×	PROPN
ejpam-4385	271	8	{	{	PUNCT
ejpam-4385	271	9	rt	rt	PROPN
ejpam-4385	271	10	}	}	PUNCT
ejpam-4385	271	11	×	×	PROPN
ejpam-4385	271	12	(	(	PUNCT
ejpam-4385	271	13	0,∞	0,∞	NOUN
ejpam-4385	271	14	)	)	PUNCT
ejpam-4385	272	1	⊂	⊂	PROPN
ejpam-4385	273	1	d	d	X
ejpam-4385	273	2	(	(	PUNCT
ejpam-4385	273	3	32	32	NUM
ejpam-4385	273	4	)	)	PUNCT
ejpam-4385	273	5	and	and	CCONJ
ejpam-4385	273	6	d	d	NOUN
ejpam-4385	273	7	=	=	PRON
ejpam-4385	273	8	{	{	PUNCT
ejpam-4385	273	9	(	(	PUNCT
ejpam-4385	273	10	t	t	PROPN
ejpam-4385	273	11	,	,	PUNCT
ejpam-4385	273	12	rt	rt	PROPN
ejpam-4385	273	13	,	,	PUNCT
ejpam-4385	273	14	x	x	NOUN
ejpam-4385	273	15	)	)	PUNCT
ejpam-4385	273	16	∈	∈	PROPN
ejpam-4385	274	1	[	[	X
ejpam-4385	274	2	0	0	NUM
ejpam-4385	274	3	,	,	PUNCT
ejpam-4385	274	4	t	t	X
ejpam-4385	274	5	]	]	X
ejpam-4385	274	6	×	×	X
ejpam-4385	274	7	r×	r×	NOUN
ejpam-4385	274	8	(	(	PUNCT
ejpam-4385	274	9	0,∞)|v	0,∞)|v	NUM
ejpam-4385	274	10	(	(	PUNCT
ejpam-4385	274	11	t	t	PROPN
ejpam-4385	274	12	,	,	PUNCT
ejpam-4385	274	13	rt	rt	PROPN
ejpam-4385	274	14	,	,	PUNCT
ejpam-4385	274	15	x)−gµc(t	x)−gµc(t	PROPN
ejpam-4385	274	16	,	,	PUNCT
ejpam-4385	274	17	x	x	X
ejpam-4385	274	18	)	)	PUNCT
ejpam-4385	274	19	≥	≥	NOUN
ejpam-4385	274	20	0	0	NUM
ejpam-4385	274	21	}	}	PUNCT
ejpam-4385	274	22	.	.	PUNCT
ejpam-4385	275	1	(	(	PUNCT
ejpam-4385	275	2	33	33	NUM
ejpam-4385	275	3	)	)	PUNCT
ejpam-4385	275	4	proof	proof	NOUN
ejpam-4385	275	5	.	.	PUNCT
ejpam-4385	276	1	let	let	VERB
ejpam-4385	276	2	(	(	PUNCT
ejpam-4385	276	3	t	t	PROPN
ejpam-4385	276	4	,	,	PUNCT
ejpam-4385	276	5	rt	rt	PROPN
ejpam-4385	276	6	,	,	PUNCT
ejpam-4385	276	7	x	x	NOUN
ejpam-4385	276	8	)	)	PUNCT
ejpam-4385	276	9	∈	∈	PROPN
ejpam-4385	276	10	{	{	PUNCT
ejpam-4385	276	11	t	t	PROPN
ejpam-4385	276	12	}	}	PUNCT
ejpam-4385	276	13	×	×	PROPN
ejpam-4385	276	14	{	{	PUNCT
ejpam-4385	276	15	rt	rt	PROPN
ejpam-4385	276	16	}	}	PUNCT
ejpam-4385	276	17	×	×	NOUN
ejpam-4385	276	18	(	(	PUNCT
ejpam-4385	276	19	0	0	NUM
ejpam-4385	276	20	,	,	PUNCT
ejpam-4385	276	21	x	x	NOUN
ejpam-4385	276	22	)	)	PUNCT
ejpam-4385	276	23	.	.	PUNCT
ejpam-4385	277	1	since	since	SCONJ
ejpam-4385	277	2	(	(	PUNCT
ejpam-4385	277	3	t	t	PROPN
ejpam-4385	277	4	,	,	PUNCT
ejpam-4385	277	5	rt	rt	PROPN
ejpam-4385	277	6	,	,	PUNCT
ejpam-4385	277	7	x	x	NOUN
ejpam-4385	277	8	)	)	PUNCT
ejpam-4385	277	9	∈	∈	PROPN
ejpam-4385	277	10	d	d	NOUN
ejpam-4385	277	11	and	and	CCONJ
ejpam-4385	277	12	v	v	PROPN
ejpam-4385	277	13	(	(	PUNCT
ejpam-4385	277	14	t	t	PROPN
ejpam-4385	277	15	,	,	PUNCT
ejpam-4385	277	16	rt	rt	PROPN
ejpam-4385	277	17	,	,	PUNCT
ejpam-4385	277	18	x	x	NOUN
ejpam-4385	277	19	)	)	PUNCT
ejpam-4385	277	20	≥	≥	X
ejpam-4385	277	21	gµc(t	gµc(t	NOUN
ejpam-4385	277	22	,	,	PUNCT
ejpam-4385	277	23	x	x	NOUN
ejpam-4385	277	24	)	)	PUNCT
ejpam-4385	277	25	for	for	ADP
ejpam-4385	277	26	all	all	DET
ejpam-4385	277	27	x	x	SYM
ejpam-4385	277	28	∈	∈	PROPN
ejpam-4385	277	29	(	(	PUNCT
ejpam-4385	277	30	0,∞	0,∞	NOUN
ejpam-4385	277	31	)	)	PUNCT
ejpam-4385	277	32	,	,	PUNCT
ejpam-4385	277	33	we	we	PRON
ejpam-4385	277	34	have	have	VERB
ejpam-4385	277	35	v	v	NUM
ejpam-4385	277	36	(	(	PUNCT
ejpam-4385	277	37	t	t	PROPN
ejpam-4385	277	38	,	,	PUNCT
ejpam-4385	277	39	rt	rt	PROPN
ejpam-4385	277	40	,	,	PUNCT
ejpam-4385	277	41	x)−	x)−	PROPN
ejpam-4385	277	42	v	v	PROPN
ejpam-4385	277	43	(	(	PUNCT
ejpam-4385	277	44	t	t	PROPN
ejpam-4385	277	45	,	,	PUNCT
ejpam-4385	277	46	rt	rt	PROPN
ejpam-4385	277	47	,	,	PUNCT
ejpam-4385	277	48	y	y	PROPN
ejpam-4385	277	49	)	)	PUNCT
ejpam-4385	277	50	x−	x−	PROPN
ejpam-4385	277	51	y	y	PROPN
ejpam-4385	277	52	=	=	SYM
ejpam-4385	277	53	gµc(t	gµc(t	PROPN
ejpam-4385	277	54	,	,	PUNCT
ejpam-4385	277	55	x)−	x)−	PROPN
ejpam-4385	277	56	v	v	PROPN
ejpam-4385	277	57	(	(	PUNCT
ejpam-4385	277	58	t	t	PROPN
ejpam-4385	277	59	,	,	PUNCT
ejpam-4385	277	60	rt	rt	PROPN
ejpam-4385	277	61	,	,	PUNCT
ejpam-4385	277	62	y	y	PROPN
ejpam-4385	277	63	)	)	PUNCT
ejpam-4385	277	64	x−	x−	PROPN
ejpam-4385	278	1	y	y	PROPN
ejpam-4385	278	2	≤	≤	PROPN
ejpam-4385	278	3	gµc(t	gµc(t	PROPN
ejpam-4385	278	4	,	,	PUNCT
ejpam-4385	278	5	x)−gµc(t	x)−gµc(t	PROPN
ejpam-4385	278	6	,	,	PUNCT
ejpam-4385	278	7	y	y	PROPN
ejpam-4385	278	8	)	)	PUNCT
ejpam-4385	278	9	x−	x−	PROPN
ejpam-4385	278	10	y	y	PROPN
ejpam-4385	278	11	.	.	PUNCT
ejpam-4385	279	1	taking	take	VERB
ejpam-4385	279	2	the	the	DET
ejpam-4385	279	3	limit	limit	NOUN
ejpam-4385	279	4	on	on	ADP
ejpam-4385	279	5	both	both	DET
ejpam-4385	279	6	sides	side	NOUN
ejpam-4385	279	7	as	as	ADP
ejpam-4385	279	8	x−	x−	PROPN
ejpam-4385	279	9	y	y	PROPN
ejpam-4385	279	10	→	→	SYM
ejpam-4385	279	11	0	0	NUM
ejpam-4385	279	12	and	and	CCONJ
ejpam-4385	279	13	by	by	ADP
ejpam-4385	279	14	lemma	lemma	PROPN
ejpam-4385	279	15	1	1	NUM
ejpam-4385	279	16	,	,	PUNCT
ejpam-4385	279	17	we	we	PRON
ejpam-4385	279	18	have	have	VERB
ejpam-4385	279	19	(	(	PUNCT
ejpam-4385	279	20	t	t	PROPN
ejpam-4385	279	21	,	,	PUNCT
ejpam-4385	279	22	rt	rt	PROPN
ejpam-4385	279	23	,	,	PUNCT
ejpam-4385	279	24	y	y	PROPN
ejpam-4385	279	25	)	)	PUNCT
ejpam-4385	279	26	∈	∈	PROPN
ejpam-4385	279	27	d	d	NOUN
ejpam-4385	279	28	and	and	CCONJ
ejpam-4385	279	29	conclude	conclude	VERB
ejpam-4385	279	30	that	that	SCONJ
ejpam-4385	279	31	{	{	PUNCT
ejpam-4385	279	32	t	t	NOUN
ejpam-4385	279	33	}	}	PUNCT
ejpam-4385	279	34	×	×	PROPN
ejpam-4385	279	35	{	{	PUNCT
ejpam-4385	279	36	rt	rt	PROPN
ejpam-4385	279	37	}	}	PUNCT
ejpam-4385	279	38	×	×	PROPN
ejpam-4385	279	39	(	(	PUNCT
ejpam-4385	279	40	0,∞	0,∞	NOUN
ejpam-4385	279	41	)	)	PUNCT
ejpam-4385	280	1	⊂	⊂	PROPN
ejpam-4385	280	2	d.	d.	PROPN
ejpam-4385	280	3	furthermore	furthermore	ADV
ejpam-4385	280	4	,	,	PUNCT
ejpam-4385	280	5	by	by	ADP
ejpam-4385	280	6	the	the	DET
ejpam-4385	280	7	definition	definition	NOUN
ejpam-4385	280	8	of	of	ADP
ejpam-4385	280	9	the	the	DET
ejpam-4385	280	10	optimal	optimal	ADJ
ejpam-4385	280	11	stopping	stopping	NOUN
ejpam-4385	280	12	boundary	boundary	ADJ
ejpam-4385	280	13	bd(t	bd(t	PROPN
ejpam-4385	280	14	,	,	PUNCT
ejpam-4385	280	15	rt	rt	PROPN
ejpam-4385	280	16	)	)	PUNCT
ejpam-4385	280	17	=	=	SYM
ejpam-4385	280	18	sup	sup	NOUN
ejpam-4385	280	19	{	{	PUNCT
ejpam-4385	280	20	x	x	SYM
ejpam-4385	280	21	∈	∈	PROPN
ejpam-4385	280	22	(	(	PUNCT
ejpam-4385	280	23	0,∞	0,∞	NOUN
ejpam-4385	280	24	)	)	PUNCT
ejpam-4385	280	25	:	:	PUNCT
ejpam-4385	280	26	(	(	PUNCT
ejpam-4385	280	27	t	t	PROPN
ejpam-4385	280	28	,	,	PUNCT
ejpam-4385	280	29	rt	rt	PROPN
ejpam-4385	280	30	,	,	PUNCT
ejpam-4385	280	31	x	x	NOUN
ejpam-4385	280	32	)	)	PUNCT
ejpam-4385	280	33	∈	∈	PROPN
ejpam-4385	281	1	d	d	NOUN
ejpam-4385	281	2	}	}	PUNCT
ejpam-4385	281	3	,	,	PUNCT
ejpam-4385	281	4	we	we	PRON
ejpam-4385	281	5	have	have	VERB
ejpam-4385	281	6	the	the	DET
ejpam-4385	281	7	equivalence	equivalence	NOUN
ejpam-4385	281	8	(	(	PUNCT
ejpam-4385	281	9	t	t	PROPN
ejpam-4385	281	10	,	,	PUNCT
ejpam-4385	281	11	rt	rt	PROPN
ejpam-4385	281	12	,	,	PUNCT
ejpam-4385	281	13	x	x	NOUN
ejpam-4385	281	14	)	)	PUNCT
ejpam-4385	281	15	∈	∈	PROPN
ejpam-4385	282	1	d	d	X
ejpam-4385	282	2	⇐	⇐	ADJ
ejpam-4385	282	3	⇒	⇒	PROPN
ejpam-4385	282	4	{	{	PUNCT
ejpam-4385	282	5	t	t	PROPN
ejpam-4385	282	6	}	}	PUNCT
ejpam-4385	282	7	×	×	PROPN
ejpam-4385	282	8	{	{	PUNCT
ejpam-4385	282	9	rt	rt	PROPN
ejpam-4385	282	10	}	}	PUNCT
ejpam-4385	282	11	×	×	PROPN
ejpam-4385	282	12	(	(	PUNCT
ejpam-4385	282	13	0,∞	0,∞	NOUN
ejpam-4385	282	14	)	)	PUNCT
ejpam-4385	282	15	⊂	⊂	PROPN
ejpam-4385	283	1	d	d	X
ejpam-4385	283	2	⇐	⇐	ADJ
ejpam-4385	283	3	⇒	⇒	PROPN
ejpam-4385	283	4	x	x	PUNCT
ejpam-4385	283	5	≥	≥	PROPN
ejpam-4385	283	6	bd(t	bd(t	PROPN
ejpam-4385	283	7	,	,	PUNCT
ejpam-4385	283	8	rt	rt	PROPN
ejpam-4385	283	9	)	)	PUNCT
ejpam-4385	283	10	.	.	PUNCT
ejpam-4385	284	1	k.	k.	PROPN
ejpam-4385	284	2	falcasantos	falcasantos	PROPN
ejpam-4385	284	3	,	,	PUNCT
ejpam-4385	284	4	f.	f.	PROPN
ejpam-4385	284	5	sumalpong	sumalpong	PROPN
ejpam-4385	284	6	/	/	SYM
ejpam-4385	284	7	eur	eur	PROPN
ejpam-4385	284	8	.	.	PUNCT
ejpam-4385	285	1	j.	j.	PROPN
ejpam-4385	285	2	pure	pure	PROPN
ejpam-4385	285	3	appl	appl	PROPN
ejpam-4385	285	4	.	.	PROPN
ejpam-4385	285	5	math	math	PROPN
ejpam-4385	285	6	,	,	PUNCT
ejpam-4385	285	7	15	15	NUM
ejpam-4385	285	8	(	(	PUNCT
ejpam-4385	285	9	3	3	NUM
ejpam-4385	285	10	)	)	PUNCT
ejpam-4385	285	11	(	(	PUNCT
ejpam-4385	285	12	2022	2022	NUM
ejpam-4385	285	13	)	)	PUNCT
ejpam-4385	285	14	,	,	PUNCT
ejpam-4385	285	15	948	948	NUM
ejpam-4385	285	16	-	-	SYM
ejpam-4385	285	17	970	970	NUM
ejpam-4385	285	18	959	959	NUM
ejpam-4385	285	19	5	5	NUM
ejpam-4385	285	20	.	.	PUNCT
ejpam-4385	286	1	continuity	continuity	NOUN
ejpam-4385	286	2	lemmas	lemma	VERB
ejpam-4385	286	3	we	we	PRON
ejpam-4385	286	4	next	next	ADV
ejpam-4385	286	5	discuss	discuss	VERB
ejpam-4385	286	6	the	the	DET
ejpam-4385	286	7	following	follow	VERB
ejpam-4385	286	8	continuity	continuity	NOUN
ejpam-4385	286	9	results	result	NOUN
ejpam-4385	286	10	on	on	ADP
ejpam-4385	286	11	the	the	DET
ejpam-4385	286	12	payoff	payoff	NOUN
ejpam-4385	286	13	and	and	CCONJ
ejpam-4385	286	14	option	option	NOUN
ejpam-4385	286	15	price	price	NOUN
ejpam-4385	286	16	functions	function	NOUN
ejpam-4385	286	17	to	to	PART
ejpam-4385	286	18	show	show	VERB
ejpam-4385	286	19	that	that	SCONJ
ejpam-4385	286	20	the	the	DET
ejpam-4385	286	21	stopping	stopping	NOUN
ejpam-4385	286	22	set	set	VERB
ejpam-4385	286	23	d	d	NOUN
ejpam-4385	286	24	given	give	VERB
ejpam-4385	286	25	by	by	ADP
ejpam-4385	286	26	d	d	PROPN
ejpam-4385	286	27	=	=	SYM
ejpam-4385	286	28	{	{	PUNCT
ejpam-4385	286	29	(	(	PUNCT
ejpam-4385	286	30	t	t	PROPN
ejpam-4385	286	31	,	,	PUNCT
ejpam-4385	286	32	rt	rt	PROPN
ejpam-4385	286	33	,	,	PUNCT
ejpam-4385	286	34	x	x	NOUN
ejpam-4385	286	35	)	)	PUNCT
ejpam-4385	286	36	=	=	SYM
ejpam-4385	286	37	v	v	NOUN
ejpam-4385	286	38	(	(	PUNCT
ejpam-4385	286	39	t	t	PROPN
ejpam-4385	286	40	,	,	PUNCT
ejpam-4385	286	41	rt	rt	PROPN
ejpam-4385	286	42	,	,	PUNCT
ejpam-4385	286	43	x)−gµc(t	x)−gµc(t	PROPN
ejpam-4385	286	44	,	,	PUNCT
ejpam-4385	286	45	x	x	X
ejpam-4385	286	46	)	)	PUNCT
ejpam-4385	286	47	≥	≥	NOUN
ejpam-4385	286	48	0	0	NUM
ejpam-4385	286	49	}	}	PUNCT
ejpam-4385	286	50	is	be	AUX
ejpam-4385	286	51	closed	closed	ADJ
ejpam-4385	286	52	.	.	PUNCT
ejpam-4385	287	1	lemma	lemma	PROPN
ejpam-4385	287	2	2	2	NUM
ejpam-4385	287	3	.	.	PUNCT
ejpam-4385	288	1	the	the	DET
ejpam-4385	288	2	mapping	mapping	NOUN
ejpam-4385	288	3	(	(	PUNCT
ejpam-4385	288	4	t	t	PROPN
ejpam-4385	288	5	,	,	PUNCT
ejpam-4385	288	6	x	x	NOUN
ejpam-4385	288	7	)	)	PUNCT
ejpam-4385	288	8	7→	7→	PROPN
ejpam-4385	288	9	gµc(t	gµc(t	NOUN
ejpam-4385	288	10	,	,	PUNCT
ejpam-4385	288	11	x	x	PRON
ejpam-4385	288	12	)	)	PUNCT
ejpam-4385	288	13	is	be	AUX
ejpam-4385	288	14	jointly	jointly	ADV
ejpam-4385	288	15	continuous	continuous	ADJ
ejpam-4385	288	16	on	on	ADP
ejpam-4385	288	17	[	[	X
ejpam-4385	288	18	0	0	NUM
ejpam-4385	288	19	,	,	PUNCT
ejpam-4385	288	20	t	t	X
ejpam-4385	288	21	]	]	X
ejpam-4385	288	22	×	×	NOUN
ejpam-4385	288	23	(	(	PUNCT
ejpam-4385	288	24	0,∞	0,∞	NUM
ejpam-4385	288	25	)	)	PUNCT
ejpam-4385	288	26	.	.	PUNCT
ejpam-4385	289	1	proof	proof	NOUN
ejpam-4385	289	2	.	.	PUNCT
ejpam-4385	290	1	the	the	DET
ejpam-4385	290	2	continuity	continuity	NOUN
ejpam-4385	290	3	of	of	ADP
ejpam-4385	290	4	the	the	DET
ejpam-4385	290	5	mapping	mapping	NOUN
ejpam-4385	290	6	x	x	PUNCT
ejpam-4385	290	7	7→	7→	NUM
ejpam-4385	290	8	gµc(t	gµc(t	NOUN
ejpam-4385	290	9	,	,	PUNCT
ejpam-4385	290	10	x	x	PRON
ejpam-4385	290	11	)	)	PUNCT
ejpam-4385	290	12	follows	follow	VERB
ejpam-4385	290	13	from	from	ADP
ejpam-4385	290	14	the	the	DET
ejpam-4385	290	15	fact	fact	NOUN
ejpam-4385	290	16	that	that	SCONJ
ejpam-4385	290	17	gµc(t	gµc(t	PROPN
ejpam-4385	290	18	,	,	PUNCT
ejpam-4385	290	19	x	x	PRON
ejpam-4385	290	20	)	)	PUNCT
ejpam-4385	290	21	is	be	AUX
ejpam-4385	290	22	convex	convex	ADJ
ejpam-4385	290	23	with	with	ADP
ejpam-4385	290	24	respect	respect	NOUN
ejpam-4385	290	25	to	to	ADP
ejpam-4385	290	26	x	x	SYM
ejpam-4385	290	27	∈	∈	PROPN
ejpam-4385	290	28	(	(	PUNCT
ejpam-4385	290	29	0,∞	0,∞	NOUN
ejpam-4385	290	30	)	)	PUNCT
ejpam-4385	290	31	for	for	ADP
ejpam-4385	290	32	any	any	DET
ejpam-4385	290	33	t	t	NOUN
ejpam-4385	290	34	∈	∈	PROPN
ejpam-4385	291	1	[	[	X
ejpam-4385	291	2	0	0	NUM
ejpam-4385	291	3	,	,	PUNCT
ejpam-4385	291	4	t	t	NOUN
ejpam-4385	291	5	]	]	PUNCT
ejpam-4385	291	6	given	give	VERB
ejpam-4385	291	7	and	and	CCONJ
ejpam-4385	291	8	fixed	fix	VERB
ejpam-4385	291	9	.	.	PUNCT
ejpam-4385	292	1	it	it	PRON
ejpam-4385	292	2	remains	remain	VERB
ejpam-4385	292	3	to	to	PART
ejpam-4385	292	4	show	show	VERB
ejpam-4385	292	5	the	the	DET
ejpam-4385	292	6	uniform	uniform	ADJ
ejpam-4385	292	7	continuity	continuity	NOUN
ejpam-4385	292	8	of	of	ADP
ejpam-4385	292	9	the	the	DET
ejpam-4385	292	10	mapping	mapping	NOUN
ejpam-4385	292	11	t	t	PROPN
ejpam-4385	292	12	7→	7→	PROPN
ejpam-4385	292	13	gµc(t	gµc(t	PROPN
ejpam-4385	292	14	,	,	PUNCT
ejpam-4385	292	15	x	x	NOUN
ejpam-4385	292	16	)	)	PUNCT
ejpam-4385	292	17	.	.	PUNCT
ejpam-4385	293	1	let	let	VERB
ejpam-4385	293	2	x	x	X
ejpam-4385	293	3	∈	∈	PROPN
ejpam-4385	293	4	(	(	PUNCT
ejpam-4385	293	5	0,∞	0,∞	NOUN
ejpam-4385	293	6	)	)	PUNCT
ejpam-4385	293	7	be	be	AUX
ejpam-4385	293	8	given	give	VERB
ejpam-4385	293	9	and	and	CCONJ
ejpam-4385	293	10	fixed	fix	VERB
ejpam-4385	293	11	and	and	CCONJ
ejpam-4385	293	12	0	0	NUM
ejpam-4385	293	13	≤	≤	NUM
ejpam-4385	293	14	t1	t1	NOUN
ejpam-4385	293	15	≤	≤	PUNCT
ejpam-4385	293	16	t2	t2	PROPN
ejpam-4385	293	17	≤	≤	PROPN
ejpam-4385	293	18	t	t	NOUN
ejpam-4385	293	19	.	.	PUNCT
ejpam-4385	294	1	thus	thus	ADV
ejpam-4385	294	2	0	0	NUM
ejpam-4385	294	3	≤	≤	NUM
ejpam-4385	294	4	∣∣∣∣gµc(t2	∣∣∣∣gµc(t2	PROPN
ejpam-4385	294	5	,	,	PUNCT
ejpam-4385	294	6	x)−gµc(t1	x)−gµc(t1	PROPN
ejpam-4385	294	7	,	,	PUNCT
ejpam-4385	294	8	x	x	X
ejpam-4385	294	9	)	)	PUNCT
ejpam-4385	294	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4385	294	11	by	by	ADP
ejpam-4385	294	12	definition	definition	NOUN
ejpam-4385	294	13	of	of	ADP
ejpam-4385	294	14	absolute	absolute	ADJ
ejpam-4385	294	15	value	value	NOUN
ejpam-4385	294	16	=	=	SYM
ejpam-4385	294	17	∣∣∣∣eµc	∣∣∣∣eµc	PROPN
ejpam-4385	294	18	[	[	PUNCT
ejpam-4385	294	19	(	(	PUNCT
ejpam-4385	294	20	xzµc	xzµc	PROPN
ejpam-4385	294	21	t−t2	t−t2	X
ejpam-4385	294	22	−k	−k	PROPN
ejpam-4385	294	23	)	)	PUNCT
ejpam-4385	294	24	+	+	X
ejpam-4385	294	25	|ft2	|ft2	PROPN
ejpam-4385	294	26	]	]	PUNCT
ejpam-4385	294	27	−	−	PROPN
ejpam-4385	294	28	eµc	eµc	PROPN
ejpam-4385	294	29	[	[	PUNCT
ejpam-4385	294	30	(	(	PUNCT
ejpam-4385	294	31	xzµc	xzµc	X
ejpam-4385	294	32	t−t1	t−t1	CCONJ
ejpam-4385	294	33	−k	−k	PROPN
ejpam-4385	294	34	)	)	PUNCT
ejpam-4385	295	1	+	+	ADJ
ejpam-4385	295	2	|ft1	|ft1	ADV
ejpam-4385	295	3	]	]	X
ejpam-4385	295	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4385	295	5	by	by	ADP
ejpam-4385	295	6	equation	equation	NOUN
ejpam-4385	295	7	(	(	PUNCT
ejpam-4385	295	8	17	17	NUM
ejpam-4385	295	9	)	)	PUNCT
ejpam-4385	295	10	≤	≤	NOUN
ejpam-4385	295	11	∣∣∣∣eµc	∣∣∣∣eµc	PROPN
ejpam-4385	295	12	[	[	PUNCT
ejpam-4385	295	13	(	(	PUNCT
ejpam-4385	295	14	xzµc	xzµc	PROPN
ejpam-4385	295	15	t−t2	t−t2	X
ejpam-4385	295	16	−k	−k	PROPN
ejpam-4385	295	17	)	)	PUNCT
ejpam-4385	295	18	+	+	CCONJ
ejpam-4385	295	19	−	−	PROPN
ejpam-4385	295	20	(	(	PUNCT
ejpam-4385	295	21	xzµc	xzµc	X
ejpam-4385	295	22	t−t1	t−t1	CCONJ
ejpam-4385	295	23	−k	−k	PROPN
ejpam-4385	295	24	)	)	PUNCT
ejpam-4385	295	25	+	+	X
ejpam-4385	295	26	|ft2	|ft2	PROPN
ejpam-4385	295	27	]	]	PUNCT
ejpam-4385	295	28	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4385	295	29	by	by	ADP
ejpam-4385	295	30	monotonicity	monotonicity	NOUN
ejpam-4385	295	31	≤	≤	NUM
ejpam-4385	295	32	eµc	eµc	PROPN
ejpam-4385	296	1	[	[	X
ejpam-4385	296	2	∣∣∣(xzµc	∣∣∣(xzµc	X
ejpam-4385	296	3	t−t2	t−t2	NOUN
ejpam-4385	296	4	−k	−k	NOUN
ejpam-4385	296	5	)	)	PUNCT
ejpam-4385	297	1	+	+	CCONJ
ejpam-4385	297	2	−	−	PROPN
ejpam-4385	297	3	(	(	PUNCT
ejpam-4385	297	4	xzµc	xzµc	X
ejpam-4385	297	5	t−t1	t−t1	CCONJ
ejpam-4385	297	6	−k	−k	PROPN
ejpam-4385	297	7	)	)	PUNCT
ejpam-4385	298	1	+	+	CCONJ
ejpam-4385	298	2	∣∣∣	∣∣∣	X
ejpam-4385	298	3	|ft2	|ft2	PROPN
ejpam-4385	298	4	]	]	PUNCT
ejpam-4385	298	5	since	since	SCONJ
ejpam-4385	298	6	|e(x)|	|e(x)|	PROPN
ejpam-4385	298	7	≤	≤	NUM
ejpam-4385	298	8	e(|x|	e(|x|	PROPN
ejpam-4385	298	9	)	)	PUNCT
ejpam-4385	298	10	=	=	PUNCT
ejpam-4385	299	1	xeµc	xeµc	NOUN
ejpam-4385	300	1	[	[	X
ejpam-4385	300	2	∣∣∣(zµc	∣∣∣(zµc	NOUN
ejpam-4385	300	3	t−t1	t−t1	CCONJ
ejpam-4385	300	4	−	−	PROPN
ejpam-4385	300	5	zµc	zµc	NOUN
ejpam-4385	300	6	t−t2	t−t2	NOUN
ejpam-4385	300	7	)	)	PUNCT
ejpam-4385	300	8	+	+	CCONJ
ejpam-4385	300	9	∣∣∣	∣∣∣	X
ejpam-4385	300	10	|ft2	|ft2	PROPN
ejpam-4385	300	11	]	]	PUNCT
ejpam-4385	300	12	since	since	SCONJ
ejpam-4385	300	13	−k	−k	NOUN
ejpam-4385	300	14	−−k	−−k	NOUN
ejpam-4385	300	15	=	=	SYM
ejpam-4385	300	16	0	0	NUM
ejpam-4385	300	17	.	.	PUNCT
ejpam-4385	301	1	therefore	therefore	ADV
ejpam-4385	301	2	,	,	PUNCT
ejpam-4385	301	3	as	as	ADP
ejpam-4385	301	4	|t2	|t2	ADP
ejpam-4385	301	5	−	−	PROPN
ejpam-4385	301	6	t1|	t1|	PROPN
ejpam-4385	301	7	→	→	PROPN
ejpam-4385	301	8	0	0	NUM
ejpam-4385	301	9	,	,	PUNCT
ejpam-4385	301	10	we	we	PRON
ejpam-4385	301	11	have	have	VERB
ejpam-4385	301	12	gµc(t2	gµc(t2	NOUN
ejpam-4385	301	13	,	,	PUNCT
ejpam-4385	301	14	x	x	NOUN
ejpam-4385	301	15	)	)	PUNCT
ejpam-4385	302	1	−	−	PROPN
ejpam-4385	302	2	gµc(t	gµc(t	PROPN
ejpam-4385	302	3	,	,	PUNCT
ejpam-4385	302	4	x	x	NOUN
ejpam-4385	302	5	)	)	PUNCT
ejpam-4385	302	6	→	→	SYM
ejpam-4385	302	7	0	0	NUM
ejpam-4385	302	8	,	,	PUNCT
ejpam-4385	302	9	which	which	PRON
ejpam-4385	302	10	completes	complete	VERB
ejpam-4385	302	11	our	our	PRON
ejpam-4385	302	12	proof	proof	NOUN
ejpam-4385	302	13	.	.	PUNCT
ejpam-4385	303	1	lemma	lemma	PROPN
ejpam-4385	303	2	3	3	NUM
ejpam-4385	303	3	.	.	PUNCT
ejpam-4385	304	1	the	the	DET
ejpam-4385	304	2	mapping	mapping	NOUN
ejpam-4385	304	3	(	(	PUNCT
ejpam-4385	304	4	t	t	PROPN
ejpam-4385	304	5	,	,	PUNCT
ejpam-4385	304	6	rt	rt	PROPN
ejpam-4385	304	7	,	,	PUNCT
ejpam-4385	304	8	x	x	NOUN
ejpam-4385	304	9	)	)	PUNCT
ejpam-4385	304	10	7→	7→	NUM
ejpam-4385	304	11	v	v	NOUN
ejpam-4385	304	12	(	(	PUNCT
ejpam-4385	304	13	t	t	PROPN
ejpam-4385	304	14	,	,	PUNCT
ejpam-4385	304	15	rt	rt	PROPN
ejpam-4385	304	16	,	,	PUNCT
ejpam-4385	304	17	x	x	X
ejpam-4385	304	18	)	)	PUNCT
ejpam-4385	304	19	is	be	AUX
ejpam-4385	304	20	jointly	jointly	ADV
ejpam-4385	304	21	continuous	continuous	ADJ
ejpam-4385	304	22	on	on	ADP
ejpam-4385	304	23	[	[	X
ejpam-4385	304	24	0	0	NUM
ejpam-4385	304	25	,	,	PUNCT
ejpam-4385	304	26	t	t	NOUN
ejpam-4385	304	27	]	]	SYM
ejpam-4385	304	28	×r×(0,∞	×r×(0,∞	NOUN
ejpam-4385	304	29	)	)	PUNCT
ejpam-4385	304	30	.	.	PUNCT
ejpam-4385	305	1	proof	proof	NOUN
ejpam-4385	305	2	.	.	PUNCT
ejpam-4385	306	1	for	for	ADP
ejpam-4385	306	2	t	t	PROPN
ejpam-4385	306	3	∈	∈	PROPN
ejpam-4385	307	1	[	[	X
ejpam-4385	307	2	0	0	NUM
ejpam-4385	307	3	,	,	PUNCT
ejpam-4385	307	4	t	t	NOUN
ejpam-4385	307	5	]	]	PUNCT
ejpam-4385	307	6	and	and	CCONJ
ejpam-4385	307	7	rt	rt	PROPN
ejpam-4385	307	8	∈	∈	PROPN
ejpam-4385	307	9	r	r	NOUN
ejpam-4385	307	10	given	give	VERB
ejpam-4385	307	11	and	and	CCONJ
ejpam-4385	307	12	fixed	fix	VERB
ejpam-4385	307	13	,	,	PUNCT
ejpam-4385	307	14	the	the	DET
ejpam-4385	307	15	continuity	continuity	NOUN
ejpam-4385	307	16	of	of	ADP
ejpam-4385	307	17	the	the	DET
ejpam-4385	307	18	mapping	mapping	NOUN
ejpam-4385	307	19	x	x	SYM
ejpam-4385	307	20	7→	7→	NUM
ejpam-4385	307	21	v	v	NOUN
ejpam-4385	307	22	(	(	PUNCT
ejpam-4385	307	23	t	t	PROPN
ejpam-4385	307	24	,	,	PUNCT
ejpam-4385	307	25	rt	rt	PROPN
ejpam-4385	307	26	,	,	PUNCT
ejpam-4385	307	27	x	x	NOUN
ejpam-4385	307	28	)	)	PUNCT
ejpam-4385	307	29	on	on	ADP
ejpam-4385	307	30	(	(	PUNCT
ejpam-4385	307	31	0,∞	0,∞	NOUN
ejpam-4385	307	32	)	)	PUNCT
ejpam-4385	307	33	follows	follow	VERB
ejpam-4385	307	34	from	from	ADP
ejpam-4385	307	35	the	the	DET
ejpam-4385	307	36	fact	fact	NOUN
ejpam-4385	307	37	that	that	SCONJ
ejpam-4385	307	38	it	it	PRON
ejpam-4385	307	39	is	be	AUX
ejpam-4385	307	40	convex	convex	ADJ
ejpam-4385	307	41	on	on	ADP
ejpam-4385	307	42	(	(	PUNCT
ejpam-4385	307	43	0,∞	0,∞	NOUN
ejpam-4385	307	44	)	)	PUNCT
ejpam-4385	307	45	.	.	PUNCT
ejpam-4385	308	1	also	also	ADV
ejpam-4385	308	2	,	,	PUNCT
ejpam-4385	308	3	the	the	DET
ejpam-4385	308	4	mapping	mapping	NOUN
ejpam-4385	308	5	rt	rt	PROPN
ejpam-4385	308	6	7→	7→	NUM
ejpam-4385	308	7	v	v	NOUN
ejpam-4385	308	8	(	(	PUNCT
ejpam-4385	308	9	t	t	PROPN
ejpam-4385	308	10	,	,	PUNCT
ejpam-4385	308	11	rt	rt	PROPN
ejpam-4385	308	12	,	,	PUNCT
ejpam-4385	308	13	x	x	X
ejpam-4385	308	14	)	)	PUNCT
ejpam-4385	308	15	is	be	AUX
ejpam-4385	308	16	continuous	continuous	ADJ
ejpam-4385	308	17	on	on	ADP
ejpam-4385	308	18	r	r	NOUN
ejpam-4385	308	19	since	since	SCONJ
ejpam-4385	308	20	the	the	DET
ejpam-4385	308	21	zero	zero	NUM
ejpam-4385	308	22	-	-	PUNCT
ejpam-4385	308	23	coupon	coupon	NOUN
ejpam-4385	308	24	bond	bond	NOUN
ejpam-4385	308	25	price	price	NOUN
ejpam-4385	308	26	p	p	X
ejpam-4385	308	27	(	(	PUNCT
ejpam-4385	308	28	t	t	PROPN
ejpam-4385	308	29	,	,	PUNCT
ejpam-4385	308	30	rt	rt	PROPN
ejpam-4385	308	31	;	;	PUNCT
ejpam-4385	308	32	t+	t+	X
ejpam-4385	308	33	τ	τ	X
ejpam-4385	308	34	)	)	PUNCT
ejpam-4385	308	35	is	be	AUX
ejpam-4385	308	36	continuous	continuous	ADJ
ejpam-4385	308	37	with	with	ADP
ejpam-4385	308	38	respect	respect	NOUN
ejpam-4385	308	39	to	to	ADP
ejpam-4385	308	40	rt	rt	PROPN
ejpam-4385	308	41	on	on	ADP
ejpam-4385	308	42	r	r	NOUN
ejpam-4385	308	43	for	for	ADP
ejpam-4385	308	44	t	t	PROPN
ejpam-4385	308	45	∈	∈	PROPN
ejpam-4385	309	1	[	[	X
ejpam-4385	309	2	0	0	NUM
ejpam-4385	309	3	,	,	PUNCT
ejpam-4385	309	4	t	t	NOUN
ejpam-4385	309	5	]	]	PUNCT
ejpam-4385	309	6	and	and	CCONJ
ejpam-4385	309	7	x	x	PUNCT
ejpam-4385	309	8	∈	∈	PROPN
ejpam-4385	309	9	(	(	PUNCT
ejpam-4385	309	10	0,∞	0,∞	NOUN
ejpam-4385	309	11	)	)	PUNCT
ejpam-4385	309	12	given	give	VERB
ejpam-4385	309	13	and	and	CCONJ
ejpam-4385	309	14	fixed	fix	VERB
ejpam-4385	309	15	.	.	PUNCT
ejpam-4385	310	1	it	it	PRON
ejpam-4385	310	2	remains	remain	VERB
ejpam-4385	310	3	to	to	PART
ejpam-4385	310	4	show	show	VERB
ejpam-4385	310	5	that	that	SCONJ
ejpam-4385	310	6	t	t	PROPN
ejpam-4385	310	7	7→	7→	NUM
ejpam-4385	310	8	v	v	NOUN
ejpam-4385	310	9	(	(	PUNCT
ejpam-4385	310	10	t	t	PROPN
ejpam-4385	310	11	,	,	PUNCT
ejpam-4385	310	12	rt	rt	PROPN
ejpam-4385	310	13	,	,	PUNCT
ejpam-4385	310	14	x	x	X
ejpam-4385	310	15	)	)	PUNCT
ejpam-4385	310	16	is	be	AUX
ejpam-4385	310	17	continuous	continuous	ADJ
ejpam-4385	310	18	.	.	PUNCT
ejpam-4385	311	1	let	let	VERB
ejpam-4385	311	2	0	0	NUM
ejpam-4385	311	3	≤	≤	NUM
ejpam-4385	311	4	t1	t1	NOUN
ejpam-4385	311	5	≤	≤	PUNCT
ejpam-4385	311	6	t2	t2	PROPN
ejpam-4385	311	7	≤	≤	PROPN
ejpam-4385	311	8	t	t	NOUN
ejpam-4385	311	9	,	,	PUNCT
ejpam-4385	311	10	τ1	τ1	PROPN
ejpam-4385	311	11	=	=	SYM
ejpam-4385	311	12	τd(t	τd(t	X
ejpam-4385	311	13	,	,	PUNCT
ejpam-4385	311	14	rt	rt	PROPN
ejpam-4385	311	15	,	,	PUNCT
ejpam-4385	311	16	x	x	PRON
ejpam-4385	311	17	)	)	PUNCT
ejpam-4385	311	18	be	be	VERB
ejpam-4385	311	19	the	the	DET
ejpam-4385	311	20	optimal	optimal	ADJ
ejpam-4385	311	21	stopping	stopping	NOUN
ejpam-4385	311	22	time	time	NOUN
ejpam-4385	311	23	for	for	ADP
ejpam-4385	311	24	equation	equation	NOUN
ejpam-4385	311	25	(	(	PUNCT
ejpam-4385	311	26	19	19	NUM
ejpam-4385	311	27	)	)	PUNCT
ejpam-4385	311	28	and	and	CCONJ
ejpam-4385	311	29	τ2	τ2	NOUN
ejpam-4385	311	30	=	=	SYM
ejpam-4385	311	31	τ1	τ1	NOUN
ejpam-4385	311	32	∧	∧	PROPN
ejpam-4385	311	33	(	(	PUNCT
ejpam-4385	311	34	t	t	NOUN
ejpam-4385	311	35	−	−	PROPN
ejpam-4385	311	36	t2	t2	PROPN
ejpam-4385	311	37	)	)	PUNCT
ejpam-4385	311	38	.	.	PUNCT
ejpam-4385	312	1	then	then	ADV
ejpam-4385	312	2	0	0	NUM
ejpam-4385	312	3	≤	≤	NUM
ejpam-4385	312	4	|v	|v	X
ejpam-4385	312	5	(	(	PUNCT
ejpam-4385	312	6	t1	t1	PROPN
ejpam-4385	312	7	,	,	PUNCT
ejpam-4385	312	8	rt1	rt1	PROPN
ejpam-4385	312	9	,	,	PUNCT
ejpam-4385	312	10	x)−	x)−	PROPN
ejpam-4385	312	11	v	v	PROPN
ejpam-4385	312	12	(	(	PUNCT
ejpam-4385	312	13	t2	t2	NOUN
ejpam-4385	312	14	,	,	PUNCT
ejpam-4385	312	15	rt2	rt2	PROPN
ejpam-4385	312	16	,	,	PUNCT
ejpam-4385	312	17	x)|	x)|	PROPN
ejpam-4385	312	18	=	=	SYM
ejpam-4385	312	19	|ẽt1,x	|ẽt1,x	X
ejpam-4385	312	20	[	[	PUNCT
ejpam-4385	312	21	e−	e−	PROPN
ejpam-4385	312	22	∫	∫	PROPN
ejpam-4385	313	1	t1+τ1	t1+τ1	NOUN
ejpam-4385	313	2	t1	t1	PROPN
ejpam-4385	313	3	rudugµc(t1	rudugµc(t1	VERB
ejpam-4385	313	4	+	+	CCONJ
ejpam-4385	313	5	τ1	τ1	NOUN
ejpam-4385	313	6	,	,	PUNCT
ejpam-4385	313	7	xt1+τ1)|ft1	xt1+τ1)|ft1	PUNCT
ejpam-4385	313	8	]	]	X
ejpam-4385	313	9	−	−	PUNCT
ejpam-4385	313	10	ẽt2,x	ẽt2,x	PROPN
ejpam-4385	313	11	[	[	PUNCT
ejpam-4385	313	12	e−	e−	X
ejpam-4385	313	13	∫	∫	PROPN
ejpam-4385	314	1	t2+τ2	t2+τ2	NOUN
ejpam-4385	314	2	t2	t2	NOUN
ejpam-4385	314	3	rudugµc(t2	rudugµc(t2	NOUN
ejpam-4385	314	4	+	+	CCONJ
ejpam-4385	314	5	τ2	τ2	ADJ
ejpam-4385	314	6	,	,	PUNCT
ejpam-4385	314	7	xt2+τ2)|ft2	xt2+τ2)|ft2	PUNCT
ejpam-4385	314	8	]	]	PUNCT
ejpam-4385	315	1	|	|	ADV
ejpam-4385	315	2	=	=	SYM
ejpam-4385	315	3	|ẽt1,x	|ẽt1,x	X
ejpam-4385	315	4	[	[	PUNCT
ejpam-4385	315	5	e−	e−	PROPN
ejpam-4385	315	6	∫	∫	PROPN
ejpam-4385	315	7	t1+τ2	t1+τ2	PROPN
ejpam-4385	315	8	t1	t1	PROPN
ejpam-4385	315	9	rudugµc(t1	rudugµc(t1	NOUN
ejpam-4385	315	10	+	+	CCONJ
ejpam-4385	315	11	τ1	τ1	NOUN
ejpam-4385	315	12	,	,	PUNCT
ejpam-4385	315	13	xt1+τ1)|ft1	xt1+τ1)|ft1	ADP
ejpam-4385	315	14	]	]	PUNCT
ejpam-4385	315	15	k.	k.	PROPN
ejpam-4385	315	16	falcasantos	falcasantos	PROPN
ejpam-4385	315	17	,	,	PUNCT
ejpam-4385	315	18	f.	f.	PROPN
ejpam-4385	315	19	sumalpong	sumalpong	PROPN
ejpam-4385	315	20	/	/	SYM
ejpam-4385	315	21	eur	eur	PROPN
ejpam-4385	315	22	.	.	PUNCT
ejpam-4385	316	1	j.	j.	PROPN
ejpam-4385	316	2	pure	pure	PROPN
ejpam-4385	316	3	appl	appl	PROPN
ejpam-4385	316	4	.	.	PROPN
ejpam-4385	316	5	math	math	PROPN
ejpam-4385	316	6	,	,	PUNCT
ejpam-4385	316	7	15	15	NUM
ejpam-4385	316	8	(	(	PUNCT
ejpam-4385	316	9	3	3	NUM
ejpam-4385	316	10	)	)	PUNCT
ejpam-4385	316	11	(	(	PUNCT
ejpam-4385	316	12	2022	2022	NUM
ejpam-4385	316	13	)	)	PUNCT
ejpam-4385	316	14	,	,	PUNCT
ejpam-4385	316	15	948	948	NUM
ejpam-4385	316	16	-	-	SYM
ejpam-4385	316	17	970	970	NUM
ejpam-4385	316	18	960	960	NUM
ejpam-4385	316	19	−	−	ADP
ejpam-4385	316	20	ẽt2,x	ẽt2,x	PROPN
ejpam-4385	316	21	[	[	PUNCT
ejpam-4385	316	22	e−	e−	X
ejpam-4385	316	23	∫	∫	PROPN
ejpam-4385	317	1	t2+τ2	t2+τ2	NOUN
ejpam-4385	317	2	t2	t2	NOUN
ejpam-4385	317	3	rudugµc(t2	rudugµc(t2	NOUN
ejpam-4385	317	4	+	+	CCONJ
ejpam-4385	317	5	τ2	τ2	ADJ
ejpam-4385	317	6	,	,	PUNCT
ejpam-4385	317	7	xt2+τ2)|ft2	xt2+τ2)|ft2	PUNCT
ejpam-4385	317	8	]	]	PUNCT
ejpam-4385	318	1	|	|	ADV
ejpam-4385	318	2	≤	≤	NUM
ejpam-4385	318	3	∣∣∣∣ẽt2,x	∣∣∣∣ẽt2,x	NOUN
ejpam-4385	318	4	[	[	PUNCT
ejpam-4385	318	5	e−	e−	PROPN
ejpam-4385	318	6	∫	∫	PROPN
ejpam-4385	319	1	t2+τ2	t2+τ2	DET
ejpam-4385	319	2	t2	t2	PROPN
ejpam-4385	319	3	rudu	rudu	NOUN
ejpam-4385	319	4	{	{	PUNCT
ejpam-4385	319	5	gµc(t1	gµc(t1	NOUN
ejpam-4385	319	6	+	+	CCONJ
ejpam-4385	319	7	τ1	τ1	NOUN
ejpam-4385	319	8	,	,	PUNCT
ejpam-4385	319	9	xt1+τ1)−gµc(t2	xt1+τ1)−gµc(t2	PUNCT
ejpam-4385	320	1	+	+	PUNCT
ejpam-4385	320	2	τ2	τ2	PROPN
ejpam-4385	320	3	,	,	PUNCT
ejpam-4385	320	4	xt2+τ2	xt2+τ2	PROPN
ejpam-4385	320	5	)	)	PUNCT
ejpam-4385	320	6	}	}	PUNCT
ejpam-4385	321	1	|ft2	|ft2	PRON
ejpam-4385	321	2	]	]	PUNCT
ejpam-4385	321	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4385	321	4	≤	≤	NUM
ejpam-4385	321	5	ẽt2,x	ẽt2,x	PROPN
ejpam-4385	322	1	[	[	PUNCT
ejpam-4385	322	2	e−	e−	X
ejpam-4385	322	3	∫	∫	PROPN
ejpam-4385	323	1	t2+τ2	t2+τ2	DET
ejpam-4385	323	2	t2	t2	PROPN
ejpam-4385	323	3	rudu	rudu	NOUN
ejpam-4385	323	4	|{gµc(t1	|{gµc(t1	NOUN
ejpam-4385	323	5	+	+	CCONJ
ejpam-4385	323	6	τ1	τ1	NOUN
ejpam-4385	323	7	,	,	PUNCT
ejpam-4385	323	8	xt1+τ1)−gµc(t2	xt1+τ1)−gµc(t2	PUNCT
ejpam-4385	324	1	+	+	PUNCT
ejpam-4385	324	2	τ2	τ2	ADJ
ejpam-4385	324	3	,	,	PUNCT
ejpam-4385	324	4	xt2+τ2)}|	xt2+τ2)}|	PUNCT
ejpam-4385	325	1	|ft2	|ft2	PROPN
ejpam-4385	325	2	]	]	PUNCT
ejpam-4385	325	3	.	.	PUNCT
ejpam-4385	326	1	by	by	ADP
ejpam-4385	326	2	the	the	DET
ejpam-4385	326	3	continuity	continuity	NOUN
ejpam-4385	326	4	of	of	ADP
ejpam-4385	326	5	the	the	DET
ejpam-4385	326	6	mapping	mapping	NOUN
ejpam-4385	326	7	t	t	PROPN
ejpam-4385	326	8	7→	7→	PROPN
ejpam-4385	326	9	gµc(t	gµc(t	PROPN
ejpam-4385	326	10	,	,	PUNCT
ejpam-4385	326	11	x	x	NOUN
ejpam-4385	326	12	)	)	PUNCT
ejpam-4385	326	13	in	in	ADP
ejpam-4385	326	14	lemma	lemma	PROPN
ejpam-4385	326	15	2	2	NUM
ejpam-4385	326	16	above	above	ADV
ejpam-4385	326	17	,	,	PUNCT
ejpam-4385	326	18	the	the	DET
ejpam-4385	326	19	mapping	mapping	NOUN
ejpam-4385	326	20	t	t	NOUN
ejpam-4385	326	21	7→	7→	NUM
ejpam-4385	326	22	v	v	NOUN
ejpam-4385	326	23	(	(	PUNCT
ejpam-4385	326	24	t	t	PROPN
ejpam-4385	326	25	,	,	PUNCT
ejpam-4385	326	26	rt	rt	PROPN
ejpam-4385	326	27	,	,	PUNCT
ejpam-4385	326	28	x	x	X
ejpam-4385	326	29	)	)	PUNCT
ejpam-4385	326	30	is	be	AUX
ejpam-4385	326	31	continuous	continuous	ADJ
ejpam-4385	326	32	on	on	ADP
ejpam-4385	326	33	[	[	X
ejpam-4385	326	34	0	0	NUM
ejpam-4385	326	35	,	,	PUNCT
ejpam-4385	326	36	t	t	X
ejpam-4385	326	37	]	]	PUNCT
ejpam-4385	326	38	,	,	PUNCT
ejpam-4385	326	39	uniformly	uniformly	ADV
ejpam-4385	326	40	in	in	ADP
ejpam-4385	326	41	x	x	SYM
ejpam-4385	326	42	∈	∈	PROPN
ejpam-4385	326	43	(	(	PUNCT
ejpam-4385	326	44	0,∞	0,∞	NOUN
ejpam-4385	326	45	)	)	PUNCT
ejpam-4385	326	46	.	.	PUNCT
ejpam-4385	327	1	note	note	VERB
ejpam-4385	327	2	that	that	SCONJ
ejpam-4385	327	3	from	from	ADP
ejpam-4385	327	4	the	the	DET
ejpam-4385	327	5	paper	paper	NOUN
ejpam-4385	327	6	of	of	ADP
ejpam-4385	327	7	peskir	peskir	NOUN
ejpam-4385	327	8	and	and	CCONJ
ejpam-4385	327	9	samee	samee	PROPN
ejpam-4385	327	10	(	(	PUNCT
ejpam-4385	327	11	2013	2013	NUM
ejpam-4385	327	12	)	)	PUNCT
ejpam-4385	327	13	both	both	PRON
ejpam-4385	327	14	x	x	SYM
ejpam-4385	327	15	7→	7→	NUM
ejpam-4385	327	16	gµc(t	gµc(t	NOUN
ejpam-4385	327	17	,	,	PUNCT
ejpam-4385	327	18	x	x	NOUN
ejpam-4385	327	19	)	)	PUNCT
ejpam-4385	327	20	and	and	CCONJ
ejpam-4385	327	21	x	x	SYM
ejpam-4385	327	22	7→	7→	NUM
ejpam-4385	327	23	v	v	NOUN
ejpam-4385	327	24	(	(	PUNCT
ejpam-4385	327	25	t	t	PROPN
ejpam-4385	327	26	,	,	PUNCT
ejpam-4385	327	27	rt	rt	PROPN
ejpam-4385	327	28	,	,	PUNCT
ejpam-4385	327	29	x	x	PRON
ejpam-4385	327	30	)	)	PUNCT
ejpam-4385	327	31	are	be	AUX
ejpam-4385	327	32	convex	convex	ADJ
ejpam-4385	327	33	.	.	PUNCT
ejpam-4385	328	1	furthermore	furthermore	ADV
ejpam-4385	328	2	,	,	PUNCT
ejpam-4385	328	3	recall	recall	VERB
ejpam-4385	328	4	that	that	SCONJ
ejpam-4385	328	5	every	every	DET
ejpam-4385	328	6	convex	convex	NOUN
ejpam-4385	328	7	function	function	NOUN
ejpam-4385	328	8	on	on	ADP
ejpam-4385	328	9	the	the	DET
ejpam-4385	328	10	open	open	ADJ
ejpam-4385	328	11	interval	interval	NOUN
ejpam-4385	328	12	i	i	PRON
ejpam-4385	328	13	is	be	AUX
ejpam-4385	328	14	differentiable	differentiable	ADJ
ejpam-4385	328	15	almost	almost	ADV
ejpam-4385	328	16	everywhere	everywhere	ADV
ejpam-4385	328	17	.	.	PUNCT
ejpam-4385	329	1	6	6	X
ejpam-4385	329	2	.	.	X
ejpam-4385	329	3	boundary	boundary	ADJ
ejpam-4385	329	4	value	value	NOUN
ejpam-4385	329	5	problem	problem	NOUN
ejpam-4385	329	6	applying	apply	VERB
ejpam-4385	329	7	the	the	DET
ejpam-4385	329	8	itö	itö	NOUN
ejpam-4385	329	9	’s	’s	PART
ejpam-4385	329	10	formula	formula	NOUN
ejpam-4385	329	11	on	on	ADP
ejpam-4385	329	12	the	the	DET
ejpam-4385	329	13	price	price	NOUN
ejpam-4385	329	14	function	function	NOUN
ejpam-4385	329	15	v	v	ADP
ejpam-4385	329	16	=	=	SYM
ejpam-4385	329	17	v	v	PROPN
ejpam-4385	329	18	(	(	PUNCT
ejpam-4385	329	19	t	t	PROPN
ejpam-4385	329	20	,	,	PUNCT
ejpam-4385	329	21	rt;x	rt;x	NUM
ejpam-4385	329	22	)	)	PUNCT
ejpam-4385	329	23	of	of	ADP
ejpam-4385	329	24	the	the	DET
ejpam-4385	329	25	british	british	ADJ
ejpam-4385	329	26	call	call	NOUN
ejpam-4385	329	27	option	option	NOUN
ejpam-4385	329	28	,	,	PUNCT
ejpam-4385	329	29	we	we	PRON
ejpam-4385	329	30	have	have	VERB
ejpam-4385	329	31	dv	dv	PROPN
ejpam-4385	329	32	=	=	SYM
ejpam-4385	329	33	(	(	PUNCT
ejpam-4385	329	34	∂v	∂v	PROPN
ejpam-4385	329	35	∂t	∂t	PROPN
ejpam-4385	330	1	+	+	CCONJ
ejpam-4385	330	2	1	1	NUM
ejpam-4385	330	3	2	2	NUM
ejpam-4385	330	4	σ2	σ2	NOUN
ejpam-4385	330	5	1x	1x	NUM
ejpam-4385	330	6	2	2	NUM
ejpam-4385	330	7	t	t	PROPN
ejpam-4385	330	8	∂2v	∂2v	X
ejpam-4385	330	9	∂x2	∂x2	PROPN
ejpam-4385	330	10	+	+	CCONJ
ejpam-4385	330	11	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	330	12	√	√	NUM
ejpam-4385	330	13	rtxt	rtxt	NOUN
ejpam-4385	330	14	∂2v	∂2v	NOUN
ejpam-4385	330	15	∂x∂r	∂x∂r	VERB
ejpam-4385	331	1	+	+	CCONJ
ejpam-4385	331	2	1	1	NUM
ejpam-4385	331	3	2	2	NUM
ejpam-4385	331	4	σ2	σ2	PROPN
ejpam-4385	331	5	2r	2r	NUM
ejpam-4385	331	6	∂2v	∂2v	PROPN
ejpam-4385	331	7	∂r2	∂r2	PROPN
ejpam-4385	331	8	)	)	PUNCT
ejpam-4385	331	9	dt+	dt+	NOUN
ejpam-4385	331	10	∂v	∂v	NOUN
ejpam-4385	331	11	∂x	∂x	PROPN
ejpam-4385	331	12	dxt	dxt	PROPN
ejpam-4385	331	13	+	+	PROPN
ejpam-4385	331	14	∂v	∂v	PROPN
ejpam-4385	331	15	∂r	∂r	PROPN
ejpam-4385	331	16	drt	drt	PROPN
ejpam-4385	331	17	.	.	PUNCT
ejpam-4385	332	1	(	(	PUNCT
ejpam-4385	332	2	34	34	NUM
ejpam-4385	332	3	)	)	PUNCT
ejpam-4385	332	4	we	we	PRON
ejpam-4385	332	5	now	now	ADV
ejpam-4385	332	6	derive	derive	VERB
ejpam-4385	332	7	the	the	DET
ejpam-4385	332	8	partial	partial	ADJ
ejpam-4385	332	9	differential	differential	NOUN
ejpam-4385	332	10	equation	equation	NOUN
ejpam-4385	332	11	satisfied	satisfy	VERB
ejpam-4385	332	12	by	by	ADP
ejpam-4385	332	13	v	v	PROPN
ejpam-4385	332	14	(	(	PUNCT
ejpam-4385	332	15	t	t	PROPN
ejpam-4385	332	16	,	,	PUNCT
ejpam-4385	332	17	rt	rt	PROPN
ejpam-4385	332	18	,	,	PUNCT
ejpam-4385	332	19	x	x	NOUN
ejpam-4385	332	20	)	)	PUNCT
ejpam-4385	332	21	by	by	ADP
ejpam-4385	332	22	creating	create	VERB
ejpam-4385	332	23	a	a	DET
ejpam-4385	332	24	risk	risk	NOUN
ejpam-4385	332	25	neutral	neutral	ADJ
ejpam-4385	332	26	portfolio	portfolio	NOUN
ejpam-4385	332	27	.	.	PUNCT
ejpam-4385	333	1	consider	consider	VERB
ejpam-4385	333	2	the	the	DET
ejpam-4385	333	3	time	time	NOUN
ejpam-4385	333	4	interval	interval	NOUN
ejpam-4385	333	5	[	[	X
ejpam-4385	333	6	t	t	X
ejpam-4385	333	7	,	,	PUNCT
ejpam-4385	333	8	t+∆t	t+∆t	PROPN
ejpam-4385	333	9	]	]	PUNCT
ejpam-4385	333	10	and	and	CCONJ
ejpam-4385	333	11	the	the	DET
ejpam-4385	333	12	following	follow	VERB
ejpam-4385	333	13	portfolio	portfolio	NOUN
ejpam-4385	333	14	at	at	ADP
ejpam-4385	333	15	time	time	NOUN
ejpam-4385	333	16	t	t	PROPN
ejpam-4385	333	17	:	:	PUNCT
ejpam-4385	333	18	long	long	ADJ
ejpam-4385	333	19	1	1	NUM
ejpam-4385	333	20	unit	unit	NOUN
ejpam-4385	333	21	of	of	ADP
ejpam-4385	333	22	derivative	derivative	ADJ
ejpam-4385	333	23	+	+	CCONJ
ejpam-4385	333	24	short	short	ADJ
ejpam-4385	333	25	ϵ1	ϵ1	ADJ
ejpam-4385	333	26	units	unit	NOUN
ejpam-4385	333	27	of	of	ADP
ejpam-4385	333	28	stock	stock	NOUN
ejpam-4385	333	29	+	+	CCONJ
ejpam-4385	333	30	short	short	ADJ
ejpam-4385	333	31	ϵ2	ϵ2	ADJ
ejpam-4385	333	32	units	unit	NOUN
ejpam-4385	333	33	of	of	ADP
ejpam-4385	333	34	zero	zero	NUM
ejpam-4385	333	35	-	-	PUNCT
ejpam-4385	333	36	coupon	coupon	NOUN
ejpam-4385	333	37	bond	bond	NOUN
ejpam-4385	333	38	let	let	VERB
ejpam-4385	333	39	∏	∏	NUM
ejpam-4385	333	40	t	t	PROPN
ejpam-4385	333	41	be	be	AUX
ejpam-4385	333	42	the	the	DET
ejpam-4385	333	43	value	value	NOUN
ejpam-4385	333	44	of	of	ADP
ejpam-4385	333	45	the	the	DET
ejpam-4385	333	46	portfolio	portfolio	NOUN
ejpam-4385	333	47	at	at	ADP
ejpam-4385	333	48	time	time	NOUN
ejpam-4385	333	49	t.	t.	PROPN
ejpam-4385	333	50	then∏	then∏	PROPN
ejpam-4385	333	51	t	t	PROPN
ejpam-4385	333	52	=	=	SYM
ejpam-4385	333	53	v	v	PROPN
ejpam-4385	333	54	(	(	PUNCT
ejpam-4385	333	55	t	t	PROPN
ejpam-4385	333	56	,	,	PUNCT
ejpam-4385	333	57	rt;x)−	rt;x)−	PROPN
ejpam-4385	333	58	ϵ1xt	ϵ1xt	PUNCT
ejpam-4385	334	1	−	−	ADP
ejpam-4385	334	2	ϵ2p	ϵ2p	INTJ
ejpam-4385	334	3	.	.	PUNCT
ejpam-4385	335	1	(	(	PUNCT
ejpam-4385	335	2	35	35	NUM
ejpam-4385	335	3	)	)	PUNCT
ejpam-4385	335	4	the	the	DET
ejpam-4385	335	5	change	change	NOUN
ejpam-4385	335	6	in	in	ADP
ejpam-4385	335	7	the	the	DET
ejpam-4385	335	8	value	value	NOUN
ejpam-4385	335	9	of	of	ADP
ejpam-4385	335	10	the	the	DET
ejpam-4385	335	11	portfolio	portfolio	NOUN
ejpam-4385	335	12	from	from	ADP
ejpam-4385	335	13	time	time	NOUN
ejpam-4385	335	14	t	t	PROPN
ejpam-4385	335	15	to	to	ADP
ejpam-4385	335	16	t+∆t	t+∆t	PROPN
ejpam-4385	335	17	is	be	AUX
ejpam-4385	335	18	then	then	ADV
ejpam-4385	335	19	∆	∆	PROPN
ejpam-4385	335	20	∏	∏	PROPN
ejpam-4385	335	21	t	t	PROPN
ejpam-4385	335	22	=	=	SYM
ejpam-4385	335	23	∆v	∆v	PROPN
ejpam-4385	335	24	−	−	PROPN
ejpam-4385	335	25	ϵ1∆xt	ϵ1∆xt	NOUN
ejpam-4385	335	26	−	−	NOUN
ejpam-4385	335	27	ϵ2∆p	ϵ2∆p	NOUN
ejpam-4385	335	28	.	.	PUNCT
ejpam-4385	336	1	(	(	PUNCT
ejpam-4385	336	2	36	36	NUM
ejpam-4385	336	3	)	)	PUNCT
ejpam-4385	336	4	using	use	VERB
ejpam-4385	336	5	the	the	DET
ejpam-4385	336	6	discrete	discrete	ADJ
ejpam-4385	336	7	approximation	approximation	NOUN
ejpam-4385	336	8	of	of	ADP
ejpam-4385	336	9	(	(	PUNCT
ejpam-4385	336	10	34	34	NUM
ejpam-4385	336	11	)	)	PUNCT
ejpam-4385	336	12	for	for	ADP
ejpam-4385	336	13	∆v	∆v	PROPN
ejpam-4385	336	14	,	,	PUNCT
ejpam-4385	336	15	we	we	PRON
ejpam-4385	336	16	have	have	VERB
ejpam-4385	336	17	∆	∆	PROPN
ejpam-4385	336	18	∏	∏	PROPN
ejpam-4385	336	19	t	t	NOUN
ejpam-4385	336	20	=	=	PUNCT
ejpam-4385	337	1	(	(	PUNCT
ejpam-4385	337	2	∂v	∂v	PROPN
ejpam-4385	337	3	∂t	∂t	PROPN
ejpam-4385	337	4	+	+	CCONJ
ejpam-4385	337	5	1	1	NUM
ejpam-4385	337	6	2	2	NUM
ejpam-4385	337	7	σ2	σ2	NOUN
ejpam-4385	337	8	1x	1x	NUM
ejpam-4385	337	9	2	2	NUM
ejpam-4385	337	10	t	t	PROPN
ejpam-4385	337	11	∂2v	∂2v	X
ejpam-4385	337	12	∂x2	∂x2	PROPN
ejpam-4385	337	13	+	+	CCONJ
ejpam-4385	337	14	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	337	15	√	√	NUM
ejpam-4385	337	16	rtxt	rtxt	NOUN
ejpam-4385	337	17	∂2v	∂2v	NOUN
ejpam-4385	337	18	∂x∂r	∂x∂r	VERB
ejpam-4385	338	1	+	+	CCONJ
ejpam-4385	338	2	1	1	NUM
ejpam-4385	338	3	2	2	NUM
ejpam-4385	338	4	σ2rt	σ2rt	NOUN
ejpam-4385	338	5	∂2v	∂2v	NOUN
ejpam-4385	338	6	∂r2	∂r2	PROPN
ejpam-4385	338	7	)	)	PUNCT
ejpam-4385	338	8	∆t+	∆t+	PROPN
ejpam-4385	338	9	∂v	∂v	PROPN
ejpam-4385	338	10	∂x	∂x	PROPN
ejpam-4385	338	11	∆xt	∆xt	PROPN
ejpam-4385	339	1	+	+	PUNCT
ejpam-4385	339	2	∂v	∂v	PROPN
ejpam-4385	339	3	∂r	∂r	PROPN
ejpam-4385	339	4	∆rt	∆rt	NOUN
ejpam-4385	339	5	−	−	PROPN
ejpam-4385	339	6	ϵ1∆xt	ϵ1∆xt	PROPN
ejpam-4385	340	1	−	−	PROPN
ejpam-4385	340	2	ϵ2	ϵ2	NOUN
ejpam-4385	340	3	(	(	PUNCT
ejpam-4385	340	4	∂p	∂p	PROPN
ejpam-4385	340	5	∂t	∂t	PROPN
ejpam-4385	340	6	∆t+	∆t+	NOUN
ejpam-4385	340	7	∂p	∂p	PROPN
ejpam-4385	341	1	∂r	∂r	PROPN
ejpam-4385	341	2	∆rt	∆rt	NOUN
ejpam-4385	341	3	+	+	CCONJ
ejpam-4385	341	4	1	1	NUM
ejpam-4385	341	5	2	2	NUM
ejpam-4385	341	6	σ2	σ2	NOUN
ejpam-4385	341	7	2rt	2rt	ADJ
ejpam-4385	341	8	∂2p	∂2p	NOUN
ejpam-4385	341	9	∂r2	∂r2	PROPN
ejpam-4385	341	10	∆t	∆t	PROPN
ejpam-4385	341	11	)	)	PUNCT
ejpam-4385	341	12	(	(	PUNCT
ejpam-4385	341	13	37	37	NUM
ejpam-4385	341	14	)	)	PUNCT
ejpam-4385	341	15	k.	k.	NOUN
ejpam-4385	341	16	falcasantos	falcasantos	PROPN
ejpam-4385	341	17	,	,	PUNCT
ejpam-4385	341	18	f.	f.	PROPN
ejpam-4385	341	19	sumalpong	sumalpong	PROPN
ejpam-4385	341	20	/	/	SYM
ejpam-4385	341	21	eur	eur	PROPN
ejpam-4385	341	22	.	.	PUNCT
ejpam-4385	342	1	j.	j.	PROPN
ejpam-4385	342	2	pure	pure	PROPN
ejpam-4385	342	3	appl	appl	PROPN
ejpam-4385	342	4	.	.	PROPN
ejpam-4385	342	5	math	math	PROPN
ejpam-4385	342	6	,	,	PUNCT
ejpam-4385	342	7	15	15	NUM
ejpam-4385	342	8	(	(	PUNCT
ejpam-4385	342	9	3	3	NUM
ejpam-4385	342	10	)	)	PUNCT
ejpam-4385	342	11	(	(	PUNCT
ejpam-4385	342	12	2022	2022	NUM
ejpam-4385	342	13	)	)	PUNCT
ejpam-4385	342	14	,	,	PUNCT
ejpam-4385	342	15	948	948	NUM
ejpam-4385	342	16	-	-	SYM
ejpam-4385	342	17	970	970	NUM
ejpam-4385	342	18	961	961	NUM
ejpam-4385	342	19	=	=	SYM
ejpam-4385	342	20	(	(	PUNCT
ejpam-4385	342	21	∂v	∂v	PROPN
ejpam-4385	342	22	∂t	∂t	PROPN
ejpam-4385	343	1	+	+	CCONJ
ejpam-4385	343	2	1	1	NUM
ejpam-4385	343	3	2	2	NUM
ejpam-4385	343	4	σ2	σ2	NOUN
ejpam-4385	343	5	1x	1x	NUM
ejpam-4385	343	6	2	2	NUM
ejpam-4385	343	7	t	t	PROPN
ejpam-4385	343	8	∂2v	∂2v	X
ejpam-4385	343	9	∂x2	∂x2	PROPN
ejpam-4385	343	10	+	+	CCONJ
ejpam-4385	343	11	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	343	12	√	√	NUM
ejpam-4385	343	13	rtxt	rtxt	NOUN
ejpam-4385	343	14	∂2v	∂2v	NOUN
ejpam-4385	343	15	∂x∂r	∂x∂r	VERB
ejpam-4385	344	1	+	+	CCONJ
ejpam-4385	344	2	1	1	NUM
ejpam-4385	344	3	2	2	NUM
ejpam-4385	344	4	σ2	σ2	PROPN
ejpam-4385	344	5	2r	2r	NUM
ejpam-4385	344	6	∂2v	∂2v	PROPN
ejpam-4385	344	7	∂r2	∂r2	PROPN
ejpam-4385	344	8	)	)	PUNCT
ejpam-4385	344	9	∆t	∆t	PROPN
ejpam-4385	345	1	+	+	CCONJ
ejpam-4385	345	2	(	(	PUNCT
ejpam-4385	345	3	∂v	∂v	PROPN
ejpam-4385	345	4	∂x	∂x	PROPN
ejpam-4385	345	5	−	−	ADP
ejpam-4385	345	6	ϵ1	ϵ1	PROPN
ejpam-4385	345	7	)	)	PUNCT
ejpam-4385	345	8	∆xt	∆xt	PROPN
ejpam-4385	346	1	+	+	CCONJ
ejpam-4385	346	2	(	(	PUNCT
ejpam-4385	346	3	∂v	∂v	NOUN
ejpam-4385	346	4	∂r	∂r	PROPN
ejpam-4385	346	5	−	−	PROPN
ejpam-4385	347	1	ϵ2	ϵ2	NOUN
ejpam-4385	347	2	∂p	∂p	PROPN
ejpam-4385	347	3	∂r	∂r	PROPN
ejpam-4385	347	4	)	)	PUNCT
ejpam-4385	347	5	∆rt	∆rt	PROPN
ejpam-4385	347	6	−	−	PROPN
ejpam-4385	347	7	ϵ2	ϵ2	PROPN
ejpam-4385	347	8	(	(	PUNCT
ejpam-4385	347	9	∂p	∂p	PROPN
ejpam-4385	347	10	∂t	∂t	PROPN
ejpam-4385	348	1	+	+	CCONJ
ejpam-4385	348	2	1	1	NUM
ejpam-4385	348	3	2	2	NUM
ejpam-4385	348	4	σ2	σ2	NOUN
ejpam-4385	348	5	2r	2r	NUM
ejpam-4385	348	6	∂2p	∂2p	NOUN
ejpam-4385	348	7	∂r2	∂r2	PROPN
ejpam-4385	348	8	)	)	PUNCT
ejpam-4385	348	9	∆t	∆t	VERB
ejpam-4385	348	10	to	to	PART
ejpam-4385	348	11	eliminate	eliminate	VERB
ejpam-4385	348	12	the	the	DET
ejpam-4385	348	13	risk	risk	NOUN
ejpam-4385	348	14	,	,	PUNCT
ejpam-4385	348	15	let	let	VERB
ejpam-4385	348	16	ϵ1	ϵ1	VERB
ejpam-4385	348	17	=	=	SYM
ejpam-4385	348	18	∂v	∂v	PROPN
ejpam-4385	348	19	∂x	∂x	PROPN
ejpam-4385	348	20	and	and	CCONJ
ejpam-4385	348	21	ϵ2	ϵ2	PROPN
ejpam-4385	349	1	=	=	PUNCT
ejpam-4385	349	2	∂v	∂v	PROPN
ejpam-4385	350	1	∂r	∂r	PROPN
ejpam-4385	350	2	/	/	SYM
ejpam-4385	350	3	∂p	∂p	PROPN
ejpam-4385	350	4	∂r	∂r	INTJ
ejpam-4385	350	5	.	.	PUNCT
ejpam-4385	351	1	then	then	ADV
ejpam-4385	351	2	equation	equation	NOUN
ejpam-4385	351	3	(	(	PUNCT
ejpam-4385	351	4	37	37	NUM
ejpam-4385	351	5	)	)	PUNCT
ejpam-4385	351	6	becomes	become	VERB
ejpam-4385	351	7	∆	∆	PROPN
ejpam-4385	351	8	∏	∏	PROPN
ejpam-4385	351	9	t	t	NOUN
ejpam-4385	351	10	=	=	PUNCT
ejpam-4385	351	11	(	(	PUNCT
ejpam-4385	351	12	∂v	∂v	PROPN
ejpam-4385	351	13	∂t	∂t	PROPN
ejpam-4385	352	1	+	+	CCONJ
ejpam-4385	352	2	1	1	NUM
ejpam-4385	352	3	2	2	NUM
ejpam-4385	352	4	σ2	σ2	NOUN
ejpam-4385	352	5	1x	1x	NUM
ejpam-4385	352	6	2	2	NUM
ejpam-4385	352	7	t	t	PROPN
ejpam-4385	352	8	∂2v	∂2v	X
ejpam-4385	352	9	∂x2	∂x2	PROPN
ejpam-4385	352	10	+	+	CCONJ
ejpam-4385	352	11	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	352	12	√	√	NUM
ejpam-4385	352	13	rtxt	rtxt	NOUN
ejpam-4385	352	14	∂2v	∂2v	NOUN
ejpam-4385	352	15	∂x∂r	∂x∂r	VERB
ejpam-4385	353	1	+	+	CCONJ
ejpam-4385	353	2	1	1	NUM
ejpam-4385	353	3	2	2	NUM
ejpam-4385	353	4	σ2rt	σ2rt	NOUN
ejpam-4385	353	5	∂2v	∂2v	NOUN
ejpam-4385	353	6	∂r2	∂r2	PROPN
ejpam-4385	353	7	)	)	PUNCT
ejpam-4385	353	8	∆t	∆t	PROPN
ejpam-4385	354	1	+	+	CCONJ
ejpam-4385	354	2	(	(	PUNCT
ejpam-4385	354	3	∂v	∂v	PROPN
ejpam-4385	354	4	∂x	∂x	PROPN
ejpam-4385	354	5	−	−	PROPN
ejpam-4385	354	6	∂v	∂v	PROPN
ejpam-4385	354	7	∂x	∂x	PROPN
ejpam-4385	354	8	)	)	PUNCT
ejpam-4385	354	9	∆xt	∆xt	PROPN
ejpam-4385	355	1	+	+	CCONJ
ejpam-4385	355	2	(	(	PUNCT
ejpam-4385	355	3	∂v	∂v	NOUN
ejpam-4385	355	4	∂r	∂r	PROPN
ejpam-4385	355	5	−	−	PROPN
ejpam-4385	356	1	∂v	∂v	NOUN
ejpam-4385	356	2	∂r	∂r	PROPN
ejpam-4385	357	1	/	/	SYM
ejpam-4385	357	2	∂p	∂p	PROPN
ejpam-4385	357	3	∂r	∂r	PROPN
ejpam-4385	358	1	∂p	∂p	PROPN
ejpam-4385	358	2	∂r	∂r	PROPN
ejpam-4385	358	3	)	)	PUNCT
ejpam-4385	358	4	∆rt	∆rt	PROPN
ejpam-4385	358	5	−	−	PROPN
ejpam-4385	358	6	ϵ2	ϵ2	PROPN
ejpam-4385	358	7	(	(	PUNCT
ejpam-4385	358	8	∂p	∂p	PROPN
ejpam-4385	358	9	∂t	∂t	PROPN
ejpam-4385	359	1	+	+	CCONJ
ejpam-4385	359	2	1	1	NUM
ejpam-4385	359	3	2	2	NUM
ejpam-4385	359	4	σ2	σ2	NOUN
ejpam-4385	359	5	2rt	2rt	ADJ
ejpam-4385	359	6	∂2p	∂2p	NOUN
ejpam-4385	359	7	∂r2	∂r2	PROPN
ejpam-4385	359	8	)	)	PUNCT
ejpam-4385	359	9	∆t	∆t	PROPN
ejpam-4385	360	1	=	=	SYM
ejpam-4385	360	2	(	(	PUNCT
ejpam-4385	360	3	∂v	∂v	PROPN
ejpam-4385	360	4	∂t	∂t	PROPN
ejpam-4385	360	5	+	+	CCONJ
ejpam-4385	360	6	1	1	NUM
ejpam-4385	360	7	2	2	NUM
ejpam-4385	360	8	σ2	σ2	NOUN
ejpam-4385	360	9	1x	1x	NUM
ejpam-4385	360	10	2	2	NUM
ejpam-4385	360	11	t	t	PROPN
ejpam-4385	360	12	∂2v	∂2v	X
ejpam-4385	360	13	∂x2	∂x2	PROPN
ejpam-4385	360	14	+	+	CCONJ
ejpam-4385	360	15	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	360	16	√	√	NUM
ejpam-4385	360	17	rtxt	rtxt	NOUN
ejpam-4385	360	18	∂2v	∂2v	NOUN
ejpam-4385	360	19	∂x∂r	∂x∂r	VERB
ejpam-4385	361	1	+	+	CCONJ
ejpam-4385	361	2	1	1	NUM
ejpam-4385	361	3	2	2	NUM
ejpam-4385	361	4	σ2	σ2	PROPN
ejpam-4385	361	5	2r	2r	NUM
ejpam-4385	361	6	∂2v	∂2v	PROPN
ejpam-4385	361	7	∂r2	∂r2	PROPN
ejpam-4385	361	8	)	)	PUNCT
ejpam-4385	361	9	∆t	∆t	PROPN
ejpam-4385	362	1	−	−	NOUN
ejpam-4385	362	2	ϵ2	ϵ2	NOUN
ejpam-4385	362	3	(	(	PUNCT
ejpam-4385	362	4	∂p	∂p	PROPN
ejpam-4385	362	5	∂t	∂t	PROPN
ejpam-4385	363	1	+	+	CCONJ
ejpam-4385	363	2	1	1	NUM
ejpam-4385	363	3	2	2	NUM
ejpam-4385	363	4	σ2	σ2	NOUN
ejpam-4385	363	5	2r	2r	NUM
ejpam-4385	363	6	∂2p	∂2p	NOUN
ejpam-4385	363	7	∂r2	∂r2	PROPN
ejpam-4385	363	8	)	)	PUNCT
ejpam-4385	363	9	∆t	∆t	PROPN
ejpam-4385	363	10	(	(	PUNCT
ejpam-4385	363	11	38	38	NUM
ejpam-4385	363	12	)	)	PUNCT
ejpam-4385	363	13	by	by	ADP
ejpam-4385	363	14	equation	equation	NOUN
ejpam-4385	363	15	(	(	PUNCT
ejpam-4385	363	16	5	5	NUM
ejpam-4385	363	17	)	)	PUNCT
ejpam-4385	363	18	,	,	PUNCT
ejpam-4385	363	19	∆	∆	PROPN
ejpam-4385	363	20	∏	∏	PROPN
ejpam-4385	363	21	t	t	NOUN
ejpam-4385	363	22	=	=	PUNCT
ejpam-4385	363	23	(	(	PUNCT
ejpam-4385	363	24	∂v	∂v	PROPN
ejpam-4385	363	25	∂t	∂t	PROPN
ejpam-4385	364	1	+	+	CCONJ
ejpam-4385	364	2	1	1	NUM
ejpam-4385	364	3	2	2	NUM
ejpam-4385	364	4	σ2	σ2	NOUN
ejpam-4385	364	5	1x	1x	NUM
ejpam-4385	364	6	2	2	NUM
ejpam-4385	364	7	t	t	PROPN
ejpam-4385	364	8	∂2v	∂2v	X
ejpam-4385	364	9	∂x2	∂x2	PROPN
ejpam-4385	364	10	+	+	CCONJ
ejpam-4385	364	11	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	364	12	√	√	NUM
ejpam-4385	364	13	rtxt	rtxt	NOUN
ejpam-4385	364	14	∂2v	∂2v	NOUN
ejpam-4385	364	15	∂x∂r	∂x∂r	VERB
ejpam-4385	365	1	+	+	CCONJ
ejpam-4385	365	2	1	1	NUM
ejpam-4385	365	3	2	2	NUM
ejpam-4385	365	4	σ2rt	σ2rt	NOUN
ejpam-4385	365	5	∂2v	∂2v	NOUN
ejpam-4385	365	6	∂r2	∂r2	PROPN
ejpam-4385	365	7	)	)	PUNCT
ejpam-4385	365	8	∆t	∆t	PROPN
ejpam-4385	366	1	−	−	PROPN
ejpam-4385	366	2	∂v	∂v	NOUN
ejpam-4385	367	1	∂r	∂r	PROPN
ejpam-4385	367	2	/	/	SYM
ejpam-4385	367	3	∂p	∂p	PROPN
ejpam-4385	368	1	∂r	∂r	PROPN
ejpam-4385	368	2	(	(	PUNCT
ejpam-4385	368	3	[	[	X
ejpam-4385	368	4	aθ	aθ	INTJ
ejpam-4385	368	5	−	−	X
ejpam-4385	368	6	(	(	PUNCT
ejpam-4385	368	7	a+	a+	X
ejpam-4385	368	8	λσ)r	λσ)r	X
ejpam-4385	368	9	]	]	X
ejpam-4385	369	1	∂p	∂p	PROPN
ejpam-4385	370	1	∂r	∂r	INTJ
ejpam-4385	370	2	−	−	NUM
ejpam-4385	370	3	1	1	NUM
ejpam-4385	370	4	2	2	NUM
ejpam-4385	370	5	σ2	σ2	NOUN
ejpam-4385	370	6	2r	2r	NUM
ejpam-4385	370	7	∂2p	∂2p	NOUN
ejpam-4385	370	8	∂r2	∂r2	PROPN
ejpam-4385	370	9	+	+	CCONJ
ejpam-4385	370	10	rtp	rtp	PROPN
ejpam-4385	371	1	+	+	CCONJ
ejpam-4385	371	2	1	1	NUM
ejpam-4385	371	3	2	2	NUM
ejpam-4385	371	4	σ2	σ2	NOUN
ejpam-4385	371	5	2rt	2rt	ADJ
ejpam-4385	371	6	∂2p	∂2p	NOUN
ejpam-4385	371	7	∂r2	∂r2	PROPN
ejpam-4385	371	8	)	)	PUNCT
ejpam-4385	371	9	∆t	∆t	PROPN
ejpam-4385	372	1	=	=	SYM
ejpam-4385	372	2	(	(	PUNCT
ejpam-4385	372	3	∂v	∂v	PROPN
ejpam-4385	372	4	∂t	∂t	PROPN
ejpam-4385	372	5	+	+	CCONJ
ejpam-4385	372	6	1	1	NUM
ejpam-4385	372	7	2	2	NUM
ejpam-4385	372	8	σ2	σ2	NOUN
ejpam-4385	372	9	1x	1x	NUM
ejpam-4385	372	10	2	2	NUM
ejpam-4385	372	11	t	t	PROPN
ejpam-4385	372	12	∂2v	∂2v	X
ejpam-4385	372	13	∂x2	∂x2	PROPN
ejpam-4385	372	14	+	+	CCONJ
ejpam-4385	372	15	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	372	16	√	√	NUM
ejpam-4385	372	17	rtxt	rtxt	NOUN
ejpam-4385	372	18	∂2v	∂2v	NOUN
ejpam-4385	372	19	∂x∂r	∂x∂r	VERB
ejpam-4385	373	1	+	+	CCONJ
ejpam-4385	373	2	1	1	NUM
ejpam-4385	373	3	2	2	NUM
ejpam-4385	373	4	σ2rt	σ2rt	NOUN
ejpam-4385	373	5	∂2v	∂2v	NOUN
ejpam-4385	373	6	∂r2	∂r2	PROPN
ejpam-4385	373	7	)	)	PUNCT
ejpam-4385	373	8	∆t	∆t	PROPN
ejpam-4385	374	1	−	−	PROPN
ejpam-4385	374	2	∂v	∂v	NOUN
ejpam-4385	375	1	∂r	∂r	PROPN
ejpam-4385	375	2	/	/	SYM
ejpam-4385	375	3	∂p	∂p	PROPN
ejpam-4385	376	1	∂r	∂r	PROPN
ejpam-4385	377	1	(	(	PUNCT
ejpam-4385	377	2	rtp	rtp	PROPN
ejpam-4385	377	3	−	−	PROPN
ejpam-4385	378	1	[	[	X
ejpam-4385	378	2	aθ	aθ	INTJ
ejpam-4385	378	3	−	−	PROPN
ejpam-4385	378	4	(	(	PUNCT
ejpam-4385	378	5	a+	a+	X
ejpam-4385	378	6	λσ)r	λσ)r	X
ejpam-4385	378	7	]	]	X
ejpam-4385	378	8	∂p	∂p	PROPN
ejpam-4385	378	9	∂r	∂r	ADJ
ejpam-4385	378	10	)	)	PUNCT
ejpam-4385	378	11	∆t	∆t	PROPN
ejpam-4385	378	12	=	=	SYM
ejpam-4385	379	1	(	(	PUNCT
ejpam-4385	379	2	∂v	∂v	PROPN
ejpam-4385	379	3	∂t	∂t	PROPN
ejpam-4385	379	4	+	+	CCONJ
ejpam-4385	379	5	1	1	NUM
ejpam-4385	379	6	2	2	NUM
ejpam-4385	379	7	σ2	σ2	NOUN
ejpam-4385	379	8	1x	1x	NUM
ejpam-4385	379	9	2	2	NUM
ejpam-4385	379	10	t	t	PROPN
ejpam-4385	379	11	∂2v	∂2v	X
ejpam-4385	379	12	∂x2	∂x2	PROPN
ejpam-4385	379	13	+	+	CCONJ
ejpam-4385	379	14	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	379	15	√	√	NUM
ejpam-4385	379	16	rtxt	rtxt	NOUN
ejpam-4385	379	17	∂2v	∂2v	NOUN
ejpam-4385	379	18	∂x∂r	∂x∂r	VERB
ejpam-4385	380	1	+	+	CCONJ
ejpam-4385	380	2	1	1	NUM
ejpam-4385	380	3	2	2	NUM
ejpam-4385	380	4	σ2	σ2	PROPN
ejpam-4385	380	5	2r	2r	NUM
ejpam-4385	380	6	∂2v	∂2v	PROPN
ejpam-4385	380	7	∂r2	∂r2	PROPN
ejpam-4385	380	8	−	−	PROPN
ejpam-4385	380	9	∂v	∂v	NOUN
ejpam-4385	381	1	∂r	∂r	PROPN
ejpam-4385	381	2	/	/	SYM
ejpam-4385	381	3	∂p	∂p	PROPN
ejpam-4385	382	1	∂r	∂r	INTJ
ejpam-4385	382	2	rp	rp	NOUN
ejpam-4385	383	1	+	+	CCONJ
ejpam-4385	384	1	[	[	X
ejpam-4385	384	2	aθ	aθ	INTJ
ejpam-4385	384	3	−	−	PROPN
ejpam-4385	384	4	(	(	PUNCT
ejpam-4385	384	5	a+	a+	X
ejpam-4385	384	6	λσ)r	λσ)r	X
ejpam-4385	384	7	]	]	X
ejpam-4385	384	8	∂v	∂v	PROPN
ejpam-4385	384	9	∂r	∂r	PROPN
ejpam-4385	384	10	)	)	PUNCT
ejpam-4385	384	11	∆t	∆t	PROPN
ejpam-4385	384	12	.	.	PUNCT
ejpam-4385	385	1	(	(	PUNCT
ejpam-4385	385	2	39	39	NUM
ejpam-4385	385	3	)	)	PUNCT
ejpam-4385	385	4	note	note	VERB
ejpam-4385	385	5	that	that	SCONJ
ejpam-4385	385	6	the	the	DET
ejpam-4385	385	7	change	change	NOUN
ejpam-4385	385	8	in	in	ADP
ejpam-4385	385	9	the	the	DET
ejpam-4385	385	10	value	value	NOUN
ejpam-4385	385	11	of	of	ADP
ejpam-4385	385	12	the	the	DET
ejpam-4385	385	13	portfolio	portfolio	NOUN
ejpam-4385	385	14	∆	∆	PROPN
ejpam-4385	385	15	∏	∏	PROPN
ejpam-4385	385	16	t	t	PROPN
ejpam-4385	385	17	,	,	PUNCT
ejpam-4385	385	18	is	be	AUX
ejpam-4385	385	19	deterministic	deterministic	ADJ
ejpam-4385	385	20	.	.	PUNCT
ejpam-4385	386	1	that	that	ADV
ejpam-4385	386	2	is	is	ADV
ejpam-4385	386	3	,	,	PUNCT
ejpam-4385	386	4	the	the	DET
ejpam-4385	386	5	portfolio	portfolio	NOUN
ejpam-4385	386	6	is	be	AUX
ejpam-4385	386	7	riskless	riskless	NOUN
ejpam-4385	386	8	during	during	ADP
ejpam-4385	386	9	the	the	DET
ejpam-4385	386	10	interval	interval	NOUN
ejpam-4385	386	11	[	[	X
ejpam-4385	386	12	t	t	X
ejpam-4385	386	13	,	,	PUNCT
ejpam-4385	386	14	t+∆t	t+∆t	PROPN
ejpam-4385	386	15	]	]	PUNCT
ejpam-4385	386	16	.	.	PUNCT
ejpam-4385	387	1	hence	hence	ADV
ejpam-4385	387	2	,	,	PUNCT
ejpam-4385	387	3	it	it	PRON
ejpam-4385	387	4	must	must	AUX
ejpam-4385	387	5	instantaneously	instantaneously	ADV
ejpam-4385	387	6	earn	earn	VERB
ejpam-4385	387	7	the	the	DET
ejpam-4385	387	8	same	same	ADJ
ejpam-4385	387	9	rate	rate	NOUN
ejpam-4385	387	10	of	of	ADP
ejpam-4385	387	11	return	return	NOUN
ejpam-4385	387	12	as	as	ADP
ejpam-4385	387	13	other	other	ADJ
ejpam-4385	387	14	short	short	ADJ
ejpam-4385	387	15	-	-	PUNCT
ejpam-4385	387	16	term	term	NOUN
ejpam-4385	387	17	risk	risk	NOUN
ejpam-4385	387	18	-	-	PUNCT
ejpam-4385	387	19	free	free	ADJ
ejpam-4385	387	20	securities	security	NOUN
ejpam-4385	387	21	.	.	PUNCT
ejpam-4385	388	1	that	that	DET
ejpam-4385	388	2	is,∏	is,∏	NOUN
ejpam-4385	388	3	t+∆t	t+∆t	PROPN
ejpam-4385	388	4	=	=	SYM
ejpam-4385	388	5	∏	∏	PROPN
ejpam-4385	388	6	t	t	NOUN
ejpam-4385	388	7	ert∆t	ert∆t	PROPN
ejpam-4385	388	8	(	(	PUNCT
ejpam-4385	388	9	40	40	NUM
ejpam-4385	388	10	)	)	PUNCT
ejpam-4385	388	11	k.	k.	NOUN
ejpam-4385	388	12	falcasantos	falcasantos	PROPN
ejpam-4385	388	13	,	,	PUNCT
ejpam-4385	388	14	f.	f.	PROPN
ejpam-4385	388	15	sumalpong	sumalpong	PROPN
ejpam-4385	388	16	/	/	SYM
ejpam-4385	388	17	eur	eur	PROPN
ejpam-4385	388	18	.	.	PUNCT
ejpam-4385	389	1	j.	j.	PROPN
ejpam-4385	389	2	pure	pure	PROPN
ejpam-4385	389	3	appl	appl	PROPN
ejpam-4385	389	4	.	.	PROPN
ejpam-4385	389	5	math	math	PROPN
ejpam-4385	389	6	,	,	PUNCT
ejpam-4385	389	7	15	15	NUM
ejpam-4385	389	8	(	(	PUNCT
ejpam-4385	389	9	3	3	NUM
ejpam-4385	389	10	)	)	PUNCT
ejpam-4385	389	11	(	(	PUNCT
ejpam-4385	389	12	2022	2022	NUM
ejpam-4385	389	13	)	)	PUNCT
ejpam-4385	389	14	,	,	PUNCT
ejpam-4385	389	15	948	948	NUM
ejpam-4385	389	16	-	-	SYM
ejpam-4385	389	17	970	970	NUM
ejpam-4385	389	18	962	962	NUM
ejpam-4385	389	19	since	since	SCONJ
ejpam-4385	389	20	ert∆t	ert∆t	PROPN
ejpam-4385	389	21	≈	≈	PROPN
ejpam-4385	389	22	1	1	NUM
ejpam-4385	389	23	+	+	NUM
ejpam-4385	389	24	rt∆t	rt∆t	PROPN
ejpam-4385	389	25	,	,	PUNCT
ejpam-4385	389	26	then	then	ADV
ejpam-4385	389	27	approximately	approximately	ADV
ejpam-4385	389	28	∆	∆	X
ejpam-4385	390	1	∏	∏	PROPN
ejpam-4385	390	2	t	t	PROPN
ejpam-4385	391	1	≈	≈	PROPN
ejpam-4385	391	2	rt	rt	PROPN
ejpam-4385	391	3	∏	∏	PROPN
ejpam-4385	391	4	t	t	PROPN
ejpam-4385	391	5	∆t	∆t	PROPN
ejpam-4385	391	6	(	(	PUNCT
ejpam-4385	391	7	41	41	NUM
ejpam-4385	391	8	)	)	PUNCT
ejpam-4385	391	9	substituting	substitute	VERB
ejpam-4385	391	10	equations	equation	NOUN
ejpam-4385	391	11	(	(	PUNCT
ejpam-4385	391	12	39	39	NUM
ejpam-4385	391	13	)	)	PUNCT
ejpam-4385	391	14	and	and	CCONJ
ejpam-4385	391	15	(	(	PUNCT
ejpam-4385	391	16	35	35	NUM
ejpam-4385	391	17	)	)	PUNCT
ejpam-4385	391	18	to	to	ADP
ejpam-4385	391	19	(	(	PUNCT
ejpam-4385	391	20	41	41	NUM
ejpam-4385	391	21	)	)	PUNCT
ejpam-4385	391	22	,	,	PUNCT
ejpam-4385	391	23	we	we	PRON
ejpam-4385	391	24	have	have	VERB
ejpam-4385	391	25	(	(	PUNCT
ejpam-4385	391	26	∂v	∂v	PROPN
ejpam-4385	391	27	∂t	∂t	PROPN
ejpam-4385	392	1	+	+	CCONJ
ejpam-4385	392	2	1	1	NUM
ejpam-4385	392	3	2	2	NUM
ejpam-4385	392	4	σ2	σ2	NOUN
ejpam-4385	392	5	1x	1x	NUM
ejpam-4385	392	6	2	2	NUM
ejpam-4385	392	7	t	t	PROPN
ejpam-4385	392	8	∂2v	∂2v	X
ejpam-4385	392	9	∂x2	∂x2	PROPN
ejpam-4385	392	10	+	+	CCONJ
ejpam-4385	392	11	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	392	12	√	√	NUM
ejpam-4385	392	13	rtxt	rtxt	NOUN
ejpam-4385	392	14	∂2v	∂2v	NOUN
ejpam-4385	392	15	∂x∂r	∂x∂r	VERB
ejpam-4385	393	1	+	+	CCONJ
ejpam-4385	393	2	1	1	NUM
ejpam-4385	393	3	2	2	NUM
ejpam-4385	393	4	σ2rt	σ2rt	NOUN
ejpam-4385	393	5	∂2v	∂2v	NOUN
ejpam-4385	393	6	∂r2	∂r2	PROPN
ejpam-4385	394	1	−	−	PROPN
ejpam-4385	394	2	rtp	rtp	PROPN
ejpam-4385	394	3	∂v	∂v	PROPN
ejpam-4385	395	1	∂r	∂r	PROPN
ejpam-4385	395	2	/	/	PUNCT
ejpam-4385	395	3	∂p	∂p	PROPN
ejpam-4385	395	4	∂r	∂r	PROPN
ejpam-4385	396	1	+	+	NUM
ejpam-4385	396	2	[	[	X
ejpam-4385	396	3	aθ	aθ	INTJ
ejpam-4385	396	4	−	−	PROPN
ejpam-4385	396	5	(	(	PUNCT
ejpam-4385	396	6	a+	a+	X
ejpam-4385	396	7	λσ)r	λσ)r	X
ejpam-4385	396	8	]	]	X
ejpam-4385	396	9	∂v	∂v	PROPN
ejpam-4385	396	10	∂r	∂r	PROPN
ejpam-4385	396	11	)	)	PUNCT
ejpam-4385	396	12	∆t	∆t	PROPN
ejpam-4385	397	1	=	=	SYM
ejpam-4385	397	2	rt	rt	PROPN
ejpam-4385	397	3	(	(	PUNCT
ejpam-4385	397	4	v	v	NOUN
ejpam-4385	397	5	−	−	PROPN
ejpam-4385	397	6	∂v	∂v	PROPN
ejpam-4385	397	7	∂x	∂x	PROPN
ejpam-4385	397	8	xt	xt	PUNCT
ejpam-4385	398	1	−	−	PROPN
ejpam-4385	398	2	∂v	∂v	PROPN
ejpam-4385	398	3	∂r	∂r	PROPN
ejpam-4385	399	1	/	/	SYM
ejpam-4385	399	2	∂p	∂p	PROPN
ejpam-4385	399	3	∂r	∂r	PROPN
ejpam-4385	399	4	p	p	NOUN
ejpam-4385	399	5	)	)	PUNCT
ejpam-4385	399	6	∆t	∆t	PROPN
ejpam-4385	399	7	.	.	PUNCT
ejpam-4385	400	1	(	(	PUNCT
ejpam-4385	400	2	42	42	X
ejpam-4385	400	3	)	)	PUNCT
ejpam-4385	400	4	simplifying	simplify	VERB
ejpam-4385	400	5	this	this	DET
ejpam-4385	400	6	expression	expression	NOUN
ejpam-4385	400	7	,	,	PUNCT
ejpam-4385	400	8	we	we	PRON
ejpam-4385	400	9	have	have	VERB
ejpam-4385	400	10	(	(	PUNCT
ejpam-4385	400	11	∂v	∂v	VERB
ejpam-4385	400	12	∂t	∂t	PROPN
ejpam-4385	401	1	+	+	CCONJ
ejpam-4385	401	2	1	1	NUM
ejpam-4385	401	3	2	2	NUM
ejpam-4385	401	4	σ2	σ2	NOUN
ejpam-4385	401	5	1x	1x	NUM
ejpam-4385	401	6	2	2	NUM
ejpam-4385	401	7	t	t	PROPN
ejpam-4385	401	8	∂2v	∂2v	X
ejpam-4385	401	9	∂x2	∂x2	PROPN
ejpam-4385	401	10	+	+	CCONJ
ejpam-4385	401	11	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	401	12	√	√	NUM
ejpam-4385	401	13	rtxt	rtxt	NOUN
ejpam-4385	401	14	∂2v	∂2v	NOUN
ejpam-4385	401	15	∂x∂r	∂x∂r	VERB
ejpam-4385	402	1	+	+	CCONJ
ejpam-4385	402	2	1	1	NUM
ejpam-4385	402	3	2	2	NUM
ejpam-4385	402	4	σ2	σ2	NOUN
ejpam-4385	402	5	2r	2r	NUM
ejpam-4385	402	6	∂2v	∂2v	PROPN
ejpam-4385	402	7	∂r2	∂r2	PROPN
ejpam-4385	402	8	+	+	CCONJ
ejpam-4385	402	9	rtxt	rtxt	PROPN
ejpam-4385	402	10	∂v	∂v	PROPN
ejpam-4385	402	11	∂x	∂x	PROPN
ejpam-4385	402	12	+	+	CCONJ
ejpam-4385	403	1	[	[	X
ejpam-4385	403	2	aθ	aθ	INTJ
ejpam-4385	403	3	−	−	PROPN
ejpam-4385	403	4	(	(	PUNCT
ejpam-4385	403	5	a+	a+	X
ejpam-4385	403	6	λσ)r	λσ)r	X
ejpam-4385	403	7	]	]	X
ejpam-4385	403	8	∂v	∂v	PROPN
ejpam-4385	403	9	∂r	∂r	INTJ
ejpam-4385	403	10	)	)	PUNCT
ejpam-4385	404	1	−	−	PROPN
ejpam-4385	404	2	rtv	rtv	NOUN
ejpam-4385	404	3	=	=	NOUN
ejpam-4385	404	4	0	0	PROPN
ejpam-4385	404	5	.	.	PUNCT
ejpam-4385	405	1	(	(	PUNCT
ejpam-4385	405	2	43	43	NUM
ejpam-4385	405	3	)	)	PUNCT
ejpam-4385	405	4	now	now	ADV
ejpam-4385	405	5	,	,	PUNCT
ejpam-4385	405	6	we	we	PRON
ejpam-4385	405	7	define	define	VERB
ejpam-4385	405	8	the	the	DET
ejpam-4385	405	9	infinitesimal	infinitesimal	ADJ
ejpam-4385	405	10	generator	generator	NOUN
ejpam-4385	405	11	lf(s	lf(s	X
ejpam-4385	405	12	,	,	PUNCT
ejpam-4385	405	13	y1	y1	NOUN
ejpam-4385	405	14	,	,	PUNCT
ejpam-4385	405	15	y2	y2	NOUN
ejpam-4385	405	16	)	)	PUNCT
ejpam-4385	406	1	=	=	PUNCT
ejpam-4385	407	1			PROPN
ejpam-4385	407	2	∂	∂	NOUN
ejpam-4385	407	3	∂s	∂s	PROPN
ejpam-4385	408	1	+	+	CCONJ
ejpam-4385	408	2	∑	∑	PROPN
ejpam-4385	408	3	i	i	PRON
ejpam-4385	408	4	∂	∂	VERB
ejpam-4385	408	5	yi	yi	NOUN
ejpam-4385	408	6	ai	ai	VERB
ejpam-4385	408	7	+	+	PROPN
ejpam-4385	408	8	1	1	NUM
ejpam-4385	408	9	2	2	NUM
ejpam-4385	408	10	∑	∑	PROPN
ejpam-4385	408	11	i	i	PRON
ejpam-4385	408	12	∑	∑	PROPN
ejpam-4385	408	13	j	j	PROPN
ejpam-4385	408	14	∂2	∂2	PROPN
ejpam-4385	408	15	∂yiyj	∂yiyj	PROPN
ejpam-4385	408	16	bibjρij	bibjρij	NOUN
ejpam-4385	408	17			PROPN
ejpam-4385	408	18	f(s	f(	NOUN
ejpam-4385	408	19	,	,	PUNCT
ejpam-4385	408	20	y1	y1	NOUN
ejpam-4385	408	21	,	,	PUNCT
ejpam-4385	408	22	y2	y2	PROPN
ejpam-4385	408	23	)	)	PUNCT
ejpam-4385	408	24	(	(	PUNCT
ejpam-4385	408	25	44	44	NUM
ejpam-4385	408	26	)	)	PUNCT
ejpam-4385	408	27	for	for	ADP
ejpam-4385	408	28	any	any	DET
ejpam-4385	408	29	differentiable	differentiable	ADJ
ejpam-4385	408	30	function	function	NOUN
ejpam-4385	408	31	f(s	f(s	PROPN
ejpam-4385	408	32	,	,	PUNCT
ejpam-4385	408	33	y1	y1	INTJ
ejpam-4385	408	34	,	,	PUNCT
ejpam-4385	408	35	y2	y2	PROPN
ejpam-4385	408	36	)	)	PUNCT
ejpam-4385	408	37	on	on	ADP
ejpam-4385	408	38	[	[	X
ejpam-4385	408	39	0	0	NUM
ejpam-4385	408	40	,	,	PUNCT
ejpam-4385	408	41	t	t	X
ejpam-4385	408	42	]	]	X
ejpam-4385	408	43	×	×	X
ejpam-4385	408	44	r×	r×	NOUN
ejpam-4385	408	45	(	(	PUNCT
ejpam-4385	408	46	0,∞	0,∞	NOUN
ejpam-4385	408	47	)	)	PUNCT
ejpam-4385	408	48	,	,	PUNCT
ejpam-4385	408	49	where	where	SCONJ
ejpam-4385	408	50	the	the	DET
ejpam-4385	408	51	itö	itö	NOUN
ejpam-4385	408	52	’s	’s	PART
ejpam-4385	408	53	processes	process	NOUN
ejpam-4385	408	54	y1	y1	NOUN
ejpam-4385	408	55	=	=	PUNCT
ejpam-4385	408	56	(	(	PUNCT
ejpam-4385	408	57	y1,s)s≥0	y1,s)s≥0	PROPN
ejpam-4385	408	58	and	and	CCONJ
ejpam-4385	408	59	y2	y2	PROPN
ejpam-4385	408	60	=	=	PUNCT
ejpam-4385	409	1	(	(	PUNCT
ejpam-4385	409	2	y2,s)s≥0	y2,s)s≥0	PROPN
ejpam-4385	409	3	defined	define	VERB
ejpam-4385	409	4	on	on	ADP
ejpam-4385	409	5	probability	probability	NOUN
ejpam-4385	409	6	space	space	NOUN
ejpam-4385	409	7	(	(	PUNCT
ejpam-4385	409	8	ω	ω	NOUN
ejpam-4385	409	9	,	,	PUNCT
ejpam-4385	409	10	fs	fs	ADP
ejpam-4385	409	11	,	,	PUNCT
ejpam-4385	409	12	p	p	NOUN
ejpam-4385	409	13	)	)	PUNCT
ejpam-4385	409	14	satisfy	satisfy	VERB
ejpam-4385	409	15	the	the	DET
ejpam-4385	409	16	stochastic	stochastic	ADJ
ejpam-4385	409	17	differential	differential	ADJ
ejpam-4385	409	18	equations	equation	NOUN
ejpam-4385	409	19	dy1,s	dy1,s	NOUN
ejpam-4385	409	20	=	=	SYM
ejpam-4385	409	21	a1y1,sds+	a1y1,sds+	PROPN
ejpam-4385	409	22	b1y1,sdw1,s	b1y1,sdw1,s	NOUN
ejpam-4385	409	23	(	(	PUNCT
ejpam-4385	409	24	y1,0	y1,0	PROPN
ejpam-4385	409	25	=	=	SYM
ejpam-4385	409	26	y1	y1	PROPN
ejpam-4385	409	27	)	)	PUNCT
ejpam-4385	409	28	dy2,s	dy2,s	NOUN
ejpam-4385	409	29	=	=	SYM
ejpam-4385	409	30	a2y2,sds+	a2y2,sds+	X
ejpam-4385	409	31	b2y2,sdw2,s	b2y2,sdw2,	NOUN
ejpam-4385	409	32	(	(	PUNCT
ejpam-4385	409	33	y2,0	y2,0	PROPN
ejpam-4385	409	34	=	=	PUNCT
ejpam-4385	409	35	y2	y2	PROPN
ejpam-4385	409	36	)	)	PUNCT
ejpam-4385	409	37	,	,	PUNCT
ejpam-4385	409	38	respectively	respectively	ADV
ejpam-4385	409	39	,	,	PUNCT
ejpam-4385	409	40	and	and	CCONJ
ejpam-4385	409	41	ρij	ρij	NOUN
ejpam-4385	409	42	=	=	PUNCT
ejpam-4385	409	43	cov(dwi	cov(dwi	X
ejpam-4385	409	44	,	,	PUNCT
ejpam-4385	409	45	s	s	PROPN
ejpam-4385	409	46	,	,	PUNCT
ejpam-4385	409	47	dwj	dwj	PROPN
ejpam-4385	409	48	,	,	PUNCT
ejpam-4385	409	49	s	s	PART
ejpam-4385	409	50	)	)	PUNCT
ejpam-4385	409	51	(	(	PUNCT
ejpam-4385	409	52	see	see	VERB
ejpam-4385	409	53	[	[	X
ejpam-4385	409	54	1	1	NUM
ejpam-4385	409	55	]	]	NUM
ejpam-4385	409	56	)	)	PUNCT
ejpam-4385	409	57	.	.	PUNCT
ejpam-4385	410	1	lemma	lemma	PROPN
ejpam-4385	410	2	4	4	X
ejpam-4385	410	3	.	.	PUNCT
ejpam-4385	411	1	we	we	PRON
ejpam-4385	411	2	have	have	VERB
ejpam-4385	411	3	d	d	NOUN
ejpam-4385	411	4	=	=	PRON
ejpam-4385	411	5	{	{	PUNCT
ejpam-4385	411	6	(	(	PUNCT
ejpam-4385	411	7	t	t	PROPN
ejpam-4385	411	8	,	,	PUNCT
ejpam-4385	411	9	rt	rt	PROPN
ejpam-4385	411	10	,	,	PUNCT
ejpam-4385	411	11	x	x	NOUN
ejpam-4385	411	12	)	)	PUNCT
ejpam-4385	411	13	∈	∈	PROPN
ejpam-4385	412	1	[	[	X
ejpam-4385	412	2	0	0	NUM
ejpam-4385	412	3	,	,	PUNCT
ejpam-4385	412	4	t	t	X
ejpam-4385	412	5	]	]	X
ejpam-4385	412	6	×	×	X
ejpam-4385	412	7	r×	r×	NOUN
ejpam-4385	412	8	(	(	PUNCT
ejpam-4385	412	9	0,∞)|lx(t	0,∞)|lx(t	NUM
ejpam-4385	412	10	,	,	PUNCT
ejpam-4385	412	11	rt	rt	PROPN
ejpam-4385	412	12	,	,	PUNCT
ejpam-4385	412	13	x	x	NOUN
ejpam-4385	412	14	)	)	PUNCT
ejpam-4385	412	15	>	>	X
ejpam-4385	412	16	0	0	PUNCT
ejpam-4385	412	17	}	}	PUNCT
ejpam-4385	412	18	⊂	⊂	PROPN
ejpam-4385	412	19	c	c	X
ejpam-4385	412	20	(	(	PUNCT
ejpam-4385	412	21	45	45	NUM
ejpam-4385	412	22	)	)	PUNCT
ejpam-4385	412	23	where	where	SCONJ
ejpam-4385	412	24	c	c	NOUN
ejpam-4385	412	25	=	=	SYM
ejpam-4385	412	26	dc	dc	PROPN
ejpam-4385	412	27	is	be	AUX
ejpam-4385	412	28	the	the	DET
ejpam-4385	412	29	continuation	continuation	NOUN
ejpam-4385	412	30	set	set	NOUN
ejpam-4385	412	31	.	.	PUNCT
ejpam-4385	413	1	proof	proof	NOUN
ejpam-4385	413	2	.	.	PUNCT
ejpam-4385	414	1	let	let	VERB
ejpam-4385	414	2	(	(	PUNCT
ejpam-4385	414	3	t	t	PROPN
ejpam-4385	414	4	,	,	PUNCT
ejpam-4385	414	5	rt	rt	PROPN
ejpam-4385	414	6	,	,	PUNCT
ejpam-4385	414	7	x	x	NOUN
ejpam-4385	414	8	)	)	PUNCT
ejpam-4385	414	9	∈	∈	PROPN
ejpam-4385	415	1	[	[	X
ejpam-4385	415	2	0	0	NUM
ejpam-4385	415	3	,	,	PUNCT
ejpam-4385	415	4	t	t	X
ejpam-4385	415	5	]	]	X
ejpam-4385	415	6	×	×	X
ejpam-4385	415	7	r×	r×	NOUN
ejpam-4385	415	8	(	(	PUNCT
ejpam-4385	415	9	0,∞	0,∞	NOUN
ejpam-4385	415	10	)	)	PUNCT
ejpam-4385	415	11	be	be	VERB
ejpam-4385	415	12	such	such	ADJ
ejpam-4385	415	13	that	that	DET
ejpam-4385	415	14	lxv	lxv	NOUN
ejpam-4385	415	15	(	(	PUNCT
ejpam-4385	415	16	t	t	PROPN
ejpam-4385	415	17	,	,	PUNCT
ejpam-4385	415	18	rt	rt	PROPN
ejpam-4385	415	19	,	,	PUNCT
ejpam-4385	415	20	x	x	NOUN
ejpam-4385	415	21	)	)	PUNCT
ejpam-4385	415	22	>	>	X
ejpam-4385	415	23	0	0	X
ejpam-4385	415	24	.	.	PUNCT
ejpam-4385	416	1	by	by	ADP
ejpam-4385	416	2	lemma	lemma	PROPN
ejpam-4385	416	3	1	1	NUM
ejpam-4385	416	4	in	in	ADP
ejpam-4385	416	5	[	[	X
ejpam-4385	416	6	15	15	NUM
ejpam-4385	416	7	]	]	X
ejpam-4385	416	8	,	,	PUNCT
ejpam-4385	416	9	dynkin	dynkin	ADJ
ejpam-4385	416	10	’s	’s	PART
ejpam-4385	416	11	formula	formula	NOUN
ejpam-4385	416	12	holds	hold	VERB
ejpam-4385	416	13	.	.	PUNCT
ejpam-4385	417	1	thus	thus	ADV
ejpam-4385	417	2	we	we	PRON
ejpam-4385	417	3	have	have	VERB
ejpam-4385	417	4	,	,	PUNCT
ejpam-4385	417	5	p	p	X
ejpam-4385	417	6	(	(	PUNCT
ejpam-4385	417	7	t	t	PROPN
ejpam-4385	417	8	,	,	PUNCT
ejpam-4385	417	9	rt	rt	PROPN
ejpam-4385	417	10	;	;	PUNCT
ejpam-4385	417	11	t+	t+	NUM
ejpam-4385	417	12	s)gµc(t+	s)gµc(t+	PROPN
ejpam-4385	417	13	s	s	PROPN
ejpam-4385	417	14	,	,	PUNCT
ejpam-4385	417	15	xt+s	xt+s	PROPN
ejpam-4385	417	16	)	)	PUNCT
ejpam-4385	417	17	=	=	SYM
ejpam-4385	417	18	gµc(t	gµc(t	PROPN
ejpam-4385	417	19	,	,	PUNCT
ejpam-4385	417	20	x	x	NOUN
ejpam-4385	417	21	)	)	PUNCT
ejpam-4385	418	1	+	+	CCONJ
ejpam-4385	418	2	∫	∫	PROPN
ejpam-4385	418	3	τ	τ	PROPN
ejpam-4385	418	4	0	0	NUM
ejpam-4385	418	5	lp	lp	PROPN
ejpam-4385	418	6	(	(	PUNCT
ejpam-4385	418	7	t	t	PROPN
ejpam-4385	418	8	,	,	PUNCT
ejpam-4385	418	9	rt	rt	PROPN
ejpam-4385	418	10	;	;	PUNCT
ejpam-4385	418	11	t+	t+	NUM
ejpam-4385	418	12	s)gµc(t+	s)gµc(t+	PROPN
ejpam-4385	418	13	s	s	NOUN
ejpam-4385	418	14	,	,	PUNCT
ejpam-4385	418	15	xt+s)ds	xt+s)ds	X
ejpam-4385	419	1	+	+	PRON
ejpam-4385	419	2	ms	ms	NOUN
ejpam-4385	419	3	(	(	PUNCT
ejpam-4385	419	4	46	46	NUM
ejpam-4385	419	5	)	)	PUNCT
ejpam-4385	419	6	k.	k.	NOUN
ejpam-4385	419	7	falcasantos	falcasantos	PROPN
ejpam-4385	419	8	,	,	PUNCT
ejpam-4385	419	9	f.	f.	PROPN
ejpam-4385	419	10	sumalpong	sumalpong	PROPN
ejpam-4385	419	11	/	/	SYM
ejpam-4385	419	12	eur	eur	PROPN
ejpam-4385	419	13	.	.	PUNCT
ejpam-4385	420	1	j.	j.	PROPN
ejpam-4385	420	2	pure	pure	PROPN
ejpam-4385	420	3	appl	appl	PROPN
ejpam-4385	420	4	.	.	PROPN
ejpam-4385	420	5	math	math	PROPN
ejpam-4385	420	6	,	,	PUNCT
ejpam-4385	420	7	15	15	NUM
ejpam-4385	420	8	(	(	PUNCT
ejpam-4385	420	9	3	3	NUM
ejpam-4385	420	10	)	)	PUNCT
ejpam-4385	420	11	(	(	PUNCT
ejpam-4385	420	12	2022	2022	NUM
ejpam-4385	420	13	)	)	PUNCT
ejpam-4385	420	14	,	,	PUNCT
ejpam-4385	420	15	948	948	NUM
ejpam-4385	420	16	-	-	SYM
ejpam-4385	420	17	970	970	NUM
ejpam-4385	420	18	963	963	NUM
ejpam-4385	420	19	where	where	SCONJ
ejpam-4385	420	20	ms	ms	PROPN
ejpam-4385	420	21	=	=	PROPN
ejpam-4385	420	22	∫	∫	PROPN
ejpam-4385	420	23	τ	τ	PROPN
ejpam-4385	420	24	0	0	PUNCT
ejpam-4385	420	25	σ1x	σ1x	PRON
ejpam-4385	420	26	∂gµc	∂gµc	NOUN
ejpam-4385	420	27	∂x	∂x	PROPN
ejpam-4385	420	28	dws	dws	PROPN
ejpam-4385	420	29	+	+	CCONJ
ejpam-4385	420	30	∫	∫	PROPN
ejpam-4385	420	31	τ	τ	PROPN
ejpam-4385	420	32	0	0	PROPN
ejpam-4385	420	33	σ2	σ2	PROPN
ejpam-4385	420	34	√	√	PROPN
ejpam-4385	420	35	rsg	rsg	PROPN
ejpam-4385	420	36	µc	µc	PROPN
ejpam-4385	420	37	∂p	∂p	PROPN
ejpam-4385	420	38	∂rs	∂rs	PROPN
ejpam-4385	420	39	dw̄s	dw̄s	PROPN
ejpam-4385	420	40	defines	define	VERB
ejpam-4385	420	41	a	a	DET
ejpam-4385	420	42	continuous	continuous	ADJ
ejpam-4385	420	43	martingale	martingale	NOUN
ejpam-4385	420	44	for	for	ADP
ejpam-4385	420	45	s	s	X
ejpam-4385	420	46	∈	∈	PROPN
ejpam-4385	421	1	[	[	X
ejpam-4385	421	2	0	0	NUM
ejpam-4385	421	3	,	,	PUNCT
ejpam-4385	421	4	t	t	PROPN
ejpam-4385	421	5	−	−	PROPN
ejpam-4385	421	6	t	t	PROPN
ejpam-4385	421	7	]	]	PUNCT
ejpam-4385	421	8	with	with	ADP
ejpam-4385	421	9	t	t	PROPN
ejpam-4385	421	10	∈	∈	PROPN
ejpam-4385	422	1	[	[	X
ejpam-4385	422	2	0	0	NUM
ejpam-4385	422	3	,	,	PUNCT
ejpam-4385	422	4	t	t	X
ejpam-4385	422	5	]	]	PUNCT
ejpam-4385	422	6	.	.	PUNCT
ejpam-4385	423	1	by	by	ADP
ejpam-4385	423	2	lemma	lemma	PROPN
ejpam-4385	423	3	5.2	5.2	NUM
ejpam-4385	423	4	and	and	CCONJ
ejpam-4385	423	5	the	the	DET
ejpam-4385	423	6	fact	fact	NOUN
ejpam-4385	423	7	that	that	SCONJ
ejpam-4385	423	8	gµc	gµc	NOUN
ejpam-4385	423	9	∈	∈	PROPN
ejpam-4385	423	10	c1,2	c1,2	PROPN
ejpam-4385	423	11	(	(	PUNCT
ejpam-4385	423	12	see	see	VERB
ejpam-4385	423	13	[	[	X
ejpam-4385	423	14	11	11	NUM
ejpam-4385	423	15	]	]	NUM
ejpam-4385	423	16	)	)	PUNCT
ejpam-4385	423	17	,	,	PUNCT
ejpam-4385	423	18	the	the	DET
ejpam-4385	423	19	infinitesimal	infinitesimal	ADJ
ejpam-4385	423	20	generator	generator	NOUN
ejpam-4385	423	21	lp	lp	PROPN
ejpam-4385	423	22	(	(	PUNCT
ejpam-4385	423	23	t	t	PROPN
ejpam-4385	423	24	,	,	PUNCT
ejpam-4385	423	25	ru	ru	PROPN
ejpam-4385	423	26	;	;	PUNCT
ejpam-4385	423	27	t	t	PROPN
ejpam-4385	423	28	+	+	NUM
ejpam-4385	423	29	s)gµc(t	s)gµc(t	PROPN
ejpam-4385	423	30	,	,	PUNCT
ejpam-4385	423	31	x	x	PRON
ejpam-4385	423	32	)	)	PUNCT
ejpam-4385	423	33	is	be	AUX
ejpam-4385	423	34	continuous	continuous	ADJ
ejpam-4385	423	35	with	with	ADP
ejpam-4385	423	36	respect	respect	NOUN
ejpam-4385	423	37	to	to	ADP
ejpam-4385	423	38	(	(	PUNCT
ejpam-4385	423	39	t	t	PROPN
ejpam-4385	423	40	,	,	PUNCT
ejpam-4385	423	41	x	x	NOUN
ejpam-4385	423	42	)	)	PUNCT
ejpam-4385	423	43	∈	∈	PROPN
ejpam-4385	424	1	[	[	X
ejpam-4385	424	2	0	0	NUM
ejpam-4385	424	3	,	,	PUNCT
ejpam-4385	424	4	t	t	X
ejpam-4385	424	5	]	]	X
ejpam-4385	424	6	×	×	NOUN
ejpam-4385	424	7	(	(	PUNCT
ejpam-4385	424	8	0,∞	0,∞	NOUN
ejpam-4385	424	9	)	)	PUNCT
ejpam-4385	424	10	.	.	PUNCT
ejpam-4385	425	1	thus	thus	ADV
ejpam-4385	425	2	,	,	PUNCT
ejpam-4385	425	3	there	there	PRON
ejpam-4385	425	4	exists	exist	VERB
ejpam-4385	425	5	an	an	DET
ejpam-4385	425	6	open	open	ADJ
ejpam-4385	425	7	neighborhood	neighborhood	NOUN
ejpam-4385	425	8	u	u	NOUN
ejpam-4385	425	9	×	×	NOUN
ejpam-4385	425	10	v	v	ADP
ejpam-4385	425	11	⊂	⊂	PROPN
ejpam-4385	426	1	[	[	X
ejpam-4385	426	2	0	0	NUM
ejpam-4385	426	3	,	,	PUNCT
ejpam-4385	426	4	t	t	X
ejpam-4385	426	5	]	]	X
ejpam-4385	426	6	×	×	NOUN
ejpam-4385	426	7	(	(	PUNCT
ejpam-4385	426	8	0,∞	0,∞	NOUN
ejpam-4385	426	9	)	)	PUNCT
ejpam-4385	426	10	of	of	ADP
ejpam-4385	426	11	(	(	PUNCT
ejpam-4385	426	12	t	t	PROPN
ejpam-4385	426	13	,	,	PUNCT
ejpam-4385	426	14	x	x	NOUN
ejpam-4385	426	15	)	)	PUNCT
ejpam-4385	426	16	such	such	ADJ
ejpam-4385	426	17	that	that	DET
ejpam-4385	426	18	lxv	lxv	NOUN
ejpam-4385	426	19	(	(	PUNCT
ejpam-4385	426	20	t	t	PROPN
ejpam-4385	426	21	,	,	PUNCT
ejpam-4385	426	22	rt	rt	PROPN
ejpam-4385	426	23	,	,	PUNCT
ejpam-4385	426	24	x	x	NOUN
ejpam-4385	426	25	)	)	PUNCT
ejpam-4385	426	26	>	>	X
ejpam-4385	426	27	0	0	PUNCT
ejpam-4385	427	1	for	for	ADP
ejpam-4385	427	2	all	all	PRON
ejpam-4385	427	3	(	(	PUNCT
ejpam-4385	427	4	s	s	NOUN
ejpam-4385	427	5	,	,	PUNCT
ejpam-4385	427	6	rs	rs	NOUN
ejpam-4385	427	7	,	,	PUNCT
ejpam-4385	427	8	y	y	NOUN
ejpam-4385	427	9	)	)	PUNCT
ejpam-4385	427	10	∈	∈	PROPN
ejpam-4385	427	11	u	u	NOUN
ejpam-4385	427	12	×	×	NOUN
ejpam-4385	427	13	v	v	ADP
ejpam-4385	427	14	×	×	NOUN
ejpam-4385	427	15	0	0	NUM
ejpam-4385	427	16	.	.	PUNCT
ejpam-4385	428	1	let	let	VERB
ejpam-4385	428	2	τu	τu	ADP
ejpam-4385	428	3	=	=	PROPN
ejpam-4385	428	4	inf	inf	PROPN
ejpam-4385	428	5	{	{	PUNCT
ejpam-4385	428	6	τ	τ	PROPN
ejpam-4385	428	7	:	:	PUNCT
ejpam-4385	428	8	(	(	PUNCT
ejpam-4385	428	9	t+	t+	X
ejpam-4385	428	10	τ	τ	NOUN
ejpam-4385	428	11	,	,	PUNCT
ejpam-4385	428	12	rt+τ	rt+τ	PROPN
ejpam-4385	428	13	,	,	PUNCT
ejpam-4385	428	14	xt+τ	xt+τ	PROPN
ejpam-4385	428	15	)	)	PUNCT
ejpam-4385	429	1	∈	∈	PROPN
ejpam-4385	429	2	u	u	NOUN
ejpam-4385	429	3	×	×	NOUN
ejpam-4385	429	4	v	v	ADP
ejpam-4385	429	5	×	×	NOUN
ejpam-4385	429	6	0	0	NUM
ejpam-4385	429	7	,	,	PUNCT
ejpam-4385	429	8	xt	xt	PUNCT
ejpam-4385	429	9	=	=	SYM
ejpam-4385	429	10	x	x	PROPN
ejpam-4385	429	11	,	,	PUNCT
ejpam-4385	429	12	rt	rt	PROPN
ejpam-4385	429	13	=	=	SYM
ejpam-4385	429	14	r	r	NOUN
ejpam-4385	429	15	}	}	PUNCT
ejpam-4385	429	16	.	.	PUNCT
ejpam-4385	430	1	by	by	ADP
ejpam-4385	430	2	optimal	optimal	ADJ
ejpam-4385	430	3	sampling	sampling	NOUN
ejpam-4385	430	4	theorem	theorem	NOUN
ejpam-4385	430	5	,	,	PUNCT
ejpam-4385	430	6	the	the	DET
ejpam-4385	430	7	relation	relation	NOUN
ejpam-4385	430	8	equation	equation	NOUN
ejpam-4385	430	9	(	(	PUNCT
ejpam-4385	430	10	46	46	NUM
ejpam-4385	430	11	)	)	PUNCT
ejpam-4385	430	12	with	with	ADP
ejpam-4385	430	13	s	s	NOUN
ejpam-4385	430	14	=	=	PUNCT
ejpam-4385	430	15	τu	τu	PART
ejpam-4385	430	16	shows	show	VERB
ejpam-4385	430	17	that	that	SCONJ
ejpam-4385	430	18	e	e	PROPN
ejpam-4385	431	1	[	[	X
ejpam-4385	431	2	p	p	X
ejpam-4385	431	3	(	(	PUNCT
ejpam-4385	431	4	t	t	PROPN
ejpam-4385	431	5	,	,	PUNCT
ejpam-4385	431	6	rt	rt	PROPN
ejpam-4385	431	7	;	;	PUNCT
ejpam-4385	431	8	t+	t+	NUM
ejpam-4385	431	9	s)gµc(t+	s)gµc(t+	PROPN
ejpam-4385	431	10	s	s	PROPN
ejpam-4385	431	11	,	,	PUNCT
ejpam-4385	431	12	xt+s	xt+s	PROPN
ejpam-4385	431	13	)	)	PUNCT
ejpam-4385	431	14	]	]	PUNCT
ejpam-4385	431	15	=	=	PUNCT
ejpam-4385	431	16	gµc(t	gµc(t	PROPN
ejpam-4385	431	17	,	,	PUNCT
ejpam-4385	431	18	x	x	NOUN
ejpam-4385	431	19	)	)	PUNCT
ejpam-4385	432	1	+	+	CCONJ
ejpam-4385	432	2	e	e	X
ejpam-4385	433	1	[	[	X
ejpam-4385	433	2	∫	∫	X
ejpam-4385	433	3	t	t	PROPN
ejpam-4385	433	4	0	0	NUM
ejpam-4385	433	5	lp	lp	PROPN
ejpam-4385	433	6	(	(	PUNCT
ejpam-4385	433	7	t	t	PROPN
ejpam-4385	433	8	,	,	PUNCT
ejpam-4385	433	9	rt	rt	PROPN
ejpam-4385	433	10	;	;	PUNCT
ejpam-4385	433	11	t+	t+	NUM
ejpam-4385	433	12	s)gµc(t+	s)gµc(t+	PROPN
ejpam-4385	433	13	s	s	NOUN
ejpam-4385	433	14	,	,	PUNCT
ejpam-4385	433	15	xt+s)ds	xt+s)ds	X
ejpam-4385	433	16	]	]	PUNCT
ejpam-4385	433	17	.	.	PUNCT
ejpam-4385	434	1	(	(	PUNCT
ejpam-4385	434	2	47	47	NUM
ejpam-4385	434	3	)	)	PUNCT
ejpam-4385	434	4	since	since	SCONJ
ejpam-4385	434	5	lxv	lxv	NOUN
ejpam-4385	434	6	(	(	PUNCT
ejpam-4385	434	7	t	t	PROPN
ejpam-4385	434	8	,	,	PUNCT
ejpam-4385	434	9	rt	rt	PROPN
ejpam-4385	434	10	,	,	PUNCT
ejpam-4385	434	11	x	x	NOUN
ejpam-4385	434	12	)	)	PUNCT
ejpam-4385	434	13	>	>	X
ejpam-4385	435	1	0	0	NUM
ejpam-4385	435	2	,	,	PUNCT
ejpam-4385	435	3	the	the	DET
ejpam-4385	435	4	right	right	ADJ
ejpam-4385	435	5	hand	hand	NOUN
ejpam-4385	435	6	side	side	NOUN
ejpam-4385	435	7	of	of	ADP
ejpam-4385	435	8	(	(	PUNCT
ejpam-4385	435	9	47	47	NUM
ejpam-4385	435	10	)	)	PUNCT
ejpam-4385	435	11	is	be	AUX
ejpam-4385	435	12	strictly	strictly	ADV
ejpam-4385	435	13	greater	great	ADJ
ejpam-4385	435	14	than	than	ADP
ejpam-4385	435	15	gµc	gµc	NOUN
ejpam-4385	435	16	,	,	PUNCT
ejpam-4385	435	17	while	while	SCONJ
ejpam-4385	435	18	from	from	ADP
ejpam-4385	435	19	(	(	PUNCT
ejpam-4385	435	20	19	19	NUM
ejpam-4385	435	21	)	)	PUNCT
ejpam-4385	435	22	,	,	PUNCT
ejpam-4385	435	23	we	we	PRON
ejpam-4385	435	24	have	have	VERB
ejpam-4385	435	25	v	v	NUM
ejpam-4385	435	26	(	(	PUNCT
ejpam-4385	435	27	t	t	PROPN
ejpam-4385	435	28	,	,	PUNCT
ejpam-4385	435	29	rt	rt	PROPN
ejpam-4385	435	30	,	,	PUNCT
ejpam-4385	435	31	x	x	NOUN
ejpam-4385	435	32	)	)	PUNCT
ejpam-4385	435	33	≥	≥	NOUN
ejpam-4385	435	34	e[p	e[p	NOUN
ejpam-4385	435	35	(	(	PUNCT
ejpam-4385	435	36	t	t	PROPN
ejpam-4385	435	37	,	,	PUNCT
ejpam-4385	435	38	rt	rt	PROPN
ejpam-4385	435	39	;	;	PUNCT
ejpam-4385	435	40	t+	t+	NUM
ejpam-4385	435	41	s)gµc(t+	s)gµc(t+	PROPN
ejpam-4385	435	42	s	s	NOUN
ejpam-4385	435	43	,	,	PUNCT
ejpam-4385	435	44	xt+s)|ft	xt+s)|ft	NOUN
ejpam-4385	435	45	]	]	PUNCT
ejpam-4385	435	46	showing	show	VERB
ejpam-4385	435	47	that	that	PRON
ejpam-4385	435	48	v	v	NOUN
ejpam-4385	435	49	(	(	PUNCT
ejpam-4385	435	50	t	t	PROPN
ejpam-4385	435	51	,	,	PUNCT
ejpam-4385	435	52	rt	rt	PROPN
ejpam-4385	435	53	,	,	PUNCT
ejpam-4385	435	54	x	x	NOUN
ejpam-4385	435	55	)	)	PUNCT
ejpam-4385	435	56	>	>	X
ejpam-4385	436	1	gµc(t	gµc(t	PROPN
ejpam-4385	436	2	,	,	PUNCT
ejpam-4385	436	3	x	x	NOUN
ejpam-4385	436	4	)	)	PUNCT
ejpam-4385	436	5	,	,	PUNCT
ejpam-4385	436	6	which	which	PRON
ejpam-4385	436	7	implies	imply	VERB
ejpam-4385	436	8	that	that	SCONJ
ejpam-4385	436	9	(	(	PUNCT
ejpam-4385	436	10	t	t	PROPN
ejpam-4385	436	11	,	,	PUNCT
ejpam-4385	436	12	rt	rt	PROPN
ejpam-4385	436	13	,	,	PUNCT
ejpam-4385	436	14	x	x	NOUN
ejpam-4385	436	15	)	)	PUNCT
ejpam-4385	436	16	∈	∈	PROPN
ejpam-4385	436	17	c.	c.	NOUN
ejpam-4385	436	18	this	this	PRON
ejpam-4385	436	19	completes	complete	VERB
ejpam-4385	436	20	the	the	DET
ejpam-4385	436	21	proof	proof	NOUN
ejpam-4385	436	22	.	.	PUNCT
ejpam-4385	437	1	we	we	PRON
ejpam-4385	437	2	now	now	ADV
ejpam-4385	437	3	proceed	proceed	VERB
ejpam-4385	437	4	to	to	ADP
ejpam-4385	437	5	the	the	DET
ejpam-4385	437	6	solution	solution	NOUN
ejpam-4385	437	7	of	of	ADP
ejpam-4385	437	8	the	the	DET
ejpam-4385	437	9	free	free	ADJ
ejpam-4385	437	10	boundary	boundary	ADJ
ejpam-4385	437	11	problem	problem	NOUN
ejpam-4385	437	12	in	in	ADP
ejpam-4385	437	13	(	(	PUNCT
ejpam-4385	437	14	21	21	NUM
ejpam-4385	437	15	)	)	PUNCT
ejpam-4385	437	16	.	.	PUNCT
ejpam-4385	438	1	going	go	VERB
ejpam-4385	438	2	back	back	ADV
ejpam-4385	438	3	to	to	ADP
ejpam-4385	438	4	the	the	DET
ejpam-4385	438	5	option	option	NOUN
ejpam-4385	438	6	price	price	NOUN
ejpam-4385	438	7	in	in	ADP
ejpam-4385	438	8	(	(	PUNCT
ejpam-4385	438	9	17	17	NUM
ejpam-4385	438	10	)	)	PUNCT
ejpam-4385	438	11	,	,	PUNCT
ejpam-4385	438	12	note	note	VERB
ejpam-4385	438	13	that	that	SCONJ
ejpam-4385	438	14	it	it	PRON
ejpam-4385	438	15	can	can	AUX
ejpam-4385	438	16	be	be	AUX
ejpam-4385	438	17	written	write	VERB
ejpam-4385	438	18	as	as	ADP
ejpam-4385	438	19	v	v	NOUN
ejpam-4385	438	20	=	=	SYM
ejpam-4385	439	1	sup	sup	NOUN
ejpam-4385	439	2	0≤τ≤t	0≤τ≤t	NUM
ejpam-4385	439	3	ẽ	ẽ	PROPN
ejpam-4385	439	4	[	[	PUNCT
ejpam-4385	439	5	p	p	X
ejpam-4385	439	6	(	(	PUNCT
ejpam-4385	439	7	0	0	NUM
ejpam-4385	439	8	,	,	PUNCT
ejpam-4385	439	9	rt	rt	INTJ
ejpam-4385	439	10	;	;	PUNCT
ejpam-4385	439	11	τ)e	τ)e	PUNCT
ejpam-4385	439	12	µc(xt	µc(xt	NOUN
ejpam-4385	439	13	−k)+|fτ	−k)+|fτ	PROPN
ejpam-4385	439	14	]	]	X
ejpam-4385	439	15	(	(	PUNCT
ejpam-4385	439	16	48	48	NUM
ejpam-4385	439	17	)	)	PUNCT
ejpam-4385	439	18	similarly	similarly	ADV
ejpam-4385	439	19	,	,	PUNCT
ejpam-4385	439	20	(	(	PUNCT
ejpam-4385	439	21	20	20	NUM
ejpam-4385	439	22	)	)	PUNCT
ejpam-4385	439	23	can	can	AUX
ejpam-4385	439	24	be	be	AUX
ejpam-4385	439	25	written	write	VERB
ejpam-4385	439	26	as	as	ADP
ejpam-4385	439	27	v	v	NOUN
ejpam-4385	439	28	=	=	NOUN
ejpam-4385	439	29	sup	sup	NOUN
ejpam-4385	439	30	0≤τ≤t−t	0≤τ≤t−t	NUM
ejpam-4385	439	31	e	e	NOUN
ejpam-4385	440	1	[	[	X
ejpam-4385	440	2	p	p	X
ejpam-4385	440	3	(	(	PUNCT
ejpam-4385	440	4	0	0	NUM
ejpam-4385	440	5	,	,	PUNCT
ejpam-4385	440	6	rt	rt	INTJ
ejpam-4385	440	7	;	;	PUNCT
ejpam-4385	440	8	τ)g	τ)g	NOUN
ejpam-4385	440	9	µc(t+	µc(t+	PROPN
ejpam-4385	440	10	τ	τ	PROPN
ejpam-4385	440	11	,	,	PUNCT
ejpam-4385	440	12	xxτ	xxτ	PROPN
ejpam-4385	440	13	)	)	PUNCT
ejpam-4385	440	14	|xt	|xt	X
ejpam-4385	440	15	=	=	SYM
ejpam-4385	440	16	x	x	NOUN
ejpam-4385	440	17	,	,	PUNCT
ejpam-4385	440	18	rt	rt	PROPN
ejpam-4385	440	19	=	=	SYM
ejpam-4385	440	20	r	r	NOUN
ejpam-4385	440	21	]	]	X
ejpam-4385	440	22	(	(	PUNCT
ejpam-4385	440	23	49	49	NUM
ejpam-4385	440	24	)	)	PUNCT
ejpam-4385	440	25	now	now	ADV
ejpam-4385	440	26	,	,	PUNCT
ejpam-4385	440	27	let	let	VERB
ejpam-4385	440	28	γ(s	γ(s	PROPN
ejpam-4385	440	29	,	,	PUNCT
ejpam-4385	440	30	r	r	NOUN
ejpam-4385	440	31	,	,	PUNCT
ejpam-4385	440	32	x	x	NOUN
ejpam-4385	440	33	)	)	PUNCT
ejpam-4385	441	1	=	=	SYM
ejpam-4385	441	2	p	p	X
ejpam-4385	441	3	(	(	PUNCT
ejpam-4385	441	4	0	0	NUM
ejpam-4385	441	5	,	,	PUNCT
ejpam-4385	441	6	r	r	NOUN
ejpam-4385	441	7	;	;	PUNCT
ejpam-4385	441	8	s)gµc(s	s)gµc(s	NUM
ejpam-4385	441	9	,	,	PUNCT
ejpam-4385	441	10	x	x	NOUN
ejpam-4385	441	11	)	)	PUNCT
ejpam-4385	441	12	.	.	PUNCT
ejpam-4385	442	1	(	(	PUNCT
ejpam-4385	442	2	50	50	NUM
ejpam-4385	442	3	)	)	PUNCT
ejpam-4385	442	4	then	then	ADV
ejpam-4385	442	5	∂γ	∂γ	PROPN
ejpam-4385	442	6	∂s	∂s	PROPN
ejpam-4385	443	1	=	=	PUNCT
ejpam-4385	443	2	p	p	X
ejpam-4385	443	3	s	s	NOUN
ejpam-4385	443	4	0	0	NUM
ejpam-4385	443	5	∂gµc	∂gµc	NOUN
ejpam-4385	443	6	∂s	∂s	PROPN
ejpam-4385	443	7	+	+	NOUN
ejpam-4385	443	8	gµc	gµc	NOUN
ejpam-4385	443	9	∂p	∂p	PROPN
ejpam-4385	443	10	s	s	NOUN
ejpam-4385	443	11	0	0	NUM
ejpam-4385	443	12	∂s	∂s	PROPN
ejpam-4385	443	13	r	r	NOUN
ejpam-4385	443	14	,	,	PUNCT
ejpam-4385	443	15	∂2γ	∂2γ	NOUN
ejpam-4385	443	16	∂x2	∂x2	NOUN
ejpam-4385	443	17	=	=	SYM
ejpam-4385	443	18	p	p	X
ejpam-4385	443	19	s	s	NOUN
ejpam-4385	443	20	0	0	NUM
ejpam-4385	443	21	∂2gµc	∂2gµc	NOUN
ejpam-4385	443	22	∂x2	∂x2	NOUN
ejpam-4385	443	23	,	,	PUNCT
ejpam-4385	443	24	∂γ	∂γ	PROPN
ejpam-4385	444	1	∂r	∂r	NOUN
ejpam-4385	444	2	=	=	NOUN
ejpam-4385	444	3	gµc	gµc	NOUN
ejpam-4385	445	1	∂p	∂p	PROPN
ejpam-4385	445	2	s	s	NOUN
ejpam-4385	445	3	0	0	NUM
ejpam-4385	445	4	∂r	∂r	ADJ
ejpam-4385	445	5	,	,	PUNCT
ejpam-4385	445	6	∂γ	∂γ	PROPN
ejpam-4385	445	7	∂x	∂x	PROPN
ejpam-4385	446	1	=	=	PUNCT
ejpam-4385	447	1	p	p	X
ejpam-4385	447	2	s	s	NOUN
ejpam-4385	447	3	0	0	NUM
ejpam-4385	447	4	∂gµc	∂gµc	NOUN
ejpam-4385	447	5	∂x	∂x	PROPN
ejpam-4385	447	6	,	,	PUNCT
ejpam-4385	447	7	∂2γ	∂2γ	NOUN
ejpam-4385	447	8	∂x∂r	∂x∂r	NOUN
ejpam-4385	447	9	=	=	NOUN
ejpam-4385	447	10	∂gµc	∂gµc	NOUN
ejpam-4385	447	11	∂x	∂x	PROPN
ejpam-4385	447	12	∂p	∂p	PROPN
ejpam-4385	447	13	s	s	NOUN
ejpam-4385	447	14	0	0	NUM
ejpam-4385	447	15	∂r	∂r	ADJ
ejpam-4385	447	16	and	and	CCONJ
ejpam-4385	447	17	∂2γ	∂2γ	NOUN
ejpam-4385	447	18	∂r2	∂r2	NOUN
ejpam-4385	447	19	=	=	SYM
ejpam-4385	447	20	gµc	gµc	NOUN
ejpam-4385	447	21	∂	∂	NUM
ejpam-4385	447	22	2p	2p	NUM
ejpam-4385	447	23	s	s	PART
ejpam-4385	447	24	0	0	NUM
ejpam-4385	447	25	∂r2	∂r2	PROPN
ejpam-4385	447	26	.	.	PUNCT
ejpam-4385	448	1	by	by	ADP
ejpam-4385	448	2	itö	itö	NOUN
ejpam-4385	448	3	’s	’s	PART
ejpam-4385	448	4	formula	formula	NOUN
ejpam-4385	448	5	,	,	PUNCT
ejpam-4385	448	6	dγ	dγ	ADP
ejpam-4385	448	7	=	=	PROPN
ejpam-4385	448	8	∂γ	∂γ	PROPN
ejpam-4385	448	9	∂s	∂s	PROPN
ejpam-4385	448	10	ds+	ds+	PROPN
ejpam-4385	449	1	∂γ	∂γ	PROPN
ejpam-4385	450	1	∂r	∂r	PROPN
ejpam-4385	450	2	dr	dr	PROPN
ejpam-4385	450	3	+	+	PROPN
ejpam-4385	450	4	∂γ	∂γ	PROPN
ejpam-4385	450	5	∂x	∂x	PROPN
ejpam-4385	450	6	dx+	dx+	NOUN
ejpam-4385	450	7	1	1	NUM
ejpam-4385	450	8	2	2	NUM
ejpam-4385	450	9	σ2	σ2	NOUN
ejpam-4385	450	10	1	1	NUM
ejpam-4385	450	11	∂2γ	∂2γ	NOUN
ejpam-4385	450	12	∂r2	∂r2	NOUN
ejpam-4385	450	13	+	+	CCONJ
ejpam-4385	450	14	ρσ1σ2	ρσ1σ2	PROPN
ejpam-4385	450	15	√	√	NUM
ejpam-4385	450	16	r	r	NOUN
ejpam-4385	450	17	∂2γ	∂2γ	NOUN
ejpam-4385	450	18	∂x∂r	∂x∂r	PROPN
ejpam-4385	451	1	+	+	NOUN
ejpam-4385	451	2	1	1	NUM
ejpam-4385	451	3	2	2	NUM
ejpam-4385	451	4	σ2r	σ2r	NOUN
ejpam-4385	451	5	∂2γ	∂2γ	NOUN
ejpam-4385	451	6	∂x2	∂x2	NOUN
ejpam-4385	451	7	ds	ds	X
ejpam-4385	451	8	.	.	PUNCT
ejpam-4385	452	1	(	(	PUNCT
ejpam-4385	452	2	51	51	NUM
ejpam-4385	452	3	)	)	PUNCT
ejpam-4385	452	4	k.	k.	NOUN
ejpam-4385	452	5	falcasantos	falcasantos	PROPN
ejpam-4385	452	6	,	,	PUNCT
ejpam-4385	452	7	f.	f.	PROPN
ejpam-4385	452	8	sumalpong	sumalpong	PROPN
ejpam-4385	452	9	/	/	SYM
ejpam-4385	452	10	eur	eur	PROPN
ejpam-4385	452	11	.	.	PUNCT
ejpam-4385	453	1	j.	j.	PROPN
ejpam-4385	453	2	pure	pure	PROPN
ejpam-4385	453	3	appl	appl	PROPN
ejpam-4385	453	4	.	.	PROPN
ejpam-4385	453	5	math	math	PROPN
ejpam-4385	453	6	,	,	PUNCT
ejpam-4385	453	7	15	15	NUM
ejpam-4385	453	8	(	(	PUNCT
ejpam-4385	453	9	3	3	NUM
ejpam-4385	453	10	)	)	PUNCT
ejpam-4385	453	11	(	(	PUNCT
ejpam-4385	453	12	2022	2022	NUM
ejpam-4385	453	13	)	)	PUNCT
ejpam-4385	453	14	,	,	PUNCT
ejpam-4385	453	15	948	948	NUM
ejpam-4385	453	16	-	-	SYM
ejpam-4385	453	17	970	970	NUM
ejpam-4385	453	18	964	964	NUM
ejpam-4385	453	19	thus	thus	ADV
ejpam-4385	453	20	,	,	PUNCT
ejpam-4385	453	21	d	d	X
ejpam-4385	454	1	[	[	X
ejpam-4385	454	2	p	p	X
ejpam-4385	454	3	(	(	PUNCT
ejpam-4385	454	4	0	0	NUM
ejpam-4385	454	5	,	,	PUNCT
ejpam-4385	454	6	r	r	NOUN
ejpam-4385	454	7	;	;	PUNCT
ejpam-4385	454	8	s)gµc(s	s)gµc(s	NUM
ejpam-4385	454	9	,	,	PUNCT
ejpam-4385	454	10	xs	xs	PROPN
ejpam-4385	454	11	)	)	PUNCT
ejpam-4385	454	12	]	]	PUNCT
ejpam-4385	455	1	=	=	PUNCT
ejpam-4385	455	2	p	p	X
ejpam-4385	455	3	s	s	NOUN
ejpam-4385	455	4	0	0	NUM
ejpam-4385	455	5	∂gµc	∂gµc	NOUN
ejpam-4385	455	6	∂s	∂s	PROPN
ejpam-4385	455	7	+	+	NOUN
ejpam-4385	455	8	gµc	gµc	NOUN
ejpam-4385	456	1	∂p	∂p	PROPN
ejpam-4385	456	2	s	s	NOUN
ejpam-4385	456	3	0	0	NUM
ejpam-4385	456	4	∂s	∂s	PROPN
ejpam-4385	456	5	ds+	ds+	NOUN
ejpam-4385	457	1	[	[	X
ejpam-4385	457	2	aθ	aθ	INTJ
ejpam-4385	457	3	−	−	PROPN
ejpam-4385	457	4	(	(	PUNCT
ejpam-4385	457	5	a+	a+	PUNCT
ejpam-4385	457	6	λσ)r]gµc	λσ)r]gµc	PROPN
ejpam-4385	458	1	∂p	∂p	PROPN
ejpam-4385	458	2	s	s	NOUN
ejpam-4385	458	3	0	0	NUM
ejpam-4385	459	1	∂r	∂r	ADJ
ejpam-4385	459	2	ds	ds	NOUN
ejpam-4385	459	3	+	+	NUM
ejpam-4385	459	4	rxsp	rxsp	NOUN
ejpam-4385	459	5	s	s	PART
ejpam-4385	459	6	0	0	NUM
ejpam-4385	459	7	∂gµc	∂gµc	NOUN
ejpam-4385	459	8	∂x	∂x	PROPN
ejpam-4385	459	9	ds+	ds+	NOUN
ejpam-4385	459	10	1	1	NUM
ejpam-4385	459	11	2	2	NUM
ejpam-4385	459	12	σ2	σ2	NOUN
ejpam-4385	459	13	1x	1x	NUM
ejpam-4385	459	14	2	2	NUM
ejpam-4385	459	15	sp	sp	ADP
ejpam-4385	459	16	s	s	NOUN
ejpam-4385	459	17	0	0	NUM
ejpam-4385	459	18	∂2gµc	∂2gµc	NOUN
ejpam-4385	459	19	∂x2	∂x2	NOUN
ejpam-4385	459	20	ds	ds	ADJ
ejpam-4385	459	21	+	+	CCONJ
ejpam-4385	459	22	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	459	23	√	√	ADJ
ejpam-4385	459	24	rxs	rxs	ADJ
ejpam-4385	459	25	∂gµc	∂gµc	NOUN
ejpam-4385	459	26	∂x	∂x	PROPN
ejpam-4385	459	27	∂p	∂p	PROPN
ejpam-4385	459	28	s	s	NOUN
ejpam-4385	459	29	0	0	NUM
ejpam-4385	459	30	∂r	∂r	ADJ
ejpam-4385	459	31	ds+	ds+	NOUN
ejpam-4385	459	32	1	1	NUM
ejpam-4385	459	33	2	2	NUM
ejpam-4385	459	34	σ2	σ2	NOUN
ejpam-4385	459	35	2rg	2rg	NOUN
ejpam-4385	459	36	µc	µc	ADP
ejpam-4385	459	37	∂2p	∂2p	PROPN
ejpam-4385	459	38	s	s	PART
ejpam-4385	459	39	0	0	NUM
ejpam-4385	459	40	∂r2	∂r2	PROPN
ejpam-4385	459	41	ds	ds	PROPN
ejpam-4385	459	42	+	+	CCONJ
ejpam-4385	459	43	σ1xs	σ1xs	PRON
ejpam-4385	459	44	∂gµc	∂gµc	PRON
ejpam-4385	459	45	∂x	∂x	PROPN
ejpam-4385	459	46	dws	dws	PROPN
ejpam-4385	459	47	+	+	CCONJ
ejpam-4385	459	48	σ2	σ2	PROPN
ejpam-4385	459	49	√	√	NOUN
ejpam-4385	459	50	rgµc	rgµc	NOUN
ejpam-4385	459	51	∂p	∂p	PROPN
ejpam-4385	459	52	s	s	NOUN
ejpam-4385	459	53	0	0	NUM
ejpam-4385	459	54	∂r	∂r	PROPN
ejpam-4385	459	55	dws	dws	PROPN
ejpam-4385	459	56	.	.	PUNCT
ejpam-4385	460	1	(	(	PUNCT
ejpam-4385	460	2	52	52	NUM
ejpam-4385	460	3	)	)	PUNCT
ejpam-4385	460	4	integrating	integrate	VERB
ejpam-4385	460	5	both	both	DET
ejpam-4385	460	6	sides	side	NOUN
ejpam-4385	460	7	from	from	ADP
ejpam-4385	460	8	0	0	NUM
ejpam-4385	460	9	to	to	ADP
ejpam-4385	460	10	τ	τ	PROPN
ejpam-4385	460	11	:	:	PUNCT
ejpam-4385	460	12	p	p	X
ejpam-4385	460	13	(	(	PUNCT
ejpam-4385	460	14	t	t	PROPN
ejpam-4385	460	15	,	,	PUNCT
ejpam-4385	460	16	rt	rt	PROPN
ejpam-4385	460	17	;	;	PUNCT
ejpam-4385	460	18	t+	t+	NUM
ejpam-4385	460	19	s)gµc(t+	s)gµc(t+	PROPN
ejpam-4385	460	20	s	s	PROPN
ejpam-4385	460	21	,	,	PUNCT
ejpam-4385	460	22	xt+s	xt+s	PROPN
ejpam-4385	460	23	)	)	PUNCT
ejpam-4385	461	1	=	=	SYM
ejpam-4385	461	2	gµc(t	gµc(t	PROPN
ejpam-4385	461	3	,	,	PUNCT
ejpam-4385	461	4	xt	xt	X
ejpam-4385	461	5	)	)	PUNCT
ejpam-4385	462	1	+	+	CCONJ
ejpam-4385	462	2	∫	∫	PROPN
ejpam-4385	462	3	τ	τ	X
ejpam-4385	462	4	0	0	PUNCT
ejpam-4385	462	5	{	{	PUNCT
ejpam-4385	462	6	p	p	X
ejpam-4385	462	7	(	(	PUNCT
ejpam-4385	462	8	t	t	PROPN
ejpam-4385	462	9	,	,	PUNCT
ejpam-4385	462	10	rt	rt	PROPN
ejpam-4385	462	11	;	;	PUNCT
ejpam-4385	462	12	s	s	X
ejpam-4385	462	13	)	)	PUNCT
ejpam-4385	463	1	[	[	X
ejpam-4385	463	2	∂gµc	∂gµc	PRON
ejpam-4385	463	3	∂s	∂s	PROPN
ejpam-4385	463	4	+	+	NUM
ejpam-4385	463	5	rsxs	rsx	NOUN
ejpam-4385	463	6	∂gµc	∂gµc	NOUN
ejpam-4385	463	7	∂x	∂x	PROPN
ejpam-4385	463	8	+	+	CCONJ
ejpam-4385	463	9	1	1	NUM
ejpam-4385	463	10	2	2	NUM
ejpam-4385	463	11	σ2	σ2	NOUN
ejpam-4385	463	12	1x	1x	NUM
ejpam-4385	463	13	2	2	NUM
ejpam-4385	463	14	s	s	NOUN
ejpam-4385	463	15	∂2gµc	∂2gµc	NOUN
ejpam-4385	463	16	∂x2	∂x2	NOUN
ejpam-4385	463	17	]	]	X
ejpam-4385	464	1	+	+	CCONJ
ejpam-4385	464	2	1	1	NUM
ejpam-4385	464	3	p	p	NOUN
ejpam-4385	464	4	(	(	PUNCT
ejpam-4385	464	5	0	0	NUM
ejpam-4385	464	6	,	,	PUNCT
ejpam-4385	464	7	r0	r0	NOUN
ejpam-4385	464	8	;	;	PUNCT
ejpam-4385	464	9	t	t	PROPN
ejpam-4385	464	10	)	)	PUNCT
ejpam-4385	464	11	[	[	PUNCT
ejpam-4385	464	12	gµc(s	gµc(s	X
ejpam-4385	464	13	,	,	PUNCT
ejpam-4385	464	14	xs	xs	NOUN
ejpam-4385	464	15	)	)	PUNCT
ejpam-4385	465	1	∂p	∂p	PROPN
ejpam-4385	465	2	∂s	∂s	PROPN
ejpam-4385	466	1	+	+	PUNCT
ejpam-4385	467	1	[	[	X
ejpam-4385	467	2	aθ	aθ	INTJ
ejpam-4385	467	3	−	−	PROPN
ejpam-4385	467	4	(	(	PUNCT
ejpam-4385	467	5	a+	a+	PUNCT
ejpam-4385	467	6	λσ)rt+u]g	λσ)rt+u]g	PROPN
ejpam-4385	467	7	µc(s	µc(s	NUM
ejpam-4385	467	8	,	,	PUNCT
ejpam-4385	467	9	xs	xs	PROPN
ejpam-4385	467	10	)	)	PUNCT
ejpam-4385	468	1	∂p	∂p	PROPN
ejpam-4385	469	1	∂r	∂r	PROPN
ejpam-4385	470	1	+	+	CCONJ
ejpam-4385	470	2	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	470	3	√	√	ADJ
ejpam-4385	470	4	rsxs	rsx	NOUN
ejpam-4385	470	5	∂gµc	∂gµc	NOUN
ejpam-4385	470	6	∂x	∂x	PROPN
ejpam-4385	470	7	(	(	PUNCT
ejpam-4385	470	8	s	s	PROPN
ejpam-4385	470	9	,	,	PUNCT
ejpam-4385	470	10	xs	xs	PROPN
ejpam-4385	470	11	)	)	PUNCT
ejpam-4385	471	1	∂p	∂p	PROPN
ejpam-4385	472	1	∂r	∂r	PROPN
ejpam-4385	473	1	+	+	CCONJ
ejpam-4385	473	2	1	1	NUM
ejpam-4385	473	3	2	2	NUM
ejpam-4385	473	4	σ2	σ2	PROPN
ejpam-4385	473	5	2rsg	2rsg	PROPN
ejpam-4385	473	6	µc(s	µc(s	NUM
ejpam-4385	473	7	,	,	PUNCT
ejpam-4385	473	8	xs	xs	PROPN
ejpam-4385	473	9	)	)	PUNCT
ejpam-4385	473	10	∂2p	∂2p	VERB
ejpam-4385	473	11	∂r2	∂r2	PROPN
ejpam-4385	473	12	]	]	PUNCT
ejpam-4385	473	13	}	}	PUNCT
ejpam-4385	473	14	d	d	X
ejpam-4385	474	1	+	+	NUM
ejpam-4385	474	2	∫	∫	PROPN
ejpam-4385	474	3	τ	τ	PROPN
ejpam-4385	474	4	0	0	NUM
ejpam-4385	474	5	1	1	NUM
ejpam-4385	474	6	p	p	NOUN
ejpam-4385	474	7	(	(	PUNCT
ejpam-4385	474	8	0	0	NUM
ejpam-4385	474	9	,	,	PUNCT
ejpam-4385	474	10	r0	r0	NOUN
ejpam-4385	474	11	;	;	PUNCT
ejpam-4385	474	12	t	t	PROPN
ejpam-4385	474	13	)	)	PUNCT
ejpam-4385	474	14	[	[	PUNCT
ejpam-4385	474	15	σ1xs	σ1xs	NUM
ejpam-4385	474	16	∂gµc	∂gµc	X
ejpam-4385	474	17	∂x	∂x	PROPN
ejpam-4385	474	18	dwsσ2	dwsσ2	PROPN
ejpam-4385	474	19	√	√	VERB
ejpam-4385	474	20	rsg	rsg	PROPN
ejpam-4385	474	21	µc	µc	PROPN
ejpam-4385	474	22	∂p	∂p	PROPN
ejpam-4385	474	23	∂r	∂r	PROPN
ejpam-4385	474	24	dws	dws	PROPN
ejpam-4385	474	25	]	]	PUNCT
ejpam-4385	475	1	+	+	CCONJ
ejpam-4385	475	2	∫	∫	PROPN
ejpam-4385	475	3	τ	τ	X
ejpam-4385	475	4	0	0	NUM
ejpam-4385	475	5	1	1	NUM
ejpam-4385	475	6	p	p	NOUN
ejpam-4385	475	7	(	(	PUNCT
ejpam-4385	475	8	0	0	NUM
ejpam-4385	475	9	,	,	PUNCT
ejpam-4385	475	10	r0	r0	NOUN
ejpam-4385	475	11	;	;	PUNCT
ejpam-4385	475	12	t	t	PROPN
ejpam-4385	475	13	)	)	PUNCT
ejpam-4385	475	14	[	[	PUNCT
ejpam-4385	475	15	σ1xs	σ1xs	NUM
ejpam-4385	475	16	∂gµc	∂gµc	X
ejpam-4385	475	17	∂x	∂x	PROPN
ejpam-4385	475	18	dws	dws	PROPN
ejpam-4385	475	19	+	+	CCONJ
ejpam-4385	475	20	σ2	σ2	PROPN
ejpam-4385	475	21	√	√	PROPN
ejpam-4385	475	22	rsg	rsg	PROPN
ejpam-4385	475	23	µc	µc	ADP
ejpam-4385	475	24	∂p	∂p	PROPN
ejpam-4385	475	25	∂r	∂r	PROPN
ejpam-4385	475	26	dws	dws	PROPN
ejpam-4385	475	27	]	]	PUNCT
ejpam-4385	475	28	(	(	PUNCT
ejpam-4385	475	29	53	53	NUM
ejpam-4385	475	30	)	)	PUNCT
ejpam-4385	475	31	since	since	SCONJ
ejpam-4385	475	32	p	p	PROPN
ejpam-4385	475	33	(	(	PUNCT
ejpam-4385	475	34	t	t	PROPN
ejpam-4385	475	35	,	,	PUNCT
ejpam-4385	475	36	rt	rt	PROPN
ejpam-4385	475	37	;	;	PUNCT
ejpam-4385	475	38	t+	t+	X
ejpam-4385	475	39	τ)gµc(t+	τ)gµc(t+	ADV
ejpam-4385	475	40	τ	τ	PROPN
ejpam-4385	475	41	,	,	PUNCT
ejpam-4385	475	42	xt+τ	xt+τ	PROPN
ejpam-4385	475	43	)	)	PUNCT
ejpam-4385	475	44	is	be	AUX
ejpam-4385	475	45	a	a	DET
ejpam-4385	475	46	martingale	martingale	NOUN
ejpam-4385	475	47	,	,	PUNCT
ejpam-4385	475	48	we	we	PRON
ejpam-4385	475	49	have	have	VERB
ejpam-4385	475	50	p	p	PROPN
ejpam-4385	475	51	(	(	PUNCT
ejpam-4385	475	52	t	t	PROPN
ejpam-4385	475	53	,	,	PUNCT
ejpam-4385	475	54	rt	rt	PROPN
ejpam-4385	475	55	;	;	PUNCT
ejpam-4385	475	56	t+	t+	NOUN
ejpam-4385	475	57	u	u	NOUN
ejpam-4385	475	58	)	)	PUNCT
ejpam-4385	475	59	[	[	PUNCT
ejpam-4385	475	60	∂gµc	∂gµc	PRON
ejpam-4385	475	61	∂s	∂s	PROPN
ejpam-4385	475	62	+	+	NUM
ejpam-4385	475	63	rsxs	rsx	NOUN
ejpam-4385	475	64	∂gµc	∂gµc	NOUN
ejpam-4385	475	65	∂x	∂x	PROPN
ejpam-4385	476	1	+	+	CCONJ
ejpam-4385	476	2	1	1	NUM
ejpam-4385	476	3	2	2	NUM
ejpam-4385	476	4	σ2	σ2	NOUN
ejpam-4385	476	5	1x	1x	NUM
ejpam-4385	476	6	2∂	2∂	PROPN
ejpam-4385	477	1	2gµc	2gµc	NUM
ejpam-4385	477	2	∂x2	∂x2	NOUN
ejpam-4385	477	3	]	]	X
ejpam-4385	478	1	+	+	NUM
ejpam-4385	478	2	gµc	gµc	NOUN
ejpam-4385	478	3	p	p	NOUN
ejpam-4385	478	4	(	(	PUNCT
ejpam-4385	478	5	0	0	NUM
ejpam-4385	478	6	,	,	PUNCT
ejpam-4385	478	7	r0	r0	NOUN
ejpam-4385	478	8	;	;	PUNCT
ejpam-4385	478	9	t	t	X
ejpam-4385	478	10	)	)	PUNCT
ejpam-4385	479	1	∂p	∂p	PROPN
ejpam-4385	479	2	∂t	∂t	PROPN
ejpam-4385	480	1	+	+	PUNCT
ejpam-4385	480	2	[	[	X
ejpam-4385	480	3	aθ	aθ	INTJ
ejpam-4385	480	4	−	−	PROPN
ejpam-4385	480	5	(	(	PUNCT
ejpam-4385	480	6	a+	a+	X
ejpam-4385	480	7	λσ)r	λσ)r	PROPN
ejpam-4385	480	8	]	]	X
ejpam-4385	480	9	gµc	gµc	NOUN
ejpam-4385	480	10	p	p	NOUN
ejpam-4385	480	11	(	(	PUNCT
ejpam-4385	480	12	0	0	NUM
ejpam-4385	480	13	,	,	PUNCT
ejpam-4385	480	14	r0	r0	NOUN
ejpam-4385	480	15	;	;	PUNCT
ejpam-4385	480	16	t	t	X
ejpam-4385	480	17	)	)	PUNCT
ejpam-4385	480	18	∂p	∂p	PROPN
ejpam-4385	481	1	∂r	∂r	PROPN
ejpam-4385	482	1	+	+	CCONJ
ejpam-4385	482	2	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	482	3	√	√	ADJ
ejpam-4385	482	4	rsxs	rsx	NOUN
ejpam-4385	482	5	x	x	X
ejpam-4385	482	6	p	p	X
ejpam-4385	482	7	(	(	PUNCT
ejpam-4385	482	8	0	0	NUM
ejpam-4385	482	9	,	,	PUNCT
ejpam-4385	482	10	r0	r0	NOUN
ejpam-4385	482	11	;	;	PUNCT
ejpam-4385	482	12	t	t	PROPN
ejpam-4385	482	13	)	)	PUNCT
ejpam-4385	482	14	∂gµc	∂gµc	X
ejpam-4385	482	15	∂x	∂x	PROPN
ejpam-4385	482	16	∂p	∂p	PUNCT
ejpam-4385	483	1	∂r	∂r	PROPN
ejpam-4385	484	1	+	+	CCONJ
ejpam-4385	484	2	1	1	NUM
ejpam-4385	484	3	2	2	NUM
ejpam-4385	484	4	σ2	σ2	NOUN
ejpam-4385	484	5	2rs	2rs	ADJ
ejpam-4385	484	6	gµc	gµc	NOUN
ejpam-4385	484	7	p	p	NOUN
ejpam-4385	484	8	(	(	PUNCT
ejpam-4385	484	9	0	0	NUM
ejpam-4385	484	10	,	,	PUNCT
ejpam-4385	484	11	r0	r0	NOUN
ejpam-4385	484	12	;	;	PUNCT
ejpam-4385	484	13	t	t	PROPN
ejpam-4385	484	14	)	)	PUNCT
ejpam-4385	484	15	∂2p	∂2p	NOUN
ejpam-4385	484	16	∂r2	∂r2	NOUN
ejpam-4385	484	17	=	=	NOUN
ejpam-4385	484	18	0	0	X
ejpam-4385	484	19	.	.	PUNCT
ejpam-4385	485	1	since	since	SCONJ
ejpam-4385	485	2	the	the	DET
ejpam-4385	485	3	supremum	supremum	NOUN
ejpam-4385	485	4	in	in	ADP
ejpam-4385	485	5	(	(	PUNCT
ejpam-4385	485	6	19	19	NUM
ejpam-4385	485	7	)	)	PUNCT
ejpam-4385	485	8	is	be	AUX
ejpam-4385	485	9	taken	take	VERB
ejpam-4385	485	10	overall	overall	ADJ
ejpam-4385	485	11	stopping	stopping	NOUN
ejpam-4385	485	12	time	time	NOUN
ejpam-4385	485	13	τ	τ	X
ejpam-4385	485	14	∈	∈	PROPN
ejpam-4385	486	1	[	[	X
ejpam-4385	486	2	0	0	NUM
ejpam-4385	486	3	,	,	PUNCT
ejpam-4385	486	4	t	t	PROPN
ejpam-4385	486	5	−	−	PROPN
ejpam-4385	486	6	t	t	PROPN
ejpam-4385	486	7	]	]	PUNCT
ejpam-4385	486	8	,	,	PUNCT
ejpam-4385	486	9	we	we	PRON
ejpam-4385	486	10	have	have	VERB
ejpam-4385	486	11	lxv	lxv	NOUN
ejpam-4385	486	12	(	(	PUNCT
ejpam-4385	486	13	t	t	PROPN
ejpam-4385	486	14	,	,	PUNCT
ejpam-4385	486	15	rt	rt	PROPN
ejpam-4385	486	16	,	,	PUNCT
ejpam-4385	486	17	x	x	NOUN
ejpam-4385	486	18	)	)	PUNCT
ejpam-4385	486	19	=	=	PUNCT
ejpam-4385	487	1	[	[	PUNCT
ejpam-4385	487	2	∂v	∂v	PROPN
ejpam-4385	487	3	∂t	∂t	PROPN
ejpam-4385	487	4	+	+	CCONJ
ejpam-4385	487	5	1	1	NUM
ejpam-4385	487	6	2	2	NUM
ejpam-4385	487	7	σ2	σ2	NOUN
ejpam-4385	487	8	1x	1x	NUM
ejpam-4385	487	9	2	2	NUM
ejpam-4385	487	10	t	t	PROPN
ejpam-4385	487	11	∂2v	∂2v	X
ejpam-4385	487	12	∂x2	∂x2	PROPN
ejpam-4385	487	13	+	+	CCONJ
ejpam-4385	487	14	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	487	15	√	√	NUM
ejpam-4385	487	16	rtxt	rtxt	NOUN
ejpam-4385	487	17	∂2v	∂2v	NOUN
ejpam-4385	487	18	∂x∂r	∂x∂r	VERB
ejpam-4385	488	1	+	+	CCONJ
ejpam-4385	488	2	1	1	NUM
ejpam-4385	488	3	2	2	NUM
ejpam-4385	488	4	σ2rt	σ2rt	NOUN
ejpam-4385	488	5	∂2v	∂2v	VERB
ejpam-4385	488	6	∂r2	∂r2	PROPN
ejpam-4385	488	7	+	+	CCONJ
ejpam-4385	488	8	∂v	∂v	PROPN
ejpam-4385	488	9	∂x	∂x	PROPN
ejpam-4385	488	10	rtxt	rtxt	NOUN
ejpam-4385	488	11	−	−	PROPN
ejpam-4385	489	1	[	[	X
ejpam-4385	489	2	aθ	aθ	INTJ
ejpam-4385	489	3	−	−	PROPN
ejpam-4385	489	4	(	(	PUNCT
ejpam-4385	489	5	a+	a+	X
ejpam-4385	489	6	λσ)r	λσ)r	X
ejpam-4385	490	1	]	]	X
ejpam-4385	490	2	∂v	∂v	PROPN
ejpam-4385	491	1	∂r	∂r	X
ejpam-4385	491	2	]	]	X
ejpam-4385	491	3	v	v	X
ejpam-4385	491	4	(	(	PUNCT
ejpam-4385	491	5	t	t	PROPN
ejpam-4385	491	6	,	,	PUNCT
ejpam-4385	491	7	rt	rt	PROPN
ejpam-4385	491	8	,	,	PUNCT
ejpam-4385	491	9	x	x	NOUN
ejpam-4385	491	10	)	)	PUNCT
ejpam-4385	491	11	=	=	SYM
ejpam-4385	491	12	0	0	X
ejpam-4385	491	13	.	.	PUNCT
ejpam-4385	492	1	k.	k.	PROPN
ejpam-4385	492	2	falcasantos	falcasantos	PROPN
ejpam-4385	492	3	,	,	PUNCT
ejpam-4385	492	4	f.	f.	PROPN
ejpam-4385	492	5	sumalpong	sumalpong	PROPN
ejpam-4385	492	6	/	/	SYM
ejpam-4385	492	7	eur	eur	PROPN
ejpam-4385	492	8	.	.	PUNCT
ejpam-4385	493	1	j.	j.	PROPN
ejpam-4385	493	2	pure	pure	PROPN
ejpam-4385	493	3	appl	appl	PROPN
ejpam-4385	493	4	.	.	PROPN
ejpam-4385	493	5	math	math	PROPN
ejpam-4385	493	6	,	,	PUNCT
ejpam-4385	493	7	15	15	NUM
ejpam-4385	493	8	(	(	PUNCT
ejpam-4385	493	9	3	3	NUM
ejpam-4385	493	10	)	)	PUNCT
ejpam-4385	493	11	(	(	PUNCT
ejpam-4385	493	12	2022	2022	NUM
ejpam-4385	493	13	)	)	PUNCT
ejpam-4385	493	14	,	,	PUNCT
ejpam-4385	493	15	948	948	NUM
ejpam-4385	493	16	-	-	SYM
ejpam-4385	493	17	970	970	NUM
ejpam-4385	493	18	965	965	NUM
ejpam-4385	493	19	this	this	PRON
ejpam-4385	493	20	shows	show	VERB
ejpam-4385	493	21	that	that	SCONJ
ejpam-4385	493	22	there	there	PRON
ejpam-4385	493	23	is	be	VERB
ejpam-4385	493	24	a	a	DET
ejpam-4385	493	25	continuous	continuous	ADJ
ejpam-4385	493	26	(	(	PUNCT
ejpam-4385	493	27	smooth	smooth	ADJ
ejpam-4385	493	28	)	)	PUNCT
ejpam-4385	493	29	function	function	NOUN
ejpam-4385	493	30	h	h	NOUN
ejpam-4385	493	31	:	:	PUNCT
ejpam-4385	494	1	[	[	X
ejpam-4385	494	2	0	0	NUM
ejpam-4385	494	3	,	,	PUNCT
ejpam-4385	494	4	t	t	X
ejpam-4385	494	5	]	]	PUNCT
ejpam-4385	494	6	×r	×r	CCONJ
ejpam-4385	494	7	→	→	PUNCT
ejpam-4385	494	8	r+	r+	NOUN
ejpam-4385	494	9	such	such	ADJ
ejpam-4385	494	10	that	that	DET
ejpam-4385	494	11	lxp	lxp	NOUN
ejpam-4385	494	12	(	(	PUNCT
ejpam-4385	494	13	t	t	PROPN
ejpam-4385	494	14	,	,	PUNCT
ejpam-4385	494	15	rt	rt	PROPN
ejpam-4385	494	16	;	;	PUNCT
ejpam-4385	494	17	t+	t+	X
ejpam-4385	494	18	τ)gµc(t+	τ)gµc(t+	ADV
ejpam-4385	494	19	τ	τ	X
ejpam-4385	494	20	,	,	PUNCT
ejpam-4385	494	21	h(t	h(t	PROPN
ejpam-4385	494	22	,	,	PUNCT
ejpam-4385	494	23	rt)xτ	rt)xτ	NOUN
ejpam-4385	494	24	)	)	PUNCT
ejpam-4385	494	25	=	=	SYM
ejpam-4385	494	26	0	0	PUNCT
ejpam-4385	494	27	(	(	PUNCT
ejpam-4385	494	28	54	54	NUM
ejpam-4385	494	29	)	)	PUNCT
ejpam-4385	494	30	for	for	ADP
ejpam-4385	494	31	all	all	DET
ejpam-4385	494	32	t	t	NOUN
ejpam-4385	494	33	∈	∈	PROPN
ejpam-4385	495	1	[	[	X
ejpam-4385	495	2	0	0	NUM
ejpam-4385	495	3	,	,	PUNCT
ejpam-4385	495	4	t	t	X
ejpam-4385	495	5	]	]	PUNCT
ejpam-4385	495	6	.	.	PUNCT
ejpam-4385	496	1	linearity	linearity	NOUN
ejpam-4385	496	2	of	of	ADP
ejpam-4385	496	3	lxp	lxp	NOUN
ejpam-4385	496	4	(	(	PUNCT
ejpam-4385	496	5	t	t	PROPN
ejpam-4385	496	6	,	,	PUNCT
ejpam-4385	496	7	rt	rt	PROPN
ejpam-4385	496	8	;	;	PUNCT
ejpam-4385	496	9	t+	t+	X
ejpam-4385	496	10	τ)gµc(t+	τ)gµc(t+	ADV
ejpam-4385	496	11	τ	τ	PROPN
ejpam-4385	496	12	,	,	PUNCT
ejpam-4385	496	13	xt+τ	xt+τ	PROPN
ejpam-4385	496	14	)	)	PUNCT
ejpam-4385	496	15	in	in	ADP
ejpam-4385	496	16	terms	term	NOUN
ejpam-4385	496	17	of	of	ADP
ejpam-4385	496	18	xt+τ	xt+τ	PROPN
ejpam-4385	496	19	>	>	X
ejpam-4385	496	20	0	0	PUNCT
ejpam-4385	496	21	shows	show	VERB
ejpam-4385	496	22	that	that	SCONJ
ejpam-4385	496	23	lxp	lxp	NOUN
ejpam-4385	496	24	(	(	PUNCT
ejpam-4385	496	25	t	t	PROPN
ejpam-4385	496	26	,	,	PUNCT
ejpam-4385	496	27	rt	rt	PROPN
ejpam-4385	496	28	;	;	PUNCT
ejpam-4385	496	29	t	t	PROPN
ejpam-4385	496	30	+	+	CCONJ
ejpam-4385	496	31	τ)gµc(t	τ)gµc(t	PRON
ejpam-4385	496	32	+	+	CCONJ
ejpam-4385	496	33	τ	τ	PROPN
ejpam-4385	496	34	,	,	PUNCT
ejpam-4385	496	35	xt+τ	xt+τ	PROPN
ejpam-4385	496	36	)	)	PUNCT
ejpam-4385	496	37	>	>	X
ejpam-4385	496	38	0	0	PUNCT
ejpam-4385	497	1	when	when	SCONJ
ejpam-4385	497	2	xt+τ	xt+τ	PROPN
ejpam-4385	497	3	<	<	X
ejpam-4385	497	4	h(t	h(t	PROPN
ejpam-4385	497	5	+	+	CCONJ
ejpam-4385	497	6	τ	τ	PROPN
ejpam-4385	497	7	,	,	PUNCT
ejpam-4385	497	8	rt	rt	PROPN
ejpam-4385	497	9	)	)	PUNCT
ejpam-4385	497	10	and	and	CCONJ
ejpam-4385	497	11	lxp	lxp	NOUN
ejpam-4385	497	12	(	(	PUNCT
ejpam-4385	497	13	t	t	PROPN
ejpam-4385	497	14	,	,	PUNCT
ejpam-4385	497	15	rt	rt	PROPN
ejpam-4385	497	16	;	;	PUNCT
ejpam-4385	497	17	t	t	PROPN
ejpam-4385	497	18	+	+	CCONJ
ejpam-4385	497	19	τ)gµc(t+τ	τ)gµc(t+τ	PROPN
ejpam-4385	497	20	,	,	PUNCT
ejpam-4385	497	21	xt+τ	xt+τ	PROPN
ejpam-4385	497	22	)	)	PUNCT
ejpam-4385	497	23	<	<	X
ejpam-4385	497	24	0	0	PUNCT
ejpam-4385	497	25	when	when	SCONJ
ejpam-4385	497	26	xt+τ	xt+τ	PROPN
ejpam-4385	497	27	>	>	X
ejpam-4385	497	28	h(t+τ	h(t+τ	PROPN
ejpam-4385	497	29	,	,	PUNCT
ejpam-4385	497	30	rt	rt	PROPN
ejpam-4385	497	31	)	)	PUNCT
ejpam-4385	497	32	.	.	PUNCT
ejpam-4385	498	1	this	this	PRON
ejpam-4385	498	2	shows	show	VERB
ejpam-4385	498	3	in	in	ADP
ejpam-4385	498	4	particular	particular	ADJ
ejpam-4385	498	5	that	that	SCONJ
ejpam-4385	498	6	it	it	PRON
ejpam-4385	498	7	is	be	AUX
ejpam-4385	498	8	optimal	optimal	ADJ
ejpam-4385	498	9	to	to	PART
ejpam-4385	498	10	exercise	exercise	VERB
ejpam-4385	498	11	immediately	immediately	ADV
ejpam-4385	498	12	when	when	SCONJ
ejpam-4385	498	13	x	x	X
ejpam-4385	498	14	>	>	X
ejpam-4385	498	15	h(t	h(t	PROPN
ejpam-4385	498	16	,	,	PUNCT
ejpam-4385	498	17	rt	rt	PROPN
ejpam-4385	498	18	)	)	PUNCT
ejpam-4385	498	19	and	and	CCONJ
ejpam-4385	498	20	t	t	X
ejpam-4385	498	21	<	<	X
ejpam-4385	498	22	t	t	PROPN
ejpam-4385	498	23	is	be	AUX
ejpam-4385	498	24	sufficiently	sufficiently	ADV
ejpam-4385	498	25	close	close	ADJ
ejpam-4385	498	26	to	to	ADP
ejpam-4385	498	27	maturity	maturity	NOUN
ejpam-4385	498	28	t	t	NOUN
ejpam-4385	498	29	for	for	ADP
ejpam-4385	498	30	the	the	DET
ejpam-4385	498	31	same	same	ADJ
ejpam-4385	498	32	reason	reason	NOUN
ejpam-4385	498	33	mentioned	mention	VERB
ejpam-4385	498	34	in	in	ADP
ejpam-4385	498	35	[	[	X
ejpam-4385	498	36	10	10	NUM
ejpam-4385	498	37	]	]	PUNCT
ejpam-4385	498	38	.	.	PUNCT
ejpam-4385	499	1	from	from	ADP
ejpam-4385	499	2	here	here	ADV
ejpam-4385	499	3	,	,	PUNCT
ejpam-4385	499	4	we	we	PRON
ejpam-4385	499	5	define	define	VERB
ejpam-4385	499	6	the	the	DET
ejpam-4385	499	7	optimal	optimal	ADJ
ejpam-4385	499	8	stopping	stopping	NOUN
ejpam-4385	499	9	boundary	boundary	NOUN
ejpam-4385	499	10	(	(	PUNCT
ejpam-4385	499	11	the	the	DET
ejpam-4385	499	12	early	early	ADJ
ejpam-4385	499	13	-	-	PUNCT
ejpam-4385	499	14	exercise	exercise	NOUN
ejpam-4385	499	15	premium	premium	NOUN
ejpam-4385	499	16	representation	representation	NOUN
ejpam-4385	499	17	)	)	PUNCT
ejpam-4385	499	18	as	as	SCONJ
ejpam-4385	499	19	follows	follow	VERB
ejpam-4385	499	20	:	:	PUNCT
ejpam-4385	499	21	bd(t	bd(t	NUM
ejpam-4385	499	22	,	,	PUNCT
ejpam-4385	499	23	rt	rt	PROPN
ejpam-4385	499	24	)	)	PUNCT
ejpam-4385	499	25	=	=	SYM
ejpam-4385	499	26	sup	sup	NOUN
ejpam-4385	499	27	{	{	PUNCT
ejpam-4385	499	28	x	x	SYM
ejpam-4385	499	29	∈	∈	PROPN
ejpam-4385	499	30	(	(	PUNCT
ejpam-4385	499	31	0,∞	0,∞	NOUN
ejpam-4385	499	32	)	)	PUNCT
ejpam-4385	499	33	:	:	PUNCT
ejpam-4385	499	34	(	(	PUNCT
ejpam-4385	499	35	t	t	PROPN
ejpam-4385	499	36	,	,	PUNCT
ejpam-4385	499	37	rt	rt	PROPN
ejpam-4385	499	38	,	,	PUNCT
ejpam-4385	499	39	x	x	NOUN
ejpam-4385	499	40	)	)	PUNCT
ejpam-4385	499	41	∈	∈	PROPN
ejpam-4385	500	1	d	d	NOUN
ejpam-4385	500	2	}	}	PUNCT
ejpam-4385	500	3	.	.	PUNCT
ejpam-4385	501	1	the	the	DET
ejpam-4385	501	2	result	result	NOUN
ejpam-4385	501	3	below	below	ADV
ejpam-4385	501	4	characterizes	characterize	VERB
ejpam-4385	501	5	the	the	DET
ejpam-4385	501	6	stopping	stopping	NOUN
ejpam-4385	501	7	set	set	VERB
ejpam-4385	501	8	in	in	ADP
ejpam-4385	501	9	terms	term	NOUN
ejpam-4385	501	10	of	of	ADP
ejpam-4385	501	11	the	the	DET
ejpam-4385	501	12	boundary	boundary	ADJ
ejpam-4385	501	13	function	function	NOUN
ejpam-4385	501	14	bd(t	bd(t	PROPN
ejpam-4385	501	15	,	,	PUNCT
ejpam-4385	501	16	rt	rt	PROPN
ejpam-4385	501	17	)	)	PUNCT
ejpam-4385	501	18	.	.	PUNCT
ejpam-4385	502	1	proposition	proposition	NOUN
ejpam-4385	502	2	3	3	NUM
ejpam-4385	502	3	.	.	PUNCT
ejpam-4385	503	1	the	the	DET
ejpam-4385	503	2	boundary	boundary	ADJ
ejpam-4385	503	3	function	function	NOUN
ejpam-4385	503	4	bd(t	bd(t	PROPN
ejpam-4385	503	5	,	,	PUNCT
ejpam-4385	503	6	rt	rt	PROPN
ejpam-4385	503	7	)	)	PUNCT
ejpam-4385	503	8	is	be	AUX
ejpam-4385	503	9	continuous	continuous	ADJ
ejpam-4385	503	10	in	in	ADP
ejpam-4385	503	11	t	t	PROPN
ejpam-4385	503	12	∈	∈	PROPN
ejpam-4385	504	1	[	[	X
ejpam-4385	504	2	0	0	NUM
ejpam-4385	504	3	,	,	PUNCT
ejpam-4385	504	4	t	t	X
ejpam-4385	504	5	]	]	PUNCT
ejpam-4385	504	6	for	for	ADP
ejpam-4385	504	7	all	all	DET
ejpam-4385	504	8	rt	rt	PROPN
ejpam-4385	504	9	∈	∈	PROPN
ejpam-4385	504	10	r.	r.	NOUN
ejpam-4385	504	11	proof	proof	NOUN
ejpam-4385	504	12	.	.	PUNCT
ejpam-4385	505	1	let	let	VERB
ejpam-4385	505	2	rt	rt	PROPN
ejpam-4385	505	3	∈	∈	PROPN
ejpam-4385	505	4	r	r	NOUN
ejpam-4385	505	5	be	be	AUX
ejpam-4385	505	6	fixed	fix	VERB
ejpam-4385	505	7	.	.	PUNCT
ejpam-4385	506	1	we	we	PRON
ejpam-4385	506	2	first	first	ADV
ejpam-4385	506	3	show	show	VERB
ejpam-4385	506	4	the	the	DET
ejpam-4385	506	5	right	right	ADJ
ejpam-4385	506	6	continuity	continuity	NOUN
ejpam-4385	506	7	.	.	PUNCT
ejpam-4385	507	1	suppose	suppose	VERB
ejpam-4385	507	2	that	that	SCONJ
ejpam-4385	507	3	bd(t	bd(t	PROPN
ejpam-4385	507	4	,	,	PUNCT
ejpam-4385	507	5	rt	rt	PROPN
ejpam-4385	507	6	)	)	PUNCT
ejpam-4385	507	7	is	be	AUX
ejpam-4385	507	8	not	not	PART
ejpam-4385	507	9	continuous	continuous	ADJ
ejpam-4385	507	10	at	at	ADP
ejpam-4385	507	11	t	t	PROPN
ejpam-4385	507	12	=	=	SYM
ejpam-4385	507	13	t0	t0	PROPN
ejpam-4385	507	14	.	.	PUNCT
ejpam-4385	508	1	we	we	PRON
ejpam-4385	508	2	consider	consider	VERB
ejpam-4385	508	3	two	two	NUM
ejpam-4385	508	4	cases	case	NOUN
ejpam-4385	508	5	:	:	PUNCT
ejpam-4385	508	6	case	case	NOUN
ejpam-4385	508	7	1	1	NUM
ejpam-4385	508	8	:	:	PUNCT
ejpam-4385	508	9	bd(t0	bd(t0	NOUN
ejpam-4385	508	10	,	,	PUNCT
ejpam-4385	508	11	rt0	rt0	VERB
ejpam-4385	508	12	)	)	PUNCT
ejpam-4385	508	13	<	<	X
ejpam-4385	508	14	bd(t0	bd(t0	PROPN
ejpam-4385	508	15	+	+	X
ejpam-4385	508	16	,	,	PUNCT
ejpam-4385	508	17	rt0	rt0	VERB
ejpam-4385	508	18	+	+	CCONJ
ejpam-4385	508	19	)	)	PUNCT
ejpam-4385	508	20	let	let	VERB
ejpam-4385	508	21	(	(	PUNCT
ejpam-4385	508	22	t′	t′	NUM
ejpam-4385	508	23	,	,	PUNCT
ejpam-4385	508	24	rt.x	rt.x	NOUN
ejpam-4385	508	25	′	′	NOUN
ejpam-4385	508	26	)	)	PUNCT
ejpam-4385	508	27	∈	∈	PROPN
ejpam-4385	508	28	(	(	PUNCT
ejpam-4385	508	29	t0	t0	PROPN
ejpam-4385	508	30	,	,	PUNCT
ejpam-4385	508	31	t	t	PROPN
ejpam-4385	508	32	)	)	PUNCT
ejpam-4385	508	33	×	×	NOUN
ejpam-4385	508	34	r	r	NOUN
ejpam-4385	508	35	×	×	NOUN
ejpam-4385	508	36	(	(	PUNCT
ejpam-4385	508	37	bd(t0	bd(t0	NOUN
ejpam-4385	508	38	,	,	PUNCT
ejpam-4385	508	39	rt0	rt0	VERB
ejpam-4385	508	40	)	)	PUNCT
ejpam-4385	508	41	,	,	PUNCT
ejpam-4385	508	42	bd(t0	bd(t0	PROPN
ejpam-4385	508	43	+	+	CCONJ
ejpam-4385	508	44	,	,	PUNCT
ejpam-4385	508	45	rt0	rt0	VERB
ejpam-4385	508	46	+	+	CCONJ
ejpam-4385	508	47	)	)	PUNCT
ejpam-4385	508	48	)	)	PUNCT
ejpam-4385	508	49	be	be	AUX
ejpam-4385	508	50	a	a	DET
ejpam-4385	508	51	point	point	NOUN
ejpam-4385	508	52	in	in	ADP
ejpam-4385	508	53	the	the	DET
ejpam-4385	508	54	stopping	stopping	NOUN
ejpam-4385	508	55	set	set	VERB
ejpam-4385	508	56	d	d	NOUN
ejpam-4385	508	57	with	with	ADP
ejpam-4385	508	58	t′	t′	NOUN
ejpam-4385	508	59	close	close	ADJ
ejpam-4385	508	60	to	to	ADP
ejpam-4385	508	61	t0	t0	PROPN
ejpam-4385	508	62	and	and	CCONJ
ejpam-4385	508	63	t′	t′	NUM
ejpam-4385	508	64	↓	↓	PROPN
ejpam-4385	508	65	t0	t0	PROPN
ejpam-4385	508	66	.	.	PUNCT
ejpam-4385	509	1	by	by	ADP
ejpam-4385	509	2	newton	newton	PROPN
ejpam-4385	509	3	-	-	PUNCT
ejpam-4385	509	4	leibniz	leibniz	PROPN
ejpam-4385	509	5	formula	formula	NOUN
ejpam-4385	509	6	and	and	CCONJ
ejpam-4385	509	7	lemma	lemma	PROPN
ejpam-4385	509	8	3	3	NUM
ejpam-4385	509	9	we	we	PRON
ejpam-4385	509	10	have	have	VERB
ejpam-4385	509	11	0	0	NUM
ejpam-4385	509	12	<	<	X
ejpam-4385	509	13	∫	∫	PROPN
ejpam-4385	509	14	x′	x′	PROPN
ejpam-4385	509	15	bd(t0,rt	bd(t0,rt	PROPN
ejpam-4385	509	16	)	)	PUNCT
ejpam-4385	510	1	[	[	X
ejpam-4385	510	2	vx(t	vx(t	NOUN
ejpam-4385	510	3	′	′	NUM
ejpam-4385	510	4	,	,	PUNCT
ejpam-4385	510	5	rt	rt	PROPN
ejpam-4385	510	6	,	,	PUNCT
ejpam-4385	510	7	u)−gµc	u)−gµc	X
ejpam-4385	510	8	x	x	SYM
ejpam-4385	510	9	(	(	PUNCT
ejpam-4385	510	10	t′u)]du	t′u)]du	NOUN
ejpam-4385	510	11	=	=	SYM
ejpam-4385	510	12	v	v	NOUN
ejpam-4385	510	13	(	(	PUNCT
ejpam-4385	510	14	t′	t′	NUM
ejpam-4385	510	15	,	,	PUNCT
ejpam-4385	510	16	rt	rt	PROPN
ejpam-4385	510	17	,	,	PUNCT
ejpam-4385	510	18	x	x	PROPN
ejpam-4385	510	19	′)−gµc(t′	′)−gµc(t′	PROPN
ejpam-4385	510	20	,	,	PUNCT
ejpam-4385	510	21	x′	x′	NUM
ejpam-4385	510	22	)	)	PUNCT
ejpam-4385	510	23	as	as	ADP
ejpam-4385	510	24	t′	t′	NUM
ejpam-4385	510	25	→	→	SYM
ejpam-4385	510	26	t0	t0	PROPN
ejpam-4385	510	27	.	.	PUNCT
ejpam-4385	511	1	this	this	PRON
ejpam-4385	511	2	implies	imply	VERB
ejpam-4385	511	3	that	that	SCONJ
ejpam-4385	511	4	v	v	X
ejpam-4385	511	5	(	(	PUNCT
ejpam-4385	511	6	t0	t0	PROPN
ejpam-4385	511	7	,	,	PUNCT
ejpam-4385	511	8	rt	rt	PROPN
ejpam-4385	511	9	,	,	PUNCT
ejpam-4385	511	10	x	x	NOUN
ejpam-4385	511	11	′	′	NUM
ejpam-4385	511	12	)	)	PUNCT
ejpam-4385	511	13	−	−	PROPN
ejpam-4385	512	1	gµc(t0	gµc(t0	NOUN
ejpam-4385	512	2	,	,	PUNCT
ejpam-4385	512	3	x	x	NOUN
ejpam-4385	512	4	′	′	NUM
ejpam-4385	512	5	)	)	PUNCT
ejpam-4385	512	6	>	>	X
ejpam-4385	512	7	0	0	NUM
ejpam-4385	512	8	,	,	PUNCT
ejpam-4385	512	9	i.e.	i.e.	X
ejpam-4385	512	10	,	,	PUNCT
ejpam-4385	512	11	(	(	PUNCT
ejpam-4385	512	12	t0	t0	PROPN
ejpam-4385	512	13	,	,	PUNCT
ejpam-4385	512	14	rt	rt	PROPN
ejpam-4385	512	15	,	,	PUNCT
ejpam-4385	512	16	x	x	NOUN
ejpam-4385	512	17	′	′	X
ejpam-4385	512	18	)	)	PUNCT
ejpam-4385	512	19	∈	∈	PROPN
ejpam-4385	512	20	d	d	NOUN
ejpam-4385	512	21	,	,	PUNCT
ejpam-4385	512	22	which	which	PRON
ejpam-4385	512	23	contradicts	contradict	VERB
ejpam-4385	512	24	the	the	DET
ejpam-4385	512	25	fact	fact	NOUN
ejpam-4385	512	26	that	that	SCONJ
ejpam-4385	512	27	x′	x′	PROPN
ejpam-4385	512	28	>	>	X
ejpam-4385	512	29	bd(t0	bd(t0	PROPN
ejpam-4385	512	30	,	,	PUNCT
ejpam-4385	512	31	rt	rt	PROPN
ejpam-4385	512	32	)	)	PUNCT
ejpam-4385	512	33	,	,	PUNCT
ejpam-4385	512	34	i.e.	i.e.	X
ejpam-4385	512	35	,	,	PUNCT
ejpam-4385	512	36	(	(	PUNCT
ejpam-4385	512	37	t0	t0	PROPN
ejpam-4385	512	38	,	,	PUNCT
ejpam-4385	512	39	rt	rt	PROPN
ejpam-4385	512	40	,	,	PUNCT
ejpam-4385	512	41	x	x	NOUN
ejpam-4385	512	42	′	′	X
ejpam-4385	512	43	)	)	PUNCT
ejpam-4385	512	44	∈	∈	PROPN
ejpam-4385	512	45	c.	c.	PROPN
ejpam-4385	512	46	case	case	NOUN
ejpam-4385	512	47	2	2	NUM
ejpam-4385	512	48	:	:	PUNCT
ejpam-4385	512	49	bd(t0	bd(t0	NOUN
ejpam-4385	512	50	,	,	PUNCT
ejpam-4385	512	51	rt0	rt0	VERB
ejpam-4385	512	52	)	)	PUNCT
ejpam-4385	512	53	>	>	PUNCT
ejpam-4385	512	54	bd(t0	bd(t0	PROPN
ejpam-4385	513	1	+	+	CCONJ
ejpam-4385	513	2	,	,	PUNCT
ejpam-4385	513	3	rt0	rt0	VERB
ejpam-4385	513	4	+	+	CCONJ
ejpam-4385	513	5	)	)	PUNCT
ejpam-4385	513	6	let	let	VERB
ejpam-4385	513	7	(	(	PUNCT
ejpam-4385	513	8	t∗	t∗	NOUN
ejpam-4385	513	9	,	,	PUNCT
ejpam-4385	513	10	rt.x∗	rt.x∗	NUM
ejpam-4385	513	11	)	)	PUNCT
ejpam-4385	513	12	∈	∈	PROPN
ejpam-4385	513	13	(	(	PUNCT
ejpam-4385	513	14	t0	t0	PROPN
ejpam-4385	513	15	,	,	PUNCT
ejpam-4385	513	16	t	t	NOUN
ejpam-4385	513	17	)	)	PUNCT
ejpam-4385	513	18	×r×	×r×	PUNCT
ejpam-4385	513	19	(	(	PUNCT
ejpam-4385	513	20	bd(t0	bd(t0	NOUN
ejpam-4385	513	21	,	,	PUNCT
ejpam-4385	513	22	rt0	rt0	VERB
ejpam-4385	513	23	)	)	PUNCT
ejpam-4385	513	24	,	,	PUNCT
ejpam-4385	513	25	bd(t0	bd(t0	PROPN
ejpam-4385	513	26	+	+	CCONJ
ejpam-4385	513	27	,	,	PUNCT
ejpam-4385	513	28	rt0	rt0	VERB
ejpam-4385	513	29	+	+	CCONJ
ejpam-4385	513	30	)	)	PUNCT
ejpam-4385	513	31	)	)	PUNCT
ejpam-4385	513	32	be	be	AUX
ejpam-4385	513	33	a	a	DET
ejpam-4385	513	34	point	point	NOUN
ejpam-4385	513	35	in	in	ADP
ejpam-4385	513	36	the	the	DET
ejpam-4385	513	37	continuation	continuation	NOUN
ejpam-4385	513	38	set	set	VERB
ejpam-4385	513	39	d	d	PROPN
ejpam-4385	513	40	with	with	ADP
ejpam-4385	513	41	t∗	t∗	NOUN
ejpam-4385	513	42	close	close	ADJ
ejpam-4385	513	43	to	to	ADP
ejpam-4385	513	44	t0	t0	PROPN
ejpam-4385	513	45	and	and	CCONJ
ejpam-4385	513	46	t∗	t∗	PROPN
ejpam-4385	513	47	↓	↓	PROPN
ejpam-4385	513	48	t0	t0	PROPN
ejpam-4385	513	49	.	.	PUNCT
ejpam-4385	514	1	by	by	ADP
ejpam-4385	514	2	newton	newton	PROPN
ejpam-4385	514	3	-	-	PUNCT
ejpam-4385	514	4	leibniz	leibniz	PROPN
ejpam-4385	514	5	formula	formula	NOUN
ejpam-4385	514	6	and	and	CCONJ
ejpam-4385	514	7	lemma	lemma	PROPN
ejpam-4385	514	8	3	3	NUM
ejpam-4385	514	9	we	we	PRON
ejpam-4385	514	10	have	have	VERB
ejpam-4385	514	11	0	0	NUM
ejpam-4385	514	12	<	<	X
ejpam-4385	514	13	∫	∫	PROPN
ejpam-4385	514	14	bd(t0,rt	bd(t0,rt	NOUN
ejpam-4385	514	15	)	)	PUNCT
ejpam-4385	514	16	x∗	x∗	PROPN
ejpam-4385	515	1	[	[	X
ejpam-4385	515	2	vx(t∗	vx(t∗	NOUN
ejpam-4385	515	3	,	,	PUNCT
ejpam-4385	515	4	rt	rt	PROPN
ejpam-4385	515	5	,	,	PUNCT
ejpam-4385	515	6	u)−gµc	u)−gµc	X
ejpam-4385	515	7	x	x	SYM
ejpam-4385	515	8	(	(	PUNCT
ejpam-4385	515	9	t∗	t∗	NOUN
ejpam-4385	515	10	,	,	PUNCT
ejpam-4385	515	11	u)]du	u)]du	NOUN
ejpam-4385	515	12	=	=	PUNCT
ejpam-4385	515	13	gµc(t∗	gµc(t∗	NOUN
ejpam-4385	515	14	,	,	PUNCT
ejpam-4385	515	15	x∗)−	x∗)−	PROPN
ejpam-4385	515	16	v	v	X
ejpam-4385	515	17	(	(	PUNCT
ejpam-4385	515	18	t∗	t∗	PROPN
ejpam-4385	515	19	,	,	PUNCT
ejpam-4385	515	20	rt	rt	PROPN
ejpam-4385	515	21	,	,	PUNCT
ejpam-4385	515	22	x∗	x∗	PROPN
ejpam-4385	515	23	)	)	PUNCT
ejpam-4385	515	24	as	as	ADP
ejpam-4385	515	25	t∗	t∗	NOUN
ejpam-4385	515	26	→	→	SYM
ejpam-4385	515	27	t0	t0	PROPN
ejpam-4385	515	28	.	.	PUNCT
ejpam-4385	516	1	this	this	PRON
ejpam-4385	516	2	implies	imply	VERB
ejpam-4385	516	3	that	that	SCONJ
ejpam-4385	516	4	v	v	X
ejpam-4385	516	5	(	(	PUNCT
ejpam-4385	516	6	t0	t0	PROPN
ejpam-4385	516	7	,	,	PUNCT
ejpam-4385	516	8	rt	rt	PROPN
ejpam-4385	516	9	,	,	PUNCT
ejpam-4385	516	10	x∗	x∗	PROPN
ejpam-4385	516	11	)	)	PUNCT
ejpam-4385	516	12	>	>	X
ejpam-4385	517	1	gµc(t0	gµc(t0	PROPN
ejpam-4385	517	2	,	,	PUNCT
ejpam-4385	517	3	x	x	NOUN
ejpam-4385	517	4	′	′	NUM
ejpam-4385	517	5	)	)	PUNCT
ejpam-4385	517	6	>	>	X
ejpam-4385	517	7	0	0	NUM
ejpam-4385	517	8	,	,	PUNCT
ejpam-4385	517	9	i.e.	i.e.	X
ejpam-4385	517	10	,	,	PUNCT
ejpam-4385	517	11	(	(	PUNCT
ejpam-4385	517	12	t0	t0	PROPN
ejpam-4385	517	13	,	,	PUNCT
ejpam-4385	517	14	rt	rt	PROPN
ejpam-4385	517	15	,	,	PUNCT
ejpam-4385	517	16	x	x	NOUN
ejpam-4385	517	17	′	′	X
ejpam-4385	517	18	)	)	PUNCT
ejpam-4385	517	19	∈	∈	PROPN
ejpam-4385	517	20	d	d	NOUN
ejpam-4385	517	21	,	,	PUNCT
ejpam-4385	517	22	which	which	PRON
ejpam-4385	517	23	contradicts	contradict	VERB
ejpam-4385	517	24	the	the	DET
ejpam-4385	517	25	fact	fact	NOUN
ejpam-4385	517	26	that	that	SCONJ
ejpam-4385	517	27	(	(	PUNCT
ejpam-4385	517	28	t0	t0	PROPN
ejpam-4385	517	29	,	,	PUNCT
ejpam-4385	517	30	rt	rt	PROPN
ejpam-4385	517	31	,	,	PUNCT
ejpam-4385	517	32	x∗	x∗	PROPN
ejpam-4385	517	33	)	)	PUNCT
ejpam-4385	517	34	∈	∈	PROPN
ejpam-4385	517	35	d.	d.	PROPN
ejpam-4385	517	36	k.	k.	PROPN
ejpam-4385	517	37	falcasantos	falcasantos	PROPN
ejpam-4385	517	38	,	,	PUNCT
ejpam-4385	517	39	f.	f.	PROPN
ejpam-4385	517	40	sumalpong	sumalpong	PROPN
ejpam-4385	517	41	/	/	SYM
ejpam-4385	517	42	eur	eur	PROPN
ejpam-4385	517	43	.	.	PUNCT
ejpam-4385	518	1	j.	j.	PROPN
ejpam-4385	518	2	pure	pure	PROPN
ejpam-4385	518	3	appl	appl	PROPN
ejpam-4385	518	4	.	.	PROPN
ejpam-4385	518	5	math	math	PROPN
ejpam-4385	518	6	,	,	PUNCT
ejpam-4385	518	7	15	15	NUM
ejpam-4385	518	8	(	(	PUNCT
ejpam-4385	518	9	3	3	NUM
ejpam-4385	518	10	)	)	PUNCT
ejpam-4385	518	11	(	(	PUNCT
ejpam-4385	518	12	2022	2022	NUM
ejpam-4385	518	13	)	)	PUNCT
ejpam-4385	518	14	,	,	PUNCT
ejpam-4385	518	15	948	948	NUM
ejpam-4385	518	16	-	-	SYM
ejpam-4385	518	17	970	970	NUM
ejpam-4385	518	18	966	966	NUM
ejpam-4385	518	19	7	7	NUM
ejpam-4385	518	20	.	.	PUNCT
ejpam-4385	519	1	the	the	DET
ejpam-4385	519	2	arbitrage	arbitrage	NOUN
ejpam-4385	519	3	-	-	PUNCT
ejpam-4385	519	4	free	free	ADJ
ejpam-4385	519	5	price	price	NOUN
ejpam-4385	519	6	and	and	CCONJ
ejpam-4385	519	7	the	the	DET
ejpam-4385	519	8	rational	rational	ADJ
ejpam-4385	519	9	exercise	exercise	NOUN
ejpam-4385	519	10	boundary	boundary	ADJ
ejpam-4385	519	11	in	in	ADP
ejpam-4385	519	12	this	this	DET
ejpam-4385	519	13	section	section	NOUN
ejpam-4385	519	14	,	,	PUNCT
ejpam-4385	519	15	we	we	PRON
ejpam-4385	519	16	present	present	VERB
ejpam-4385	519	17	the	the	DET
ejpam-4385	519	18	main	main	ADJ
ejpam-4385	519	19	result	result	NOUN
ejpam-4385	519	20	which	which	PRON
ejpam-4385	519	21	is	be	AUX
ejpam-4385	519	22	a	a	DET
ejpam-4385	519	23	derivation	derivation	NOUN
ejpam-4385	519	24	of	of	ADP
ejpam-4385	519	25	the	the	DET
ejpam-4385	519	26	closed	closed	ADJ
ejpam-4385	519	27	form	form	NOUN
ejpam-4385	519	28	expression	expression	NOUN
ejpam-4385	519	29	for	for	ADP
ejpam-4385	519	30	the	the	DET
ejpam-4385	519	31	arbitrage	arbitrage	NOUN
ejpam-4385	519	32	-	-	PUNCT
ejpam-4385	519	33	free	free	ADJ
ejpam-4385	519	34	price	price	NOUN
ejpam-4385	519	35	v	v	NOUN
ejpam-4385	519	36	(	(	PUNCT
ejpam-4385	519	37	t	t	PROPN
ejpam-4385	519	38	,	,	PUNCT
ejpam-4385	519	39	rt	rt	PROPN
ejpam-4385	519	40	,	,	PUNCT
ejpam-4385	519	41	x	x	NOUN
ejpam-4385	519	42	)	)	PUNCT
ejpam-4385	519	43	of	of	ADP
ejpam-4385	519	44	the	the	DET
ejpam-4385	519	45	british	british	ADJ
ejpam-4385	519	46	call	call	NOUN
ejpam-4385	519	47	option	option	NOUN
ejpam-4385	519	48	in	in	ADP
ejpam-4385	519	49	terms	term	NOUN
ejpam-4385	519	50	of	of	ADP
ejpam-4385	519	51	the	the	DET
ejpam-4385	519	52	early	early	ADJ
ejpam-4385	519	53	-	-	PUNCT
ejpam-4385	519	54	exercise	exercise	NOUN
ejpam-4385	519	55	premium	premium	NOUN
ejpam-4385	519	56	over	over	ADP
ejpam-4385	519	57	the	the	DET
ejpam-4385	519	58	european	european	ADJ
ejpam-4385	519	59	option	option	NOUN
ejpam-4385	519	60	counterpart	counterpart	NOUN
ejpam-4385	519	61	.	.	PUNCT
ejpam-4385	520	1	first	first	ADV
ejpam-4385	520	2	,	,	PUNCT
ejpam-4385	520	3	we	we	PRON
ejpam-4385	520	4	introduce	introduce	VERB
ejpam-4385	520	5	the	the	DET
ejpam-4385	520	6	following	follow	VERB
ejpam-4385	520	7	functions	function	NOUN
ejpam-4385	520	8	:	:	PUNCT
ejpam-4385	520	9	f	f	PROPN
ejpam-4385	520	10	(	(	PUNCT
ejpam-4385	520	11	t	t	PROPN
ejpam-4385	520	12	,	,	PUNCT
ejpam-4385	520	13	rt	rt	PROPN
ejpam-4385	520	14	,	,	PUNCT
ejpam-4385	520	15	x	x	NOUN
ejpam-4385	520	16	)	)	PUNCT
ejpam-4385	520	17	:	:	PUNCT
ejpam-4385	521	1	=	=	SYM
ejpam-4385	521	2	gµc(t	gµc(t	PROPN
ejpam-4385	521	3	,	,	PUNCT
ejpam-4385	521	4	x)−	x)−	PROPN
ejpam-4385	521	5	p	p	X
ejpam-4385	521	6	(	(	PUNCT
ejpam-4385	521	7	t	t	PROPN
ejpam-4385	521	8	,	,	PUNCT
ejpam-4385	521	9	rt;t	rt;t	PROPN
ejpam-4385	521	10	)	)	PUNCT
ejpam-4385	521	11	g	g	PROPN
ejpam-4385	521	12	rt(t	rt(t	NOUN
ejpam-4385	521	13	,	,	PUNCT
ejpam-4385	521	14	x	x	X
ejpam-4385	521	15	)	)	PUNCT
ejpam-4385	521	16	(	(	PUNCT
ejpam-4385	521	17	55	55	NUM
ejpam-4385	521	18	)	)	PUNCT
ejpam-4385	521	19	j(t	j(t	PROPN
ejpam-4385	521	20	,	,	PUNCT
ejpam-4385	521	21	rr	rr	NOUN
ejpam-4385	521	22	,	,	PUNCT
ejpam-4385	521	23	x	x	PROPN
ejpam-4385	521	24	,	,	PUNCT
ejpam-4385	521	25	v	v	NOUN
ejpam-4385	521	26	,	,	PUNCT
ejpam-4385	521	27	z	z	NOUN
ejpam-4385	521	28	)	)	PUNCT
ejpam-4385	521	29	:	:	PUNCT
ejpam-4385	521	30	=	=	PUNCT
ejpam-4385	522	1	−	−	PROPN
ejpam-4385	522	2	∫	∫	PROPN
ejpam-4385	522	3	∞	∞	PROPN
ejpam-4385	522	4	z	z	PROPN
ejpam-4385	522	5	l[p	l[p	PROPN
ejpam-4385	522	6	(	(	PUNCT
ejpam-4385	522	7	t	t	PROPN
ejpam-4385	522	8	,	,	PUNCT
ejpam-4385	522	9	rt	rt	PROPN
ejpam-4385	522	10	;	;	PUNCT
ejpam-4385	522	11	v)g	v)g	NOUN
ejpam-4385	522	12	µc(v	µc(v	NOUN
ejpam-4385	522	13	,	,	PUNCT
ejpam-4385	522	14	y)]f(v	y)]f(v	ADP
ejpam-4385	522	15	−	−	PROPN
ejpam-4385	522	16	t	t	PROPN
ejpam-4385	522	17	,	,	PUNCT
ejpam-4385	522	18	x	x	X
ejpam-4385	522	19	,	,	PUNCT
ejpam-4385	522	20	y)dy	y)dy	PROPN
ejpam-4385	522	21	(	(	PUNCT
ejpam-4385	522	22	56	56	NUM
ejpam-4385	522	23	)	)	PUNCT
ejpam-4385	522	24	for	for	ADP
ejpam-4385	522	25	t	t	PROPN
ejpam-4385	522	26	∈	∈	PROPN
ejpam-4385	523	1	[	[	X
ejpam-4385	523	2	0	0	NUM
ejpam-4385	523	3	,	,	PUNCT
ejpam-4385	523	4	t	t	X
ejpam-4385	523	5	]	]	PUNCT
ejpam-4385	523	6	,	,	PUNCT
ejpam-4385	523	7	x	x	X
ejpam-4385	523	8	>	>	X
ejpam-4385	523	9	0	0	NUM
ejpam-4385	523	10	,	,	PUNCT
ejpam-4385	523	11	v	v	NOUN
ejpam-4385	523	12	∈	∈	PROPN
ejpam-4385	523	13	[	[	X
ejpam-4385	523	14	t	t	PROPN
ejpam-4385	523	15	,	,	PUNCT
ejpam-4385	523	16	t	t	X
ejpam-4385	523	17	]	]	PUNCT
ejpam-4385	523	18	and	and	CCONJ
ejpam-4385	523	19	z	z	X
ejpam-4385	523	20	>	>	X
ejpam-4385	523	21	0	0	NUM
ejpam-4385	523	22	,	,	PUNCT
ejpam-4385	523	23	where	where	SCONJ
ejpam-4385	523	24	y	y	PROPN
ejpam-4385	523	25	7→	7→	PROPN
ejpam-4385	523	26	f(v	f(v	VERB
ejpam-4385	523	27	−	−	PROPN
ejpam-4385	523	28	t	t	PROPN
ejpam-4385	523	29	,	,	PUNCT
ejpam-4385	523	30	rt	rt	PROPN
ejpam-4385	523	31	,	,	PUNCT
ejpam-4385	523	32	x	x	PROPN
ejpam-4385	523	33	,	,	PUNCT
ejpam-4385	523	34	y	y	PROPN
ejpam-4385	523	35	)	)	PUNCT
ejpam-4385	523	36	is	be	AUX
ejpam-4385	523	37	the	the	DET
ejpam-4385	523	38	probability	probability	NOUN
ejpam-4385	523	39	density	density	NOUN
ejpam-4385	523	40	function	function	NOUN
ejpam-4385	523	41	of	of	ADP
ejpam-4385	523	42	xzrt	xzrt	PROPN
ejpam-4385	523	43	v−t	v−t	PROPN
ejpam-4385	523	44	(	(	PUNCT
ejpam-4385	523	45	see	see	VERB
ejpam-4385	523	46	[	[	X
ejpam-4385	523	47	3	3	NUM
ejpam-4385	523	48	]	]	PUNCT
ejpam-4385	523	49	,	,	PUNCT
ejpam-4385	523	50	[	[	X
ejpam-4385	523	51	13	13	NUM
ejpam-4385	523	52	]	]	PUNCT
ejpam-4385	523	53	)	)	PUNCT
ejpam-4385	523	54	given	give	VERB
ejpam-4385	523	55	by	by	ADP
ejpam-4385	523	56	f(v	f(v	PROPN
ejpam-4385	523	57	−	−	PROPN
ejpam-4385	523	58	t	t	PROPN
ejpam-4385	523	59	,	,	PUNCT
ejpam-4385	523	60	x	x	NOUN
ejpam-4385	523	61	,	,	PUNCT
ejpam-4385	523	62	y	y	NOUN
ejpam-4385	523	63	)	)	PUNCT
ejpam-4385	523	64	=	=	SYM
ejpam-4385	523	65	2a	2a	NUM
ejpam-4385	523	66	σ2	σ2	NOUN
ejpam-4385	523	67	(	(	PUNCT
ejpam-4385	523	68	1−	1−	NUM
ejpam-4385	523	69	e−a(v−t	e−a(v−t	NOUN
ejpam-4385	523	70	)	)	PUNCT
ejpam-4385	523	71	)	)	PUNCT
ejpam-4385	523	72	(	(	PUNCT
ejpam-4385	523	73	yea(v−t	yea(v−t	PROPN
ejpam-4385	523	74	)	)	PUNCT
ejpam-4385	523	75	x	x	SYM
ejpam-4385	523	76	)	)	PUNCT
ejpam-4385	523	77	aθ	aθ	VERB
ejpam-4385	523	78	σ2−	σ2−	VERB
ejpam-4385	523	79	1	1	NUM
ejpam-4385	523	80	2	2	NUM
ejpam-4385	523	81	exp	exp	NOUN
ejpam-4385	523	82	{	{	PUNCT
ejpam-4385	523	83	2a(x+	2a(x+	NUM
ejpam-4385	523	84	yea(v−t	yea(v−t	NOUN
ejpam-4385	523	85	)	)	PUNCT
ejpam-4385	523	86	)	)	PUNCT
ejpam-4385	524	1	σ2(1−	σ2(1−	PROPN
ejpam-4385	524	2	ea(v−t	ea(v−t	PROPN
ejpam-4385	524	3	)	)	PUNCT
ejpam-4385	524	4	)	)	PUNCT
ejpam-4385	524	5	}	}	PUNCT
ejpam-4385	524	6	×	×	NOUN
ejpam-4385	524	7	iq	iq	INTJ
ejpam-4385	524	8	(	(	PUNCT
ejpam-4385	524	9	−4a	−4a	NOUN
ejpam-4385	524	10	√	√	NUM
ejpam-4385	524	11	xyea(v−t	xyea(v−t	NUM
ejpam-4385	524	12	)	)	PUNCT
ejpam-4385	524	13	σ2(1−	σ2(1−	PROPN
ejpam-4385	524	14	ea(v−t	ea(v−t	PROPN
ejpam-4385	524	15	)	)	PUNCT
ejpam-4385	524	16	)	)	PUNCT
ejpam-4385	524	17	)	)	PUNCT
ejpam-4385	525	1	iq	iq	INTJ
ejpam-4385	525	2	(	(	PUNCT
ejpam-4385	525	3	·	·	PUNCT
ejpam-4385	525	4	)	)	PUNCT
ejpam-4385	525	5	is	be	AUX
ejpam-4385	525	6	the	the	DET
ejpam-4385	525	7	modified	modify	VERB
ejpam-4385	525	8	bessel	bessel	NOUN
ejpam-4385	525	9	function	function	NOUN
ejpam-4385	525	10	of	of	ADP
ejpam-4385	525	11	the	the	DET
ejpam-4385	525	12	first	first	ADJ
ejpam-4385	525	13	kind	kind	NOUN
ejpam-4385	525	14	of	of	ADP
ejpam-4385	525	15	order	order	NOUN
ejpam-4385	525	16	q	q	NOUN
ejpam-4385	525	17	=	=	SYM
ejpam-4385	525	18	2aθ	2aθ	NOUN
ejpam-4385	525	19	σ2	σ2	NOUN
ejpam-4385	525	20	−	−	PROPN
ejpam-4385	525	21	1	1	NUM
ejpam-4385	525	22	.	.	PUNCT
ejpam-4385	525	23	note	note	VERB
ejpam-4385	525	24	that	that	SCONJ
ejpam-4385	525	25	f(v	f(v	VERB
ejpam-4385	525	26	−	−	PROPN
ejpam-4385	525	27	t	t	PROPN
ejpam-4385	525	28	,	,	PUNCT
ejpam-4385	525	29	x	x	X
ejpam-4385	525	30	,	,	PUNCT
ejpam-4385	525	31	y	y	PROPN
ejpam-4385	525	32	)	)	PUNCT
ejpam-4385	525	33	can	can	AUX
ejpam-4385	525	34	be	be	AUX
ejpam-4385	525	35	transformed	transform	VERB
ejpam-4385	525	36	as	as	ADP
ejpam-4385	525	37	f(v	f(v	PROPN
ejpam-4385	525	38	−	−	PROPN
ejpam-4385	525	39	t	t	PROPN
ejpam-4385	525	40	,	,	PUNCT
ejpam-4385	525	41	x	x	NOUN
ejpam-4385	525	42	,	,	PUNCT
ejpam-4385	525	43	y	y	NOUN
ejpam-4385	525	44	)	)	PUNCT
ejpam-4385	525	45	=	=	PUNCT
ejpam-4385	526	1	ehδ(x−	ehδ(x−	ADP
ejpam-4385	526	2	y	y	PROPN
ejpam-4385	526	3	)	)	PUNCT
ejpam-4385	526	4	(	(	PUNCT
ejpam-4385	526	5	57	57	NUM
ejpam-4385	526	6	)	)	PUNCT
ejpam-4385	527	1	where	where	SCONJ
ejpam-4385	527	2	h	h	NOUN
ejpam-4385	528	1	=	=	SYM
ejpam-4385	529	1	∂	∂	PROPN
ejpam-4385	530	1	∂r	∂r	PROPN
ejpam-4385	530	2	a(θ	a(θ	PROPN
ejpam-4385	530	3	−	−	PROPN
ejpam-4385	530	4	rt	rt	PROPN
ejpam-4385	530	5	)	)	PUNCT
ejpam-4385	530	6	+	+	CCONJ
ejpam-4385	531	1	∂2	∂2	PROPN
ejpam-4385	531	2	∂r	∂r	PROPN
ejpam-4385	531	3	σ2	σ2	NOUN
ejpam-4385	531	4	2	2	NUM
ejpam-4385	531	5	2	2	NUM
ejpam-4385	531	6	rt	rt	NOUN
ejpam-4385	531	7	and	and	CCONJ
ejpam-4385	531	8	δ(x−	δ(x−	NOUN
ejpam-4385	531	9	y	y	PROPN
ejpam-4385	531	10	)	)	PUNCT
ejpam-4385	531	11	is	be	AUX
ejpam-4385	531	12	the	the	DET
ejpam-4385	531	13	delta	delta	NOUN
ejpam-4385	531	14	function	function	NOUN
ejpam-4385	531	15	(	(	PUNCT
ejpam-4385	531	16	see	see	VERB
ejpam-4385	531	17	[	[	X
ejpam-4385	531	18	13	13	NUM
ejpam-4385	531	19	]	]	NUM
ejpam-4385	531	20	)	)	PUNCT
ejpam-4385	531	21	.	.	PUNCT
ejpam-4385	532	1	thus	thus	ADV
ejpam-4385	532	2	,	,	PUNCT
ejpam-4385	532	3	j(t	j(t	PROPN
ejpam-4385	532	4	,	,	PUNCT
ejpam-4385	532	5	rr	rr	NOUN
ejpam-4385	532	6	,	,	PUNCT
ejpam-4385	532	7	x	x	PROPN
ejpam-4385	532	8	,	,	PUNCT
ejpam-4385	532	9	v	v	NOUN
ejpam-4385	532	10	,	,	PUNCT
ejpam-4385	532	11	z	z	NOUN
ejpam-4385	532	12	)	)	PUNCT
ejpam-4385	532	13	>	>	X
ejpam-4385	532	14	0	0	PUNCT
ejpam-4385	533	1	for	for	ADP
ejpam-4385	533	2	all	all	DET
ejpam-4385	533	3	(	(	PUNCT
ejpam-4385	533	4	t	t	PROPN
ejpam-4385	533	5	,	,	PUNCT
ejpam-4385	533	6	rt	rt	PROPN
ejpam-4385	533	7	,	,	PUNCT
ejpam-4385	533	8	x	x	NOUN
ejpam-4385	533	9	)	)	PUNCT
ejpam-4385	533	10	∈	∈	PROPN
ejpam-4385	533	11	d.	d.	NOUN
ejpam-4385	533	12	the	the	DET
ejpam-4385	533	13	function	function	PROPN
ejpam-4385	533	14	l[p	l[p	PROPN
ejpam-4385	533	15	(	(	PUNCT
ejpam-4385	533	16	t	t	PROPN
ejpam-4385	533	17	,	,	PUNCT
ejpam-4385	533	18	rt	rt	PROPN
ejpam-4385	533	19	;	;	PUNCT
ejpam-4385	533	20	v)g	v)g	NOUN
ejpam-4385	533	21	µc(v	µc(v	NOUN
ejpam-4385	533	22	,	,	PUNCT
ejpam-4385	533	23	y	y	NOUN
ejpam-4385	533	24	)	)	PUNCT
ejpam-4385	533	25	]	]	PUNCT
ejpam-4385	533	26	is	be	AUX
ejpam-4385	533	27	given	give	VERB
ejpam-4385	533	28	by	by	ADP
ejpam-4385	533	29	l[p	l[p	PROPN
ejpam-4385	533	30	(	(	PUNCT
ejpam-4385	533	31	t	t	PROPN
ejpam-4385	533	32	,	,	PUNCT
ejpam-4385	533	33	rt	rt	PROPN
ejpam-4385	533	34	;	;	PUNCT
ejpam-4385	533	35	v)g	v)g	NOUN
ejpam-4385	533	36	µc(v	µc(v	NOUN
ejpam-4385	533	37	,	,	PUNCT
ejpam-4385	533	38	y	y	NOUN
ejpam-4385	533	39	)	)	PUNCT
ejpam-4385	533	40	]	]	PUNCT
ejpam-4385	534	1	=	=	PUNCT
ejpam-4385	535	1	[	[	X
ejpam-4385	535	2	2rt	2rt	NOUN
ejpam-4385	535	3	−	−	PUNCT
ejpam-4385	535	4	µc	µc	ADP
ejpam-4385	535	5	+	+	ADJ
ejpam-4385	535	6	ρσ1σ2	ρσ1σ2	ADJ
ejpam-4385	535	7	√	√	PROPN
ejpam-4385	535	8	rtλ(0	rtλ(0	NOUN
ejpam-4385	535	9	,	,	PUNCT
ejpam-4385	535	10	t+	t+	X
ejpam-4385	535	11	u)]xp	u)]xp	X
ejpam-4385	535	12	(	(	PUNCT
ejpam-4385	535	13	t	t	PROPN
ejpam-4385	535	14	,	,	PUNCT
ejpam-4385	535	15	rt	rt	PROPN
ejpam-4385	535	16	,	,	PUNCT
ejpam-4385	535	17	t+	t+	NOUN
ejpam-4385	535	18	u	u	NOUN
ejpam-4385	535	19	)	)	PUNCT
ejpam-4385	535	20	eµc(t−(t+u))φ(d1)−	eµc(t−(t+u))φ(d1)−	PROPN
ejpam-4385	535	21	rtp	rtp	PROPN
ejpam-4385	535	22	(	(	PUNCT
ejpam-4385	535	23	t	t	PROPN
ejpam-4385	535	24	,	,	PUNCT
ejpam-4385	535	25	rt	rt	PROPN
ejpam-4385	535	26	,	,	PUNCT
ejpam-4385	535	27	t+	t+	NOUN
ejpam-4385	535	28	u)kφ(d2	u)kφ(d2	NOUN
ejpam-4385	535	29	)	)	PUNCT
ejpam-4385	535	30	.	.	PUNCT
ejpam-4385	536	1	it	it	PRON
ejpam-4385	536	2	can	can	AUX
ejpam-4385	536	3	be	be	AUX
ejpam-4385	536	4	verified	verify	VERB
ejpam-4385	536	5	that	that	SCONJ
ejpam-4385	536	6	(	(	PUNCT
ejpam-4385	536	7	see	see	VERB
ejpam-4385	536	8	appendix	appendix	NOUN
ejpam-4385	536	9	)	)	PUNCT
ejpam-4385	536	10	j(t	j(t	PROPN
ejpam-4385	536	11	,	,	PUNCT
ejpam-4385	536	12	rt	rt	PROPN
ejpam-4385	536	13	,	,	PUNCT
ejpam-4385	536	14	x	x	PROPN
ejpam-4385	536	15	,	,	PUNCT
ejpam-4385	536	16	t	t	PROPN
ejpam-4385	536	17	,	,	PUNCT
ejpam-4385	536	18	z	z	NOUN
ejpam-4385	536	19	)	)	PUNCT
ejpam-4385	536	20	=	=	SYM
ejpam-4385	537	1	rte	rte	NOUN
ejpam-4385	538	1	−xh	−xh	PROPN
ejpam-4385	538	2	z	z	PROPN
ejpam-4385	539	1	p	p	X
ejpam-4385	539	2	(	(	PUNCT
ejpam-4385	539	3	t	t	PROPN
ejpam-4385	539	4	,	,	PUNCT
ejpam-4385	539	5	rt	rt	PROPN
ejpam-4385	539	6	,	,	PUNCT
ejpam-4385	539	7	t	t	PROPN
ejpam-4385	539	8	)	)	PUNCT
ejpam-4385	539	9	kφ(d2	kφ(d2	PROPN
ejpam-4385	539	10	)	)	PUNCT
ejpam-4385	539	11	−	−	PROPN
ejpam-4385	540	1	[	[	X
ejpam-4385	540	2	2rt	2rt	NOUN
ejpam-4385	540	3	−	−	PUNCT
ejpam-4385	540	4	µc	µc	ADP
ejpam-4385	540	5	+	+	ADJ
ejpam-4385	540	6	ρσ1σ2	ρσ1σ2	PROPN
ejpam-4385	540	7	√	√	ADJ
ejpam-4385	540	8	rtλ]xe	rtλ]xe	VERB
ejpam-4385	540	9	−xh+µc	−xh+µc	PROPN
ejpam-4385	540	10	z	z	PROPN
ejpam-4385	540	11	p	p	X
ejpam-4385	540	12	(	(	PUNCT
ejpam-4385	540	13	t	t	PROPN
ejpam-4385	540	14	,	,	PUNCT
ejpam-4385	540	15	rt	rt	PROPN
ejpam-4385	540	16	,	,	PUNCT
ejpam-4385	540	17	t	t	PROPN
ejpam-4385	540	18	)	)	PUNCT
ejpam-4385	540	19	φ(d1	φ(d1	X
ejpam-4385	540	20	)	)	PUNCT
ejpam-4385	540	21	(	(	PUNCT
ejpam-4385	540	22	58	58	NUM
ejpam-4385	540	23	)	)	PUNCT
ejpam-4385	540	24	where	where	SCONJ
ejpam-4385	540	25	k.	k.	PROPN
ejpam-4385	540	26	falcasantos	falcasantos	PROPN
ejpam-4385	540	27	,	,	PUNCT
ejpam-4385	540	28	f.	f.	PROPN
ejpam-4385	540	29	sumalpong	sumalpong	PROPN
ejpam-4385	540	30	/	/	SYM
ejpam-4385	540	31	eur	eur	PROPN
ejpam-4385	540	32	.	.	PUNCT
ejpam-4385	541	1	j.	j.	PROPN
ejpam-4385	541	2	pure	pure	PROPN
ejpam-4385	541	3	appl	appl	PROPN
ejpam-4385	541	4	.	.	PROPN
ejpam-4385	541	5	math	math	PROPN
ejpam-4385	541	6	,	,	PUNCT
ejpam-4385	541	7	15	15	NUM
ejpam-4385	541	8	(	(	PUNCT
ejpam-4385	541	9	3	3	NUM
ejpam-4385	541	10	)	)	PUNCT
ejpam-4385	541	11	(	(	PUNCT
ejpam-4385	541	12	2022	2022	NUM
ejpam-4385	541	13	)	)	PUNCT
ejpam-4385	541	14	,	,	PUNCT
ejpam-4385	541	15	948	948	NUM
ejpam-4385	541	16	-	-	SYM
ejpam-4385	541	17	970	970	NUM
ejpam-4385	541	18	967	967	NUM
ejpam-4385	541	19	d1	d1	NOUN
ejpam-4385	541	20	=	=	SYM
ejpam-4385	542	1	ln	ln	NOUN
ejpam-4385	542	2	x	x	X
ejpam-4385	543	1	k	k	X
ejpam-4385	544	1	+	+	NOUN
ejpam-4385	544	2	a(t	a(t	PROPN
ejpam-4385	544	3	,	,	PUNCT
ejpam-4385	544	4	t	t	NOUN
ejpam-4385	544	5	)	)	PUNCT
ejpam-4385	545	1	+	+	CCONJ
ejpam-4385	545	2	σ2	σ2	NOUN
ejpam-4385	545	3	1	1	NUM
ejpam-4385	545	4	2	2	NUM
ejpam-4385	545	5	(	(	PUNCT
ejpam-4385	545	6	t	t	PROPN
ejpam-4385	545	7	)	)	PUNCT
ejpam-4385	545	8	σ1	σ1	PROPN
ejpam-4385	545	9	√	√	PROPN
ejpam-4385	545	10	t	t	PROPN
ejpam-4385	545	11	d2	d2	PROPN
ejpam-4385	545	12	=	=	SYM
ejpam-4385	545	13	ln	ln	NOUN
ejpam-4385	545	14	x	x	X
ejpam-4385	546	1	k	k	X
ejpam-4385	546	2	+	+	NOUN
ejpam-4385	546	3	a(t	a(t	PROPN
ejpam-4385	546	4	,	,	PUNCT
ejpam-4385	546	5	t	t	NOUN
ejpam-4385	546	6	)	)	PUNCT
ejpam-4385	546	7	−	−	PROPN
ejpam-4385	546	8	σ2	σ2	NOUN
ejpam-4385	546	9	1	1	NUM
ejpam-4385	546	10	2	2	NUM
ejpam-4385	546	11	(	(	PUNCT
ejpam-4385	546	12	t	t	PROPN
ejpam-4385	546	13	)	)	PUNCT
ejpam-4385	546	14	σ1	σ1	PROPN
ejpam-4385	546	15	√	√	PROPN
ejpam-4385	546	16	t	t	PROPN
ejpam-4385	546	17	a(t	a(t	PROPN
ejpam-4385	546	18	,	,	PUNCT
ejpam-4385	546	19	t	t	NOUN
ejpam-4385	546	20	)	)	PUNCT
ejpam-4385	546	21	=	=	PUNCT
ejpam-4385	546	22	r0	r0	NOUN
ejpam-4385	546	23	−	−	PROPN
ejpam-4385	546	24	θ	θ	PROPN
ejpam-4385	546	25	a	a	PRON
ejpam-4385	546	26	(	(	PUNCT
ejpam-4385	546	27	1−	1−	NUM
ejpam-4385	546	28	e−at	e−at	NOUN
ejpam-4385	546	29	)	)	PUNCT
ejpam-4385	547	1	+	+	CCONJ
ejpam-4385	547	2	θ(t	θ(t	NUM
ejpam-4385	547	3	)	)	PUNCT
ejpam-4385	547	4	φ(x	φ(x	NOUN
ejpam-4385	547	5	)	)	PUNCT
ejpam-4385	547	6	=	=	SYM
ejpam-4385	548	1	1√	1√	NUM
ejpam-4385	548	2	2π	2π	NUM
ejpam-4385	548	3	∫	∫	NOUN
ejpam-4385	548	4	x	x	X
ejpam-4385	548	5	−∞	−∞	ADP
ejpam-4385	548	6	e	e	PROPN
ejpam-4385	548	7	−y2	−y2	PROPN
ejpam-4385	548	8	2	2	NUM
ejpam-4385	548	9	dy	dy	NOUN
ejpam-4385	548	10	ϕ(x	ϕ(x	NOUN
ejpam-4385	548	11	)	)	PUNCT
ejpam-4385	548	12	=	=	SYM
ejpam-4385	549	1	1√	1√	NUM
ejpam-4385	549	2	2π	2π	NOUN
ejpam-4385	549	3	e−	e−	PROPN
ejpam-4385	549	4	x2	x2	PROPN
ejpam-4385	549	5	2	2	NUM
ejpam-4385	549	6	p	p	NOUN
ejpam-4385	549	7	(	(	PUNCT
ejpam-4385	549	8	t	t	PROPN
ejpam-4385	549	9	,	,	PUNCT
ejpam-4385	549	10	rt	rt	PROPN
ejpam-4385	549	11	,	,	PUNCT
ejpam-4385	549	12	t	t	PROPN
ejpam-4385	549	13	)	)	PUNCT
ejpam-4385	550	1	=	=	PUNCT
ejpam-4385	551	1	[	[	X
ejpam-4385	551	2	[	[	PUNCT
ejpam-4385	551	3	xφ(d1)−ke−a(t	xφ(d1)−ke−a(t	PROPN
ejpam-4385	551	4	,	,	PUNCT
ejpam-4385	551	5	t	t	NOUN
ejpam-4385	551	6	)	)	PUNCT
ejpam-4385	551	7	φ(d2	φ(d2	NUM
ejpam-4385	551	8	)	)	PUNCT
ejpam-4385	551	9	]	]	PUNCT
ejpam-4385	552	1	+	+	CCONJ
ejpam-4385	552	2	σc0	σc0	VERB
ejpam-4385	552	3	[	[	PUNCT
ejpam-4385	552	4	xφ(d1)−ke−a(t	xφ(d1)−ke−a(t	PROPN
ejpam-4385	552	5	,	,	PUNCT
ejpam-4385	552	6	t	t	NOUN
ejpam-4385	552	7	)	)	PUNCT
ejpam-4385	552	8	(	(	PUNCT
ejpam-4385	552	9	ϕ(d2)−	ϕ(d2)−	PROPN
ejpam-4385	552	10	σ1	σ1	PROPN
ejpam-4385	552	11	√	√	ADP
ejpam-4385	552	12	t	t	PROPN
ejpam-4385	552	13	−	−	PROPN
ejpam-4385	552	14	tφ(d2	tφ(d2	PROPN
ejpam-4385	552	15	)	)	PUNCT
ejpam-4385	552	16	)	)	PUNCT
ejpam-4385	552	17	]	]	PUNCT
ejpam-4385	553	1	+	+	CCONJ
ejpam-4385	553	2	σc1	σc1	NOUN
ejpam-4385	553	3	[	[	PUNCT
ejpam-4385	553	4	d2xϕ(d1)−	d2xϕ(d1)−	ADJ
ejpam-4385	553	5	d1ke−a(t	d1ke−a(t	NOUN
ejpam-4385	553	6	,	,	PUNCT
ejpam-4385	553	7	t	t	NOUN
ejpam-4385	553	8	)	)	PUNCT
ejpam-4385	553	9	)	)	PUNCT
ejpam-4385	553	10	ϕ(d2	ϕ(d2	X
ejpam-4385	553	11	)	)	PUNCT
ejpam-4385	553	12	]	]	PUNCT
ejpam-4385	554	1	+	+	CCONJ
ejpam-4385	555	1	0(σ	0(σ	NOUN
ejpam-4385	555	2	)	)	PUNCT
ejpam-4385	555	3	]	]	PUNCT
ejpam-4385	555	4	where	where	SCONJ
ejpam-4385	555	5	0(σ	0(σ	NOUN
ejpam-4385	555	6	)	)	PUNCT
ejpam-4385	555	7	is	be	AUX
ejpam-4385	555	8	a	a	DET
ejpam-4385	555	9	zero	zero	NUM
ejpam-4385	555	10	-	-	PUNCT
ejpam-4385	555	11	mean	mean	NOUN
ejpam-4385	555	12	error	error	NOUN
ejpam-4385	555	13	(	(	PUNCT
ejpam-4385	555	14	see	see	VERB
ejpam-4385	555	15	[	[	X
ejpam-4385	555	16	6	6	NUM
ejpam-4385	555	17	]	]	PUNCT
ejpam-4385	555	18	)	)	PUNCT
ejpam-4385	555	19	theorem	theorem	NOUN
ejpam-4385	555	20	1	1	NUM
ejpam-4385	555	21	.	.	PUNCT
ejpam-4385	556	1	the	the	DET
ejpam-4385	556	2	arbitrage	arbitrage	NOUN
ejpam-4385	556	3	free	free	ADJ
ejpam-4385	556	4	-	-	PUNCT
ejpam-4385	556	5	price	price	NOUN
ejpam-4385	556	6	of	of	ADP
ejpam-4385	556	7	the	the	DET
ejpam-4385	556	8	british	british	ADJ
ejpam-4385	556	9	call	call	NOUN
ejpam-4385	556	10	option	option	NOUN
ejpam-4385	556	11	with	with	ADP
ejpam-4385	556	12	stochastic	stochastic	ADJ
ejpam-4385	556	13	interest	interest	NOUN
ejpam-4385	556	14	rate	rate	NOUN
ejpam-4385	556	15	admits	admit	VERB
ejpam-4385	556	16	the	the	DET
ejpam-4385	556	17	following	follow	VERB
ejpam-4385	556	18	early	early	ADJ
ejpam-4385	556	19	-	-	PUNCT
ejpam-4385	556	20	exercise	exercise	NOUN
ejpam-4385	556	21	premium	premium	NOUN
ejpam-4385	556	22	representation	representation	NOUN
ejpam-4385	556	23	v	v	ADP
ejpam-4385	556	24	(	(	PUNCT
ejpam-4385	556	25	t	t	PROPN
ejpam-4385	556	26	,	,	PUNCT
ejpam-4385	556	27	rt	rt	PROPN
ejpam-4385	556	28	,	,	PUNCT
ejpam-4385	556	29	x	x	NOUN
ejpam-4385	556	30	)	)	PUNCT
ejpam-4385	557	1	=	=	SYM
ejpam-4385	557	2	p	p	X
ejpam-4385	557	3	(	(	PUNCT
ejpam-4385	557	4	t	t	PROPN
ejpam-4385	557	5	,	,	PUNCT
ejpam-4385	557	6	rt;t	rt;t	PROPN
ejpam-4385	557	7	)	)	PUNCT
ejpam-4385	558	1	+	+	CCONJ
ejpam-4385	558	2	∫	∫	PROPN
ejpam-4385	558	3	t	t	PROPN
ejpam-4385	558	4	t	t	PROPN
ejpam-4385	558	5	j(t	j(t	PROPN
ejpam-4385	558	6	,	,	PUNCT
ejpam-4385	558	7	rt	rt	PROPN
ejpam-4385	558	8	,	,	PUNCT
ejpam-4385	558	9	x	x	NOUN
ejpam-4385	558	10	,	,	PUNCT
ejpam-4385	558	11	v	v	NOUN
ejpam-4385	558	12	,	,	PUNCT
ejpam-4385	558	13	bd(v	bd(v	PROPN
ejpam-4385	558	14	,	,	PUNCT
ejpam-4385	558	15	rv))dv	rv))dv	PROPN
ejpam-4385	558	16	(	(	PUNCT
ejpam-4385	558	17	59	59	NUM
ejpam-4385	558	18	)	)	PUNCT
ejpam-4385	558	19	for	for	ADP
ejpam-4385	558	20	all	all	DET
ejpam-4385	558	21	(	(	PUNCT
ejpam-4385	558	22	t	t	PROPN
ejpam-4385	558	23	,	,	PUNCT
ejpam-4385	558	24	rt	rt	PROPN
ejpam-4385	558	25	,	,	PUNCT
ejpam-4385	558	26	x	x	NOUN
ejpam-4385	558	27	)	)	PUNCT
ejpam-4385	558	28	∈	∈	PROPN
ejpam-4385	559	1	[	[	X
ejpam-4385	559	2	0	0	NUM
ejpam-4385	559	3	,	,	PUNCT
ejpam-4385	559	4	t	t	X
ejpam-4385	559	5	]	]	PUNCT
ejpam-4385	559	6	×	×	PROPN
ejpam-4385	559	7	r	r	NOUN
ejpam-4385	559	8	×	×	NOUN
ejpam-4385	559	9	(	(	PUNCT
ejpam-4385	559	10	0,∞	0,∞	NOUN
ejpam-4385	559	11	)	)	PUNCT
ejpam-4385	559	12	,	,	PUNCT
ejpam-4385	559	13	where	where	SCONJ
ejpam-4385	559	14	the	the	DET
ejpam-4385	559	15	first	first	ADJ
ejpam-4385	559	16	term	term	NOUN
ejpam-4385	559	17	is	be	AUX
ejpam-4385	559	18	the	the	DET
ejpam-4385	559	19	arbitrage	arbitrage	NOUN
ejpam-4385	559	20	-	-	PUNCT
ejpam-4385	559	21	free	free	ADJ
ejpam-4385	559	22	price	price	NOUN
ejpam-4385	559	23	of	of	ADP
ejpam-4385	559	24	the	the	DET
ejpam-4385	559	25	european	european	ADJ
ejpam-4385	559	26	call	call	NOUN
ejpam-4385	559	27	option	option	NOUN
ejpam-4385	559	28	under	under	ADP
ejpam-4385	559	29	stochastic	stochastic	ADJ
ejpam-4385	559	30	interest	interest	NOUN
ejpam-4385	559	31	rate	rate	NOUN
ejpam-4385	559	32	and	and	CCONJ
ejpam-4385	559	33	the	the	DET
ejpam-4385	559	34	second	second	ADJ
ejpam-4385	559	35	term	term	NOUN
ejpam-4385	559	36	is	be	AUX
ejpam-4385	559	37	the	the	DET
ejpam-4385	559	38	earlyexercise	earlyexercise	ADJ
ejpam-4385	559	39	premium	premium	NOUN
ejpam-4385	559	40	.	.	PUNCT
ejpam-4385	560	1	the	the	DET
ejpam-4385	560	2	rational	rational	ADJ
ejpam-4385	560	3	exercise	exercise	NOUN
ejpam-4385	560	4	boundary	boundary	NOUN
ejpam-4385	560	5	of	of	ADP
ejpam-4385	560	6	the	the	DET
ejpam-4385	560	7	british	british	ADJ
ejpam-4385	560	8	call	call	NOUN
ejpam-4385	560	9	option	option	NOUN
ejpam-4385	560	10	can	can	AUX
ejpam-4385	560	11	be	be	AUX
ejpam-4385	560	12	characterized	characterize	VERB
ejpam-4385	560	13	as	as	ADP
ejpam-4385	560	14	the	the	DET
ejpam-4385	560	15	unique	unique	ADJ
ejpam-4385	560	16	continuous	continuous	ADJ
ejpam-4385	560	17	solution	solution	NOUN
ejpam-4385	560	18	bd	bd	NOUN
ejpam-4385	560	19	:	:	PUNCT
ejpam-4385	561	1	[	[	X
ejpam-4385	561	2	0	0	NUM
ejpam-4385	561	3	,	,	PUNCT
ejpam-4385	561	4	t	t	X
ejpam-4385	561	5	]	]	X
ejpam-4385	561	6	×	×	NOUN
ejpam-4385	561	7	r	r	NOUN
ejpam-4385	561	8	→	→	PUNCT
ejpam-4385	561	9	r+	r+	NOUN
ejpam-4385	561	10	to	to	ADP
ejpam-4385	561	11	the	the	DET
ejpam-4385	561	12	nonlinear	nonlinear	ADJ
ejpam-4385	561	13	integral	integral	ADJ
ejpam-4385	561	14	equation	equation	NOUN
ejpam-4385	561	15	f	f	X
ejpam-4385	561	16	(	(	PUNCT
ejpam-4385	561	17	t	t	PROPN
ejpam-4385	561	18	,	,	PUNCT
ejpam-4385	561	19	rt	rt	PROPN
ejpam-4385	561	20	,	,	PUNCT
ejpam-4385	561	21	bd(t	bd(t	PROPN
ejpam-4385	561	22	,	,	PUNCT
ejpam-4385	561	23	rt	rt	PROPN
ejpam-4385	561	24	)	)	PUNCT
ejpam-4385	561	25	)	)	PUNCT
ejpam-4385	562	1	=	=	SYM
ejpam-4385	563	1	∫	∫	PROPN
ejpam-4385	563	2	t	t	PROPN
ejpam-4385	563	3	t	t	PROPN
ejpam-4385	563	4	j(t	j(t	PROPN
ejpam-4385	563	5	,	,	PUNCT
ejpam-4385	563	6	rt	rt	PROPN
ejpam-4385	563	7	,	,	PUNCT
ejpam-4385	563	8	x	x	NOUN
ejpam-4385	563	9	,	,	PUNCT
ejpam-4385	563	10	v	v	NOUN
ejpam-4385	563	11	,	,	PUNCT
ejpam-4385	563	12	bd(v	bd(v	PROPN
ejpam-4385	563	13	,	,	PUNCT
ejpam-4385	563	14	rv))dv	rv))dv	PROPN
ejpam-4385	563	15	(	(	PUNCT
ejpam-4385	563	16	60	60	NUM
ejpam-4385	563	17	)	)	PUNCT
ejpam-4385	563	18	which	which	PRON
ejpam-4385	563	19	satisfies	satisfy	VERB
ejpam-4385	563	20	bd(t	bd(t	PROPN
ejpam-4385	563	21	,	,	PUNCT
ejpam-4385	563	22	rt	rt	PROPN
ejpam-4385	563	23	)	)	PUNCT
ejpam-4385	563	24	≥	≥	NOUN
ejpam-4385	563	25	h(t	h(t	PROPN
ejpam-4385	563	26	,	,	PUNCT
ejpam-4385	563	27	rt	rt	PROPN
ejpam-4385	563	28	)	)	PUNCT
ejpam-4385	563	29	for	for	ADP
ejpam-4385	563	30	all	all	DET
ejpam-4385	563	31	t	t	NOUN
ejpam-4385	563	32	∈	∈	PROPN
ejpam-4385	564	1	[	[	X
ejpam-4385	564	2	0	0	NUM
ejpam-4385	564	3	,	,	PUNCT
ejpam-4385	564	4	t	t	NOUN
ejpam-4385	564	5	]	]	PUNCT
ejpam-4385	564	6	where	where	SCONJ
ejpam-4385	564	7	h	h	NOUN
ejpam-4385	564	8	is	be	AUX
ejpam-4385	564	9	defined	define	VERB
ejpam-4385	564	10	as	as	ADP
ejpam-4385	564	11	a	a	DET
ejpam-4385	564	12	continuous	continuous	ADJ
ejpam-4385	564	13	(	(	PUNCT
ejpam-4385	564	14	smooth	smooth	ADJ
ejpam-4385	564	15	)	)	PUNCT
ejpam-4385	564	16	function	function	NOUN
ejpam-4385	564	17	h	h	NOUN
ejpam-4385	564	18	:	:	PUNCT
ejpam-4385	565	1	[	[	X
ejpam-4385	565	2	0	0	NUM
ejpam-4385	565	3	,	,	PUNCT
ejpam-4385	565	4	t	t	X
ejpam-4385	565	5	]	]	PUNCT
ejpam-4385	565	6	×	×	PROPN
ejpam-4385	565	7	r	r	NOUN
ejpam-4385	565	8	→	→	PUNCT
ejpam-4385	565	9	r+	r+	NOUN
ejpam-4385	565	10	such	such	ADJ
ejpam-4385	565	11	that	that	SCONJ
ejpam-4385	565	12	lp	lp	PROPN
ejpam-4385	565	13	(	(	PUNCT
ejpam-4385	565	14	t	t	PROPN
ejpam-4385	565	15	,	,	PUNCT
ejpam-4385	565	16	rt	rt	PROPN
ejpam-4385	565	17	;	;	PUNCT
ejpam-4385	565	18	t	t	PROPN
ejpam-4385	565	19	+	+	CCONJ
ejpam-4385	565	20	u)gµc(t	u)gµc(t	PROPN
ejpam-4385	565	21	+	+	NUM
ejpam-4385	565	22	u	u	NOUN
ejpam-4385	565	23	,	,	PUNCT
ejpam-4385	565	24	xt+u	xt+u	PROPN
ejpam-4385	565	25	)	)	PUNCT
ejpam-4385	566	1	=	=	SYM
ejpam-4385	566	2	0	0	NUM
ejpam-4385	567	1	for	for	ADP
ejpam-4385	567	2	all	all	DET
ejpam-4385	567	3	t	t	NOUN
ejpam-4385	567	4	∈	∈	PROPN
ejpam-4385	568	1	[	[	X
ejpam-4385	568	2	0	0	NUM
ejpam-4385	568	3	,	,	PUNCT
ejpam-4385	568	4	t	t	X
ejpam-4385	568	5	]	]	PUNCT
ejpam-4385	568	6	.	.	PUNCT
ejpam-4385	569	1	proof	proof	NOUN
ejpam-4385	569	2	:	:	PUNCT
ejpam-4385	569	3	for	for	ADP
ejpam-4385	569	4	any	any	DET
ejpam-4385	569	5	(	(	PUNCT
ejpam-4385	569	6	t	t	PROPN
ejpam-4385	569	7	,	,	PUNCT
ejpam-4385	569	8	rt	rt	PROPN
ejpam-4385	569	9	,	,	PUNCT
ejpam-4385	569	10	x	x	NOUN
ejpam-4385	569	11	)	)	PUNCT
ejpam-4385	569	12	∈	∈	PROPN
ejpam-4385	569	13	c	c	X
ejpam-4385	569	14	,	,	PUNCT
ejpam-4385	569	15	we	we	PRON
ejpam-4385	569	16	have	have	VERB
ejpam-4385	569	17	k.	k.	PROPN
ejpam-4385	569	18	falcasantos	falcasanto	NOUN
ejpam-4385	569	19	,	,	PUNCT
ejpam-4385	569	20	f.	f.	PROPN
ejpam-4385	569	21	sumalpong	sumalpong	PROPN
ejpam-4385	569	22	/	/	SYM
ejpam-4385	569	23	eur	eur	PROPN
ejpam-4385	569	24	.	.	PUNCT
ejpam-4385	570	1	j.	j.	PROPN
ejpam-4385	570	2	pure	pure	PROPN
ejpam-4385	570	3	appl	appl	PROPN
ejpam-4385	570	4	.	.	PROPN
ejpam-4385	570	5	math	math	PROPN
ejpam-4385	570	6	,	,	PUNCT
ejpam-4385	570	7	15	15	NUM
ejpam-4385	570	8	(	(	PUNCT
ejpam-4385	570	9	3	3	NUM
ejpam-4385	570	10	)	)	PUNCT
ejpam-4385	570	11	(	(	PUNCT
ejpam-4385	570	12	2022	2022	NUM
ejpam-4385	570	13	)	)	PUNCT
ejpam-4385	570	14	,	,	PUNCT
ejpam-4385	570	15	948	948	NUM
ejpam-4385	570	16	-	-	SYM
ejpam-4385	570	17	970	970	NUM
ejpam-4385	570	18	968	968	NUM
ejpam-4385	570	19	v	v	NOUN
ejpam-4385	570	20	(	(	PUNCT
ejpam-4385	570	21	t	t	PROPN
ejpam-4385	570	22	,	,	PUNCT
ejpam-4385	570	23	rt	rt	PROPN
ejpam-4385	570	24	,	,	PUNCT
ejpam-4385	570	25	x	x	NOUN
ejpam-4385	570	26	)	)	PUNCT
ejpam-4385	570	27	=	=	SYM
ejpam-4385	571	1	e	e	X
ejpam-4385	572	1	[	[	X
ejpam-4385	572	2	p	p	X
ejpam-4385	572	3	(	(	PUNCT
ejpam-4385	572	4	t	t	PROPN
ejpam-4385	572	5	,	,	PUNCT
ejpam-4385	572	6	rt	rt	PROPN
ejpam-4385	572	7	;	;	PUNCT
ejpam-4385	572	8	t+	t+	NUM
ejpam-4385	572	9	τd)g	τd)g	PROPN
ejpam-4385	572	10	µc(t+	µc(t+	PROPN
ejpam-4385	572	11	τd	τd	NOUN
ejpam-4385	572	12	,	,	PUNCT
ejpam-4385	572	13	xt+τd	xt+τd	PROPN
ejpam-4385	572	14	)	)	PUNCT
ejpam-4385	572	15	]	]	PUNCT
ejpam-4385	572	16	(	(	PUNCT
ejpam-4385	572	17	61	61	NUM
ejpam-4385	572	18	)	)	PUNCT
ejpam-4385	572	19	with	with	ADP
ejpam-4385	572	20	xt	xt	PROPN
ejpam-4385	572	21	=	=	SYM
ejpam-4385	572	22	x	x	SYM
ejpam-4385	572	23	∈	∈	PROPN
ejpam-4385	572	24	(	(	PUNCT
ejpam-4385	572	25	0,∞	0,∞	NOUN
ejpam-4385	572	26	)	)	PUNCT
ejpam-4385	572	27	and	and	CCONJ
ejpam-4385	572	28	rt	rt	NOUN
ejpam-4385	572	29	=	=	PUNCT
ejpam-4385	572	30	r	r	NOUN
ejpam-4385	572	31	∈	∈	NOUN
ejpam-4385	572	32	r	r	NOUN
ejpam-4385	572	33	where	where	SCONJ
ejpam-4385	572	34	τd	τd	ADV
ejpam-4385	572	35	=	=	SYM
ejpam-4385	572	36	τd(t	τd(t	PROPN
ejpam-4385	572	37	,	,	PUNCT
ejpam-4385	572	38	rt	rt	PROPN
ejpam-4385	572	39	,	,	PUNCT
ejpam-4385	572	40	x	x	X
ejpam-4385	572	41	)	)	PUNCT
ejpam-4385	572	42	is	be	AUX
ejpam-4385	572	43	the	the	DET
ejpam-4385	572	44	optimal	optimal	ADJ
ejpam-4385	572	45	stopping	stopping	NOUN
ejpam-4385	572	46	defined	define	VERB
ejpam-4385	572	47	as	as	ADP
ejpam-4385	572	48	τd(t	τd(t	NOUN
ejpam-4385	572	49	,	,	PUNCT
ejpam-4385	572	50	rt	rt	PROPN
ejpam-4385	572	51	,	,	PUNCT
ejpam-4385	572	52	x	x	NOUN
ejpam-4385	572	53	)	)	PUNCT
ejpam-4385	572	54	:	:	PUNCT
ejpam-4385	572	55	=	=	SYM
ejpam-4385	572	56	inf	inf	PROPN
ejpam-4385	572	57	{	{	PUNCT
ejpam-4385	572	58	s	s	NOUN
ejpam-4385	572	59	∈	∈	X
ejpam-4385	572	60	[	[	X
ejpam-4385	572	61	0	0	NUM
ejpam-4385	572	62	,	,	PUNCT
ejpam-4385	572	63	t	t	PROPN
ejpam-4385	572	64	−	−	PROPN
ejpam-4385	572	65	t	t	PROPN
ejpam-4385	572	66	]	]	PUNCT
ejpam-4385	572	67	:	:	PUNCT
ejpam-4385	572	68	(	(	PUNCT
ejpam-4385	572	69	t+	t+	NOUN
ejpam-4385	572	70	s	s	NOUN
ejpam-4385	572	71	,	,	PUNCT
ejpam-4385	572	72	rt+s	rt+s	PROPN
ejpam-4385	572	73	,	,	PUNCT
ejpam-4385	572	74	xt+s	xt+s	NUM
ejpam-4385	572	75	)	)	PUNCT
ejpam-4385	572	76	∈	∈	PROPN
ejpam-4385	573	1	d	d	NOUN
ejpam-4385	573	2	}	}	PUNCT
ejpam-4385	573	3	.	.	PUNCT
ejpam-4385	574	1	it	it	PRON
ejpam-4385	574	2	can	can	AUX
ejpam-4385	574	3	easily	easily	ADV
ejpam-4385	574	4	be	be	AUX
ejpam-4385	574	5	verified	verify	VERB
ejpam-4385	574	6	from	from	ADP
ejpam-4385	574	7	(	(	PUNCT
ejpam-4385	574	8	7	7	NUM
ejpam-4385	574	9	)	)	PUNCT
ejpam-4385	574	10	that	that	PRON
ejpam-4385	574	11	p	p	X
ejpam-4385	574	12	(	(	PUNCT
ejpam-4385	574	13	t	t	PROPN
ejpam-4385	574	14	,	,	PUNCT
ejpam-4385	574	15	rt	rt	PROPN
ejpam-4385	574	16	,	,	PUNCT
ejpam-4385	574	17	x	x	X
ejpam-4385	574	18	)	)	PUNCT
ejpam-4385	574	19	has	have	AUX
ejpam-4385	574	20	continuous	continuous	ADJ
ejpam-4385	574	21	∂2p	∂2p	NOUN
ejpam-4385	574	22	∂r2	∂r2	PROPN
ejpam-4385	574	23	(	(	PUNCT
ejpam-4385	574	24	t	t	PROPN
ejpam-4385	574	25	,	,	PUNCT
ejpam-4385	574	26	rt	rt	PROPN
ejpam-4385	574	27	,	,	PUNCT
ejpam-4385	574	28	x	x	NOUN
ejpam-4385	574	29	)	)	PUNCT
ejpam-4385	574	30	.	.	PUNCT
ejpam-4385	575	1	this	this	PRON
ejpam-4385	575	2	implies	imply	VERB
ejpam-4385	575	3	that	that	SCONJ
ejpam-4385	575	4	v	v	X
ejpam-4385	575	5	(	(	PUNCT
ejpam-4385	575	6	t	t	PROPN
ejpam-4385	575	7	,	,	PUNCT
ejpam-4385	575	8	rt	rt	PROPN
ejpam-4385	575	9	,	,	PUNCT
ejpam-4385	575	10	x	x	X
ejpam-4385	575	11	)	)	PUNCT
ejpam-4385	575	12	has	have	VERB
ejpam-4385	575	13	also	also	ADV
ejpam-4385	575	14	continuous	continuous	ADJ
ejpam-4385	575	15	∂2v	∂2v	NOUN
ejpam-4385	575	16	∂r2	∂r2	PROPN
ejpam-4385	575	17	(	(	PUNCT
ejpam-4385	575	18	t	t	PROPN
ejpam-4385	575	19	,	,	PUNCT
ejpam-4385	575	20	rt	rt	PROPN
ejpam-4385	575	21	,	,	PUNCT
ejpam-4385	575	22	x	x	NOUN
ejpam-4385	575	23	)	)	PUNCT
ejpam-4385	575	24	.	.	PUNCT
ejpam-4385	576	1	moreover	moreover	ADV
ejpam-4385	576	2	,	,	PUNCT
ejpam-4385	576	3	it	it	PRON
ejpam-4385	576	4	is	be	AUX
ejpam-4385	576	5	well	well	ADV
ejpam-4385	576	6	-	-	PUNCT
ejpam-4385	576	7	known	know	VERB
ejpam-4385	576	8	from	from	ADP
ejpam-4385	576	9	the	the	DET
ejpam-4385	576	10	theory	theory	NOUN
ejpam-4385	576	11	of	of	ADP
ejpam-4385	576	12	markov	markov	NOUN
ejpam-4385	576	13	processes	process	NOUN
ejpam-4385	576	14	that	that	PRON
ejpam-4385	576	15	v	v	NOUN
ejpam-4385	576	16	in	in	ADP
ejpam-4385	576	17	(	(	PUNCT
ejpam-4385	576	18	61	61	NUM
ejpam-4385	576	19	)	)	PUNCT
ejpam-4385	576	20	is	be	AUX
ejpam-4385	576	21	c1,2	c1,2	ADJ
ejpam-4385	576	22	;	;	PUNCT
ejpam-4385	576	23	hence	hence	ADV
ejpam-4385	576	24	is	be	AUX
ejpam-4385	576	25	c1,2,2	c1,2,2	PROPN
ejpam-4385	576	26	,	,	PUNCT
ejpam-4385	576	27	and	and	CCONJ
ejpam-4385	576	28	it	it	PRON
ejpam-4385	576	29	solves	solve	VERB
ejpam-4385	576	30	the	the	DET
ejpam-4385	576	31	cauchy	cauchy	PROPN
ejpam-4385	576	32	-	-	PUNCT
ejpam-4385	576	33	dirichlet	dirichlet	PROPN
ejpam-4385	576	34	free	free	PROPN
ejpam-4385	576	35	boundary	boundary	PROPN
ejpam-4385	576	36	problem	problem	NOUN
ejpam-4385	576	37	lxv	lxv	NOUN
ejpam-4385	576	38	(	(	PUNCT
ejpam-4385	576	39	t	t	PROPN
ejpam-4385	576	40	,	,	PUNCT
ejpam-4385	576	41	rt	rt	PROPN
ejpam-4385	576	42	,	,	PUNCT
ejpam-4385	576	43	xt	xt	X
ejpam-4385	576	44	)	)	PUNCT
ejpam-4385	577	1	=	=	SYM
ejpam-4385	577	2	0	0	NUM
ejpam-4385	577	3	(	(	PUNCT
ejpam-4385	577	4	t	t	PROPN
ejpam-4385	577	5	,	,	PUNCT
ejpam-4385	577	6	rt	rt	PROPN
ejpam-4385	577	7	,	,	PUNCT
ejpam-4385	577	8	xt	xt	X
ejpam-4385	577	9	)	)	PUNCT
ejpam-4385	578	1	∈	∈	PROPN
ejpam-4385	578	2	c	c	PROPN
ejpam-4385	578	3	(	(	PUNCT
ejpam-4385	578	4	62	62	NUM
ejpam-4385	578	5	)	)	PUNCT
ejpam-4385	578	6	v	v	NOUN
ejpam-4385	578	7	(	(	PUNCT
ejpam-4385	578	8	t	t	PROPN
ejpam-4385	578	9	,	,	PUNCT
ejpam-4385	578	10	rt	rt	PROPN
ejpam-4385	578	11	,	,	PUNCT
ejpam-4385	578	12	xt	xt	X
ejpam-4385	578	13	)	)	PUNCT
ejpam-4385	578	14	=	=	SYM
ejpam-4385	578	15	gµc(t	gµc(t	PROPN
ejpam-4385	578	16	,	,	PUNCT
ejpam-4385	578	17	xt)(t	xt)(t	PROPN
ejpam-4385	578	18	,	,	PUNCT
ejpam-4385	578	19	rt	rt	PROPN
ejpam-4385	578	20	,	,	PUNCT
ejpam-4385	578	21	xt	xt	X
ejpam-4385	578	22	)	)	PUNCT
ejpam-4385	578	23	∈	∈	PROPN
ejpam-4385	578	24	∂c	∂c	PROPN
ejpam-4385	578	25	(	(	PUNCT
ejpam-4385	578	26	63	63	NUM
ejpam-4385	578	27	)	)	PUNCT
ejpam-4385	578	28	where	where	SCONJ
ejpam-4385	578	29	∂c	∂c	PROPN
ejpam-4385	579	1	⊂	⊂	PROPN
ejpam-4385	579	2	d	d	PROPN
ejpam-4385	579	3	denotes	denote	VERB
ejpam-4385	579	4	the	the	DET
ejpam-4385	579	5	open	open	ADJ
ejpam-4385	579	6	set	set	NOUN
ejpam-4385	579	7	c.	c.	NOUN
ejpam-4385	579	8	by	by	ADP
ejpam-4385	579	9	applying	apply	VERB
ejpam-4385	579	10	the	the	DET
ejpam-4385	579	11	change	change	NOUN
ejpam-4385	579	12	of	of	ADP
ejpam-4385	579	13	variable	variable	ADJ
ejpam-4385	579	14	formula	formula	NOUN
ejpam-4385	579	15	with	with	ADP
ejpam-4385	579	16	local	local	ADJ
ejpam-4385	579	17	time	time	NOUN
ejpam-4385	579	18	on	on	ADP
ejpam-4385	579	19	surfaces	surface	NOUN
ejpam-4385	579	20	in	in	ADP
ejpam-4385	579	21	[	[	X
ejpam-4385	579	22	9	9	NUM
ejpam-4385	579	23	]	]	PUNCT
ejpam-4385	579	24	to	to	ADP
ejpam-4385	579	25	(	(	PUNCT
ejpam-4385	579	26	s	s	PROPN
ejpam-4385	579	27	,	,	PUNCT
ejpam-4385	579	28	rt	rt	PROPN
ejpam-4385	579	29	,	,	PUNCT
ejpam-4385	579	30	y	y	PROPN
ejpam-4385	579	31	)	)	PUNCT
ejpam-4385	579	32	7→	7→	NUM
ejpam-4385	579	33	p	p	NOUN
ejpam-4385	579	34	(	(	PUNCT
ejpam-4385	579	35	t	t	PROPN
ejpam-4385	579	36	,	,	PUNCT
ejpam-4385	579	37	rt	rt	PROPN
ejpam-4385	579	38	;	;	PUNCT
ejpam-4385	579	39	t+	t+	NOUN
ejpam-4385	579	40	s)v	s)v	NOUN
ejpam-4385	579	41	(	(	PUNCT
ejpam-4385	579	42	t+	t+	NOUN
ejpam-4385	579	43	s	s	NOUN
ejpam-4385	579	44	,	,	PUNCT
ejpam-4385	579	45	rt+s	rt+s	PROPN
ejpam-4385	579	46	,	,	PUNCT
ejpam-4385	579	47	y	y	NOUN
ejpam-4385	579	48	)	)	PUNCT
ejpam-4385	579	49	with	with	ADP
ejpam-4385	579	50	t	t	PROPN
ejpam-4385	579	51	∈	∈	PROPN
ejpam-4385	580	1	[	[	X
ejpam-4385	580	2	0	0	NUM
ejpam-4385	580	3	,	,	PUNCT
ejpam-4385	580	4	t	t	NOUN
ejpam-4385	580	5	]	]	PUNCT
ejpam-4385	580	6	and	and	CCONJ
ejpam-4385	580	7	xt	xt	X
ejpam-4385	580	8	=	=	SYM
ejpam-4385	580	9	x	x	SYM
ejpam-4385	580	10	∈	∈	PROPN
ejpam-4385	580	11	(	(	PUNCT
ejpam-4385	580	12	0,∞	0,∞	NOUN
ejpam-4385	580	13	)	)	PUNCT
ejpam-4385	580	14	given	give	VERB
ejpam-4385	580	15	and	and	CCONJ
ejpam-4385	580	16	fixed	fix	VERB
ejpam-4385	580	17	,	,	PUNCT
ejpam-4385	580	18	we	we	PRON
ejpam-4385	580	19	have	have	VERB
ejpam-4385	580	20	e[p	e[p	PROPN
ejpam-4385	580	21	(	(	PUNCT
ejpam-4385	580	22	t	t	PROPN
ejpam-4385	580	23	,	,	PUNCT
ejpam-4385	580	24	rt	rt	PROPN
ejpam-4385	580	25	;	;	PUNCT
ejpam-4385	580	26	t+	t+	NOUN
ejpam-4385	580	27	s)v	s)v	NOUN
ejpam-4385	580	28	(	(	PUNCT
ejpam-4385	580	29	t+	t+	NOUN
ejpam-4385	580	30	s	s	NOUN
ejpam-4385	580	31	,	,	PUNCT
ejpam-4385	580	32	rt+s	rt+s	PROPN
ejpam-4385	580	33	,	,	PUNCT
ejpam-4385	580	34	xt+s)|rt	xt+s)|rt	NOUN
ejpam-4385	580	35	]	]	X
ejpam-4385	580	36	=	=	SYM
ejpam-4385	580	37	v	v	X
ejpam-4385	580	38	(	(	PUNCT
ejpam-4385	580	39	t	t	PROPN
ejpam-4385	580	40	,	,	PUNCT
ejpam-4385	580	41	rt	rt	PROPN
ejpam-4385	580	42	,	,	PUNCT
ejpam-4385	580	43	x	x	NOUN
ejpam-4385	580	44	)	)	PUNCT
ejpam-4385	580	45	+	+	CCONJ
ejpam-4385	580	46	e	e	X
ejpam-4385	580	47	[	[	PUNCT
ejpam-4385	580	48	∫	∫	PROPN
ejpam-4385	580	49	s	s	PART
ejpam-4385	580	50	0	0	NUM
ejpam-4385	580	51	lxp	lxp	NOUN
ejpam-4385	580	52	(	(	PUNCT
ejpam-4385	580	53	t	t	PROPN
ejpam-4385	580	54	,	,	PUNCT
ejpam-4385	580	55	rt	rt	PROPN
ejpam-4385	580	56	;	;	PUNCT
ejpam-4385	580	57	t+	t+	NUM
ejpam-4385	580	58	v)v	v)v	ADV
ejpam-4385	580	59	(	(	PUNCT
ejpam-4385	580	60	t+	t+	NOUN
ejpam-4385	580	61	v	v	NOUN
ejpam-4385	580	62	,	,	PUNCT
ejpam-4385	580	63	rt+v	rt+v	PROPN
ejpam-4385	580	64	,	,	PUNCT
ejpam-4385	580	65	xxv)i(xt+v	xxv)i(xt+v	X
ejpam-4385	580	66	̸=	̸=	PROPN
ejpam-4385	580	67	b(t+	b(t+	VERB
ejpam-4385	580	68	v	v	NOUN
ejpam-4385	580	69	,	,	PUNCT
ejpam-4385	580	70	rt+v))dv|rt	rt+v))dv|rt	PROPN
ejpam-4385	580	71	]	]	PUNCT
ejpam-4385	580	72	+	+	NUM
ejpam-4385	580	73	e[m	e[m	PROPN
ejpam-4385	580	74	b	b	NOUN
ejpam-4385	580	75	s	s	ADP
ejpam-4385	580	76	|rt	|rt	NOUN
ejpam-4385	580	77	]	]	X
ejpam-4385	580	78	+	+	CCONJ
ejpam-4385	580	79	1	1	NUM
ejpam-4385	580	80	2	2	NUM
ejpam-4385	580	81	e	e	NOUN
ejpam-4385	580	82	[	[	PUNCT
ejpam-4385	580	83	∫	∫	PROPN
ejpam-4385	580	84	s	s	PART
ejpam-4385	580	85	0	0	NUM
ejpam-4385	580	86	p	p	NOUN
ejpam-4385	580	87	(	(	PUNCT
ejpam-4385	580	88	t	t	PROPN
ejpam-4385	580	89	,	,	PUNCT
ejpam-4385	580	90	rt	rt	PROPN
ejpam-4385	580	91	;	;	PUNCT
ejpam-4385	580	92	t+	t+	PUNCT
ejpam-4385	580	93	v)[vx(t+	v)[vx(t+	PROPN
ejpam-4385	580	94	v	v	NOUN
ejpam-4385	580	95	,	,	PUNCT
ejpam-4385	580	96	rt+v	rt+v	NOUN
ejpam-4385	580	97	,	,	PUNCT
ejpam-4385	580	98	xt+v+)−	xt+v+)−	NOUN
ejpam-4385	580	99	vx(t+	vx(t+	NOUN
ejpam-4385	580	100	v	v	NOUN
ejpam-4385	580	101	,	,	PUNCT
ejpam-4385	580	102	rt+v	rt+v	NOUN
ejpam-4385	580	103	,	,	PUNCT
ejpam-4385	580	104	xt+v−	xt+v−	PROPN
ejpam-4385	580	105	)	)	PUNCT
ejpam-4385	580	106	]	]	PUNCT
ejpam-4385	581	1	i(xt+v	i(xt+v	NOUN
ejpam-4385	581	2	=	=	PUNCT
ejpam-4385	581	3	b(t+	b(t+	VERB
ejpam-4385	581	4	v	v	NOUN
ejpam-4385	581	5	,	,	PUNCT
ejpam-4385	581	6	rt+v))dℓ	rt+v))dℓ	PROPN
ejpam-4385	581	7	b	b	NUM
ejpam-4385	581	8	v(x	v(x	NOUN
ejpam-4385	581	9	x)|rt	x)|rt	NOUN
ejpam-4385	581	10	]	]	X
ejpam-4385	581	11	(	(	PUNCT
ejpam-4385	581	12	64	64	NUM
ejpam-4385	581	13	)	)	PUNCT
ejpam-4385	581	14	where	where	SCONJ
ejpam-4385	581	15	m	m	PROPN
ejpam-4385	581	16	b	b	X
ejpam-4385	581	17	s	s	X
ejpam-4385	581	18	=	=	NOUN
ejpam-4385	581	19	∫	∫	PROPN
ejpam-4385	581	20	s	s	PART
ejpam-4385	581	21	0	0	NUM
ejpam-4385	581	22	[	[	PUNCT
ejpam-4385	581	23	σ1xt+vp	σ1xt+vp	PROPN
ejpam-4385	581	24	∂gµc	∂gµc	NOUN
ejpam-4385	581	25	∂x	∂x	PROPN
ejpam-4385	581	26	dwt+v	dwt+v	PROPN
ejpam-4385	581	27	+	+	PROPN
ejpam-4385	581	28	σ2	σ2	PROPN
ejpam-4385	581	29	g	g	NOUN
ejpam-4385	581	30	µc	µc	NOUN
ejpam-4385	581	31	∂p	∂p	PROPN
ejpam-4385	581	32	∂r	∂r	PROPN
ejpam-4385	581	33	dw̄t+v	dw̄t+v	NOUN
ejpam-4385	581	34	]	]	PUNCT
ejpam-4385	581	35	defines	define	VERB
ejpam-4385	581	36	a	a	DET
ejpam-4385	581	37	continuous	continuous	ADJ
ejpam-4385	581	38	local	local	ADJ
ejpam-4385	581	39	martingale	martingale	NOUN
ejpam-4385	581	40	for	for	ADP
ejpam-4385	581	41	s	s	X
ejpam-4385	581	42	∈	∈	PROPN
ejpam-4385	582	1	[	[	X
ejpam-4385	582	2	0	0	NUM
ejpam-4385	582	3	,	,	PUNCT
ejpam-4385	582	4	t	t	PROPN
ejpam-4385	582	5	−	−	PROPN
ejpam-4385	582	6	t	t	PROPN
ejpam-4385	582	7	]	]	PUNCT
ejpam-4385	582	8	and	and	CCONJ
ejpam-4385	582	9	ℓb	ℓb	NOUN
ejpam-4385	582	10	=	=	PUNCT
ejpam-4385	582	11	(	(	PUNCT
ejpam-4385	582	12	ℓbv)0≤v≤s	ℓbv)0≤v≤s	PROPN
ejpam-4385	582	13	is	be	AUX
ejpam-4385	582	14	the	the	DET
ejpam-4385	582	15	local	local	ADJ
ejpam-4385	582	16	time	time	NOUN
ejpam-4385	582	17	of	of	ADP
ejpam-4385	582	18	xx	xx	NUM
ejpam-4385	582	19	=	=	SYM
ejpam-4385	582	20	(	(	PUNCT
ejpam-4385	582	21	xt+v)0≤v≤s	xt+v)0≤v≤s	PROPN
ejpam-4385	582	22	on	on	ADP
ejpam-4385	582	23	the	the	DET
ejpam-4385	582	24	curve	curve	NOUN
ejpam-4385	582	25	bd	bd	PROPN
ejpam-4385	582	26	for	for	ADP
ejpam-4385	582	27	s	s	PROPN
ejpam-4385	582	28	∈	∈	PROPN
ejpam-4385	583	1	[	[	X
ejpam-4385	583	2	0	0	NUM
ejpam-4385	583	3	,	,	PUNCT
ejpam-4385	583	4	t	t	PROPN
ejpam-4385	583	5	−	−	PROPN
ejpam-4385	583	6	t	t	PROPN
ejpam-4385	583	7	]	]	PUNCT
ejpam-4385	583	8	.	.	PUNCT
ejpam-4385	584	1	since	since	SCONJ
ejpam-4385	584	2	the	the	DET
ejpam-4385	584	3	coefficients	coefficient	NOUN
ejpam-4385	584	4	of	of	ADP
ejpam-4385	584	5	the	the	DET
ejpam-4385	584	6	respective	respective	ADJ
ejpam-4385	584	7	wiener	wiener	NOUN
ejpam-4385	584	8	processes	process	NOUN
ejpam-4385	584	9	of	of	ADP
ejpam-4385	584	10	m	m	PROPN
ejpam-4385	584	11	b	b	PROPN
ejpam-4385	584	12	s	s	NOUN
ejpam-4385	584	13	are	be	AUX
ejpam-4385	584	14	finite	finite	ADJ
ejpam-4385	584	15	(	(	PUNCT
ejpam-4385	584	16	and	and	CCONJ
ejpam-4385	584	17	so	so	ADV
ejpam-4385	584	18	are	be	AUX
ejpam-4385	584	19	their	their	PRON
ejpam-4385	584	20	respective	respective	ADJ
ejpam-4385	584	21	squares	square	NOUN
ejpam-4385	584	22	)	)	PUNCT
ejpam-4385	584	23	and	and	CCONJ
ejpam-4385	584	24	that	that	DET
ejpam-4385	584	25	gµc	gµc	NOUN
ejpam-4385	584	26	and	and	CCONJ
ejpam-4385	584	27	p	p	NOUN
ejpam-4385	584	28	are	be	AUX
ejpam-4385	584	29	ft	ft	NOUN
ejpam-4385	584	30	-	-	PUNCT
ejpam-4385	584	31	adapted	adapt	VERB
ejpam-4385	584	32	,	,	PUNCT
ejpam-4385	584	33	hence	hence	ADV
ejpam-4385	584	34	we	we	PRON
ejpam-4385	584	35	have	have	VERB
ejpam-4385	584	36	e	e	NOUN
ejpam-4385	584	37	[	[	PUNCT
ejpam-4385	584	38	m	m	PROPN
ejpam-4385	584	39	b	b	NOUN
ejpam-4385	584	40	s	s	X
ejpam-4385	584	41	]	]	X
ejpam-4385	584	42	=	=	SYM
ejpam-4385	584	43	0	0	X
ejpam-4385	584	44	.	.	PUNCT
ejpam-4385	585	1	by	by	ADP
ejpam-4385	585	2	the	the	DET
ejpam-4385	585	3	smooth	smooth	ADJ
ejpam-4385	585	4	-	-	PUNCT
ejpam-4385	585	5	fit	fit	NOUN
ejpam-4385	585	6	property	property	NOUN
ejpam-4385	585	7	[	[	X
ejpam-4385	585	8	11	11	NUM
ejpam-4385	585	9	]	]	PUNCT
ejpam-4385	585	10	or	or	CCONJ
ejpam-4385	585	11	convexity	convexity	NOUN
ejpam-4385	585	12	of	of	ADP
ejpam-4385	585	13	v	v	NOUN
ejpam-4385	585	14	,	,	PUNCT
ejpam-4385	585	15	the	the	DET
ejpam-4385	585	16	last	last	ADJ
ejpam-4385	585	17	term	term	NOUN
ejpam-4385	585	18	in	in	ADP
ejpam-4385	585	19	(	(	PUNCT
ejpam-4385	585	20	64	64	NUM
ejpam-4385	585	21	)	)	PUNCT
ejpam-4385	585	22	vanishes	vanish	VERB
ejpam-4385	585	23	.	.	PUNCT
ejpam-4385	586	1	hence	hence	ADV
ejpam-4385	586	2	,	,	PUNCT
ejpam-4385	586	3	e	e	X
ejpam-4385	586	4	[	[	X
ejpam-4385	586	5	p	p	X
ejpam-4385	586	6	(	(	PUNCT
ejpam-4385	586	7	t	t	PROPN
ejpam-4385	586	8	,	,	PUNCT
ejpam-4385	586	9	rt	rt	PROPN
ejpam-4385	586	10	;	;	PUNCT
ejpam-4385	586	11	t+	t+	NOUN
ejpam-4385	586	12	s)v	s)v	NOUN
ejpam-4385	586	13	(	(	PUNCT
ejpam-4385	586	14	t+	t+	NOUN
ejpam-4385	586	15	s	s	NOUN
ejpam-4385	586	16	,	,	PUNCT
ejpam-4385	586	17	rt+s	rt+s	PROPN
ejpam-4385	586	18	,	,	PUNCT
ejpam-4385	586	19	xt+s)|rt	xt+s)|rt	NOUN
ejpam-4385	586	20	]	]	X
ejpam-4385	586	21	=	=	SYM
ejpam-4385	586	22	v	v	X
ejpam-4385	586	23	(	(	PUNCT
ejpam-4385	586	24	t	t	PROPN
ejpam-4385	586	25	,	,	PUNCT
ejpam-4385	586	26	rt	rt	PROPN
ejpam-4385	586	27	,	,	PUNCT
ejpam-4385	586	28	x	x	NOUN
ejpam-4385	586	29	)	)	PUNCT
ejpam-4385	587	1	+	+	CCONJ
ejpam-4385	587	2	∫	∫	PROPN
ejpam-4385	587	3	s	s	PART
ejpam-4385	587	4	0	0	NUM
ejpam-4385	587	5	e	e	NOUN
ejpam-4385	587	6	[	[	X
ejpam-4385	587	7	lxp	lxp	X
ejpam-4385	587	8	(	(	PUNCT
ejpam-4385	587	9	t	t	PROPN
ejpam-4385	587	10	,	,	PUNCT
ejpam-4385	587	11	rt	rt	PROPN
ejpam-4385	587	12	;	;	PUNCT
ejpam-4385	587	13	t+	t+	PUNCT
ejpam-4385	587	14	v)gµc(t+	v)gµc(t+	NOUN
ejpam-4385	587	15	v	v	ADP
ejpam-4385	587	16	,	,	PUNCT
ejpam-4385	587	17	xt+v)i(xt+v	xt+v)i(xt+v	PROPN
ejpam-4385	587	18	>	>	X
ejpam-4385	587	19	b(t+	b(t+	PROPN
ejpam-4385	587	20	v	v	NOUN
ejpam-4385	587	21	,	,	PUNCT
ejpam-4385	587	22	rt+v))|rt	rt+v))|rt	NOUN
ejpam-4385	587	23	]	]	X
ejpam-4385	587	24	dv	dv	PROPN
ejpam-4385	587	25	,	,	PUNCT
ejpam-4385	587	26	(	(	PUNCT
ejpam-4385	587	27	65	65	NUM
ejpam-4385	587	28	)	)	PUNCT
ejpam-4385	587	29	where	where	SCONJ
ejpam-4385	587	30	we	we	PRON
ejpam-4385	587	31	use	use	VERB
ejpam-4385	587	32	(	(	PUNCT
ejpam-4385	587	33	62	62	NUM
ejpam-4385	587	34	)	)	PUNCT
ejpam-4385	587	35	above	above	ADV
ejpam-4385	587	36	and	and	CCONJ
ejpam-4385	587	37	the	the	DET
ejpam-4385	587	38	fact	fact	NOUN
ejpam-4385	587	39	that	that	SCONJ
ejpam-4385	587	40	v	v	X
ejpam-4385	587	41	=	=	SYM
ejpam-4385	587	42	g	g	NOUN
ejpam-4385	587	43	in	in	ADP
ejpam-4385	587	44	the	the	DET
ejpam-4385	587	45	stopping	stopping	NOUN
ejpam-4385	587	46	set	set	VERB
ejpam-4385	587	47	d	d	NOUN
ejpam-4385	587	48	to	to	PART
ejpam-4385	587	49	obtain	obtain	VERB
ejpam-4385	587	50	the	the	DET
ejpam-4385	587	51	second	second	ADJ
ejpam-4385	587	52	term	term	NOUN
ejpam-4385	587	53	above	above	ADV
ejpam-4385	587	54	.	.	PUNCT
ejpam-4385	588	1	by	by	ADP
ejpam-4385	588	2	replacing	replace	VERB
ejpam-4385	588	3	s	s	PRON
ejpam-4385	588	4	by	by	ADP
ejpam-4385	588	5	t	t	PROPN
ejpam-4385	588	6	−	−	PROPN
ejpam-4385	588	7	t	t	PROPN
ejpam-4385	588	8	,	,	PUNCT
ejpam-4385	588	9	we	we	PRON
ejpam-4385	588	10	have	have	VERB
ejpam-4385	588	11	e	e	X
ejpam-4385	588	12	[	[	PUNCT
ejpam-4385	588	13	p	p	X
ejpam-4385	588	14	(	(	PUNCT
ejpam-4385	588	15	t	t	PROPN
ejpam-4385	588	16	,	,	PUNCT
ejpam-4385	588	17	rt;t	rt;t	PROPN
ejpam-4385	588	18	)	)	PUNCT
ejpam-4385	588	19	(	(	PUNCT
ejpam-4385	588	20	xt	xt	ADP
ejpam-4385	588	21	−k)+	−k)+	NOUN
ejpam-4385	588	22	]	]	PUNCT
ejpam-4385	589	1	=	=	SYM
ejpam-4385	589	2	v	v	X
ejpam-4385	589	3	(	(	PUNCT
ejpam-4385	589	4	t+	t+	NOUN
ejpam-4385	589	5	rt	rt	PROPN
ejpam-4385	589	6	,	,	PUNCT
ejpam-4385	589	7	x	x	NOUN
ejpam-4385	589	8	)	)	PUNCT
ejpam-4385	589	9	+	+	NUM
ejpam-4385	589	10	∫	∫	PROPN
ejpam-4385	589	11	t−t	t−t	PROPN
ejpam-4385	589	12	0	0	NUM
ejpam-4385	590	1	e	e	X
ejpam-4385	591	1	[	[	X
ejpam-4385	591	2	lp	lp	X
ejpam-4385	591	3	(	(	PUNCT
ejpam-4385	591	4	t	t	PROPN
ejpam-4385	591	5	,	,	PUNCT
ejpam-4385	591	6	rt	rt	PROPN
ejpam-4385	591	7	;	;	PUNCT
ejpam-4385	591	8	t+	t+	PUNCT
ejpam-4385	591	9	v)gµc(t+	v)gµc(t+	NOUN
ejpam-4385	591	10	v	v	ADP
ejpam-4385	591	11	,	,	PUNCT
ejpam-4385	591	12	xt+v)i(xt+v	xt+v)i(xt+v	PROPN
ejpam-4385	591	13	>	>	X
ejpam-4385	591	14	b(t+	b(t+	PROPN
ejpam-4385	591	15	v	v	NOUN
ejpam-4385	591	16	,	,	PUNCT
ejpam-4385	591	17	rt+v))|rt	rt+v))|rt	NOUN
ejpam-4385	591	18	]	]	X
ejpam-4385	591	19	dv	dv	PROPN
ejpam-4385	591	20	,	,	PUNCT
ejpam-4385	591	21	(	(	PUNCT
ejpam-4385	591	22	66	66	NUM
ejpam-4385	591	23	)	)	PUNCT
ejpam-4385	591	24	references	reference	NOUN
ejpam-4385	591	25	969	969	NUM
ejpam-4385	591	26	where	where	SCONJ
ejpam-4385	591	27	we	we	PRON
ejpam-4385	591	28	used	use	VERB
ejpam-4385	591	29	the	the	DET
ejpam-4385	591	30	fact	fact	NOUN
ejpam-4385	591	31	that	that	SCONJ
ejpam-4385	591	32	v	v	X
ejpam-4385	591	33	(	(	PUNCT
ejpam-4385	591	34	t	t	PROPN
ejpam-4385	591	35	,	,	PUNCT
ejpam-4385	591	36	rt	rt	PROPN
ejpam-4385	591	37	,	,	PUNCT
ejpam-4385	591	38	x	x	NOUN
ejpam-4385	591	39	)	)	PUNCT
ejpam-4385	591	40	=	=	SYM
ejpam-4385	591	41	gµc(t	gµc(t	PROPN
ejpam-4385	591	42	,	,	PUNCT
ejpam-4385	591	43	x	x	NOUN
ejpam-4385	591	44	)	)	PUNCT
ejpam-4385	591	45	=	=	SYM
ejpam-4385	591	46	(	(	PUNCT
ejpam-4385	591	47	x	x	X
ejpam-4385	591	48	−	−	PROPN
ejpam-4385	591	49	k)+	k)+	PROPN
ejpam-4385	591	50	.	.	PUNCT
ejpam-4385	592	1	recognizing	recognize	VERB
ejpam-4385	592	2	the	the	DET
ejpam-4385	592	3	lefthand	lefthand	PROPN
ejpam-4385	592	4	side	side	NOUN
ejpam-4385	592	5	of	of	ADP
ejpam-4385	592	6	(	(	PUNCT
ejpam-4385	592	7	66	66	NUM
ejpam-4385	592	8	)	)	PUNCT
ejpam-4385	592	9	above	above	ADV
ejpam-4385	592	10	as	as	ADP
ejpam-4385	592	11	the	the	DET
ejpam-4385	592	12	price	price	NOUN
ejpam-4385	592	13	p(t	p(t	NOUN
ejpam-4385	592	14	,	,	PUNCT
ejpam-4385	592	15	rt;t	rt;t	PROPN
ejpam-4385	592	16	)	)	PUNCT
ejpam-4385	592	17	of	of	ADP
ejpam-4385	592	18	the	the	DET
ejpam-4385	592	19	european	european	ADJ
ejpam-4385	592	20	call	call	NOUN
ejpam-4385	592	21	option	option	NOUN
ejpam-4385	592	22	under	under	ADP
ejpam-4385	592	23	stochastic	stochastic	ADJ
ejpam-4385	592	24	interest	interest	NOUN
ejpam-4385	592	25	rate	rate	NOUN
ejpam-4385	592	26	,	,	PUNCT
ejpam-4385	592	27	we	we	PRON
ejpam-4385	592	28	have	have	VERB
ejpam-4385	592	29	v	v	NUM
ejpam-4385	592	30	(	(	PUNCT
ejpam-4385	592	31	t	t	PROPN
ejpam-4385	592	32	,	,	PUNCT
ejpam-4385	592	33	rt	rt	PROPN
ejpam-4385	592	34	,	,	PUNCT
ejpam-4385	592	35	x	x	NOUN
ejpam-4385	592	36	)	)	PUNCT
ejpam-4385	592	37	=	=	SYM
ejpam-4385	592	38	p(t	p(t	NOUN
ejpam-4385	592	39	,	,	PUNCT
ejpam-4385	592	40	rt;t	rt;t	PROPN
ejpam-4385	592	41	)	)	PUNCT
ejpam-4385	593	1	+	+	CCONJ
ejpam-4385	593	2	∫	∫	PROPN
ejpam-4385	593	3	t	t	PROPN
ejpam-4385	593	4	t	t	PROPN
ejpam-4385	593	5	j(t	j(t	PROPN
ejpam-4385	593	6	,	,	PUNCT
ejpam-4385	593	7	rt	rt	PROPN
ejpam-4385	593	8	,	,	PUNCT
ejpam-4385	593	9	x	x	NOUN
ejpam-4385	593	10	,	,	PUNCT
ejpam-4385	593	11	v	v	NOUN
ejpam-4385	593	12	,	,	PUNCT
ejpam-4385	593	13	bd(v	bd(v	PUNCT
ejpam-4385	593	14	,	,	PUNCT
ejpam-4385	593	15	rv))dv	rv))dv	PROPN
ejpam-4385	593	16	.	.	PUNCT
ejpam-4385	594	1	moreover	moreover	ADV
ejpam-4385	594	2	,	,	PUNCT
ejpam-4385	594	3	since	since	SCONJ
ejpam-4385	594	4	v	v	NOUN
ejpam-4385	594	5	(	(	PUNCT
ejpam-4385	594	6	t	t	PROPN
ejpam-4385	594	7	,	,	PUNCT
ejpam-4385	594	8	rt	rt	PROPN
ejpam-4385	594	9	,	,	PUNCT
ejpam-4385	594	10	x	x	NOUN
ejpam-4385	594	11	)	)	PUNCT
ejpam-4385	594	12	=	=	SYM
ejpam-4385	594	13	gµc(t	gµc(t	PROPN
ejpam-4385	594	14	,	,	PUNCT
ejpam-4385	594	15	x	x	NOUN
ejpam-4385	594	16	)	)	PUNCT
ejpam-4385	594	17	for	for	ADP
ejpam-4385	594	18	all	all	PRON
ejpam-4385	594	19	(	(	PUNCT
ejpam-4385	594	20	t	t	PROPN
ejpam-4385	594	21	,	,	PUNCT
ejpam-4385	594	22	rt	rt	PROPN
ejpam-4385	594	23	,	,	PUNCT
ejpam-4385	594	24	x	x	NOUN
ejpam-4385	594	25	)	)	PUNCT
ejpam-4385	594	26	∈	∈	PROPN
ejpam-4385	595	1	d	d	NOUN
ejpam-4385	595	2	,	,	PUNCT
ejpam-4385	595	3	we	we	PRON
ejpam-4385	595	4	have	have	VERB
ejpam-4385	595	5	v	v	NUM
ejpam-4385	595	6	(	(	PUNCT
ejpam-4385	595	7	t	t	PROPN
ejpam-4385	595	8	,	,	PUNCT
ejpam-4385	595	9	rt	rt	PROPN
ejpam-4385	595	10	,	,	PUNCT
ejpam-4385	595	11	bd(t	bd(t	PROPN
ejpam-4385	595	12	,	,	PUNCT
ejpam-4385	595	13	rt	rt	PROPN
ejpam-4385	595	14	)	)	PUNCT
ejpam-4385	595	15	)	)	PUNCT
ejpam-4385	596	1	=	=	SYM
ejpam-4385	596	2	gµc(t	gµc(t	NOUN
ejpam-4385	596	3	,	,	PUNCT
ejpam-4385	596	4	bd(t	bd(t	NOUN
ejpam-4385	596	5	,	,	PUNCT
ejpam-4385	596	6	rt	rt	PROPN
ejpam-4385	596	7	)	)	PUNCT
ejpam-4385	596	8	)	)	PUNCT
ejpam-4385	596	9	.	.	PUNCT
ejpam-4385	597	1	this	this	PRON
ejpam-4385	597	2	implies	imply	VERB
ejpam-4385	597	3	that	that	SCONJ
ejpam-4385	597	4	the	the	DET
ejpam-4385	597	5	boundary	boundary	ADJ
ejpam-4385	597	6	functiom	functiom	NOUN
ejpam-4385	597	7	bd	bd	PROPN
ejpam-4385	597	8	solves	solve	VERB
ejpam-4385	597	9	equation	equation	NOUN
ejpam-4385	597	10	(	(	PUNCT
ejpam-4385	597	11	60	60	NUM
ejpam-4385	597	12	)	)	PUNCT
ejpam-4385	597	13	.	.	PUNCT
ejpam-4385	598	1	this	this	PRON
ejpam-4385	598	2	establishes	establish	VERB
ejpam-4385	598	3	the	the	DET
ejpam-4385	598	4	existence	existence	NOUN
ejpam-4385	598	5	of	of	ADP
ejpam-4385	598	6	the	the	DET
ejpam-4385	598	7	solution	solution	NOUN
ejpam-4385	598	8	to	to	ADP
ejpam-4385	598	9	(	(	PUNCT
ejpam-4385	598	10	60	60	NUM
ejpam-4385	598	11	)	)	PUNCT
ejpam-4385	598	12	.	.	PUNCT
ejpam-4385	599	1	the	the	DET
ejpam-4385	599	2	uniqueness	uniqueness	NOUN
ejpam-4385	599	3	of	of	ADP
ejpam-4385	599	4	this	this	DET
ejpam-4385	599	5	solution	solution	NOUN
ejpam-4385	599	6	can	can	AUX
ejpam-4385	599	7	be	be	AUX
ejpam-4385	599	8	shown	show	VERB
ejpam-4385	599	9	parallel	parallel	NOUN
ejpam-4385	599	10	to	to	ADP
ejpam-4385	599	11	the	the	DET
ejpam-4385	599	12	proof	proof	NOUN
ejpam-4385	599	13	in	in	ADP
ejpam-4385	599	14	[	[	X
ejpam-4385	599	15	11	11	NUM
ejpam-4385	599	16	]	]	PUNCT
ejpam-4385	599	17	.	.	PUNCT
ejpam-4385	600	1	acknowledgements	acknowledgement	NOUN
ejpam-4385	600	2	this	this	DET
ejpam-4385	600	3	research	research	NOUN
ejpam-4385	600	4	is	be	AUX
ejpam-4385	600	5	funded	fund	VERB
ejpam-4385	600	6	by	by	ADP
ejpam-4385	600	7	the	the	DET
ejpam-4385	600	8	commission	commission	NOUN
ejpam-4385	600	9	on	on	ADP
ejpam-4385	600	10	higher	high	ADJ
ejpam-4385	600	11	education	education	NOUN
ejpam-4385	600	12	(	(	PUNCT
ejpam-4385	600	13	ched	che	VERB
ejpam-4385	600	14	)	)	PUNCT
ejpam-4385	600	15	under	under	ADP
ejpam-4385	600	16	the	the	DET
ejpam-4385	600	17	ched	che	VERB
ejpam-4385	600	18	k-12	k-12	PROPN
ejpam-4385	600	19	transition	transition	NOUN
ejpam-4385	600	20	program	program	NOUN
ejpam-4385	600	21	and	and	CCONJ
ejpam-4385	600	22	the	the	DET
ejpam-4385	600	23	ateneo	ateneo	PROPN
ejpam-4385	600	24	de	de	PROPN
ejpam-4385	600	25	zamboanga	zamboanga	PROPN
ejpam-4385	600	26	university	university	PROPN
ejpam-4385	600	27	faculty	faculty	PROPN
ejpam-4385	600	28	development	development	NOUN
ejpam-4385	600	29	program	program	NOUN
ejpam-4385	600	30	.	.	PUNCT
ejpam-4385	601	1	references	reference	NOUN
ejpam-4385	601	2	[	[	X
ejpam-4385	601	3	1	1	NUM
ejpam-4385	601	4	]	]	PUNCT
ejpam-4385	601	5	laura	laura	NOUN
ejpam-4385	601	6	ballotta	ballotta	PROPN
ejpam-4385	601	7	and	and	CCONJ
ejpam-4385	601	8	gianluca	gianluca	PROPN
ejpam-4385	601	9	fusai	fusai	PROPN
ejpam-4385	601	10	.	.	PUNCT
ejpam-4385	602	1	tools	tool	NOUN
ejpam-4385	602	2	from	from	ADP
ejpam-4385	602	3	stochastic	stochastic	ADJ
ejpam-4385	602	4	analysis	analysis	NOUN
ejpam-4385	602	5	for	for	ADP
ejpam-4385	602	6	mathematical	mathematical	ADJ
ejpam-4385	602	7	finance	finance	NOUN
ejpam-4385	602	8	:	:	PUNCT
ejpam-4385	602	9	a	a	DET
ejpam-4385	602	10	gentle	gentle	ADJ
ejpam-4385	602	11	introduction	introduction	NOUN
ejpam-4385	602	12	.	.	PUNCT
ejpam-4385	603	1	available	available	ADJ
ejpam-4385	603	2	at	at	ADP
ejpam-4385	603	3	ssrn	ssrn	NOUN
ejpam-4385	603	4	3183712	3183712	NUM
ejpam-4385	603	5	,	,	PUNCT
ejpam-4385	603	6	2018	2018	NUM
ejpam-4385	603	7	.	.	PUNCT
ejpam-4385	604	1	[	[	X
ejpam-4385	604	2	2	2	NUM
ejpam-4385	604	3	]	]	PUNCT
ejpam-4385	604	4	tomas	tomas	PROPN
ejpam-4385	604	5	björk	björk	PROPN
ejpam-4385	604	6	.	.	PUNCT
ejpam-4385	605	1	arbitrage	arbitrage	NOUN
ejpam-4385	605	2	theory	theory	NOUN
ejpam-4385	605	3	in	in	ADP
ejpam-4385	605	4	continuous	continuous	ADJ
ejpam-4385	605	5	time	time	NOUN
ejpam-4385	605	6	.	.	PUNCT
ejpam-4385	606	1	oxford	oxford	PROPN
ejpam-4385	606	2	university	university	PROPN
ejpam-4385	606	3	press	press	NOUN
ejpam-4385	606	4	,	,	PUNCT
ejpam-4385	606	5	2009	2009	NUM
ejpam-4385	606	6	.	.	PUNCT
ejpam-4385	607	1	[	[	X
ejpam-4385	607	2	3	3	X
ejpam-4385	607	3	]	]	X
ejpam-4385	607	4	john	john	PROPN
ejpam-4385	607	5	c	c	PROPN
ejpam-4385	607	6	cox	cox	PROPN
ejpam-4385	607	7	,	,	PUNCT
ejpam-4385	607	8	jonathan	jonathan	PROPN
ejpam-4385	607	9	e	e	PROPN
ejpam-4385	607	10	ingersoll	ingersoll	PROPN
ejpam-4385	607	11	,	,	PUNCT
ejpam-4385	607	12	and	and	CCONJ
ejpam-4385	607	13	stephen	stephen	VERB
ejpam-4385	607	14	a	a	DET
ejpam-4385	607	15	ross	ross	PROPN
ejpam-4385	607	16	.	.	PUNCT
ejpam-4385	608	1	a	a	DET
ejpam-4385	608	2	theory	theory	NOUN
ejpam-4385	608	3	of	of	ADP
ejpam-4385	608	4	the	the	DET
ejpam-4385	608	5	term	term	NOUN
ejpam-4385	608	6	structure	structure	NOUN
ejpam-4385	608	7	ofinterest	ofinter	ADJ
ejpam-4385	608	8	rates	rate	NOUN
ejpam-4385	608	9	.	.	PUNCT
ejpam-4385	609	1	research	research	NOUN
ejpam-4385	609	2	paper	paper	NOUN
ejpam-4385	609	3	,	,	PUNCT
ejpam-4385	609	4	graduate	graduate	NOUN
ejpam-4385	609	5	school	school	NOUN
ejpam-4385	609	6	of	of	ADP
ejpam-4385	609	7	business	business	NOUN
ejpam-4385	609	8	,	,	PUNCT
ejpam-4385	609	9	stanford	stanford	PROPN
ejpam-4385	609	10	univ	univ	PROPN
ejpam-4385	609	11	,	,	PUNCT
ejpam-4385	609	12	1978	1978	NUM
ejpam-4385	609	13	.	.	PUNCT
ejpam-4385	610	1	[	[	X
ejpam-4385	610	2	4	4	X
ejpam-4385	610	3	]	]	X
ejpam-4385	610	4	samuel	samuel	PROPN
ejpam-4385	610	5	h	h	PROPN
ejpam-4385	610	6	cox	cox	PROPN
ejpam-4385	610	7	and	and	CCONJ
ejpam-4385	610	8	gennady	gennady	PROPN
ejpam-4385	610	9	medvedev	medvedev	PROPN
ejpam-4385	610	10	.	.	PUNCT
ejpam-4385	611	1	the	the	DET
ejpam-4385	611	2	market	market	NOUN
ejpam-4385	611	3	price	price	NOUN
ejpam-4385	611	4	of	of	ADP
ejpam-4385	611	5	risk	risk	NOUN
ejpam-4385	611	6	for	for	ADP
ejpam-4385	611	7	affine	affine	NOUN
ejpam-4385	611	8	interest	interest	NOUN
ejpam-4385	611	9	rate	rate	NOUN
ejpam-4385	611	10	term	term	NOUN
ejpam-4385	611	11	structures	structure	NOUN
ejpam-4385	611	12	.	.	PUNCT
ejpam-4385	612	1	in	in	ADP
ejpam-4385	612	2	6th	6th	ADJ
ejpam-4385	612	3	international	international	ADJ
ejpam-4385	612	4	afir	afir	NOUN
ejpam-4385	612	5	-	-	PUNCT
ejpam-4385	612	6	colloquium	colloquium	NOUN
ejpam-4385	612	7	,	,	PUNCT
ejpam-4385	612	8	pages	page	NOUN
ejpam-4385	612	9	913–924	913–924	NUM
ejpam-4385	612	10	,	,	PUNCT
ejpam-4385	612	11	1996	1996	NUM
ejpam-4385	612	12	.	.	PUNCT
ejpam-4385	613	1	[	[	X
ejpam-4385	613	2	5	5	X
ejpam-4385	613	3	]	]	PUNCT
ejpam-4385	613	4	john	john	PROPN
ejpam-4385	613	5	c	c	PROPN
ejpam-4385	613	6	hull	hull	PROPN
ejpam-4385	613	7	.	.	PUNCT
ejpam-4385	614	1	options	option	NOUN
ejpam-4385	614	2	futures	future	NOUN
ejpam-4385	614	3	and	and	CCONJ
ejpam-4385	614	4	other	other	ADJ
ejpam-4385	614	5	derivatives	derivative	NOUN
ejpam-4385	614	6	.	.	PUNCT
ejpam-4385	615	1	pearson	pearson	PROPN
ejpam-4385	615	2	education	education	PROPN
ejpam-4385	615	3	india	india	PROPN
ejpam-4385	615	4	,	,	PUNCT
ejpam-4385	615	5	2003	2003	NUM
ejpam-4385	615	6	.	.	PUNCT
ejpam-4385	616	1	[	[	X
ejpam-4385	616	2	6	6	NUM
ejpam-4385	616	3	]	]	X
ejpam-4385	616	4	yong	yong	PROPN
ejpam-4385	616	5	-	-	PUNCT
ejpam-4385	616	6	jin	jin	PROPN
ejpam-4385	616	7	kim	kim	PROPN
ejpam-4385	616	8	.	.	PUNCT
ejpam-4385	617	1	option	option	NOUN
ejpam-4385	617	2	pricing	pricing	NOUN
ejpam-4385	617	3	under	under	ADP
ejpam-4385	617	4	stochastic	stochastic	ADJ
ejpam-4385	617	5	interest	interest	NOUN
ejpam-4385	617	6	rates	rate	NOUN
ejpam-4385	617	7	:	:	PUNCT
ejpam-4385	617	8	an	an	DET
ejpam-4385	617	9	empirical	empirical	ADJ
ejpam-4385	617	10	investigation	investigation	NOUN
ejpam-4385	617	11	.	.	PUNCT
ejpam-4385	618	1	asia	asia	PROPN
ejpam-4385	618	2	-	-	PUNCT
ejpam-4385	618	3	pacific	pacific	ADJ
ejpam-4385	618	4	financial	financial	ADJ
ejpam-4385	618	5	markets	market	NOUN
ejpam-4385	618	6	,	,	PUNCT
ejpam-4385	618	7	9(1):23–44	9(1):23–44	NUM
ejpam-4385	618	8	,	,	PUNCT
ejpam-4385	618	9	2002	2002	NUM
ejpam-4385	618	10	.	.	PUNCT
ejpam-4385	619	1	[	[	X
ejpam-4385	619	2	7	7	X
ejpam-4385	619	3	]	]	X
ejpam-4385	619	4	elvira	elvira	PROPN
ejpam-4385	619	5	p	p	PROPN
ejpam-4385	619	6	de	de	PROPN
ejpam-4385	619	7	lara	lara	PROPN
ejpam-4385	619	8	-	-	PUNCT
ejpam-4385	619	9	tuprio	tuprio	PROPN
ejpam-4385	619	10	and	and	CCONJ
ejpam-4385	619	11	felipe	felipe	PROPN
ejpam-4385	619	12	r	r	PROPN
ejpam-4385	619	13	sumalpong	sumalpong	PROPN
ejpam-4385	619	14	.	.	PUNCT
ejpam-4385	620	1	british	british	PROPN
ejpam-4385	620	2	put	put	VERB
ejpam-4385	620	3	option	option	NOUN
ejpam-4385	620	4	on	on	ADP
ejpam-4385	620	5	stocks	stock	NOUN
ejpam-4385	620	6	under	under	ADP
ejpam-4385	620	7	stochastic	stochastic	ADJ
ejpam-4385	620	8	interest	interest	NOUN
ejpam-4385	620	9	rate	rate	NOUN
ejpam-4385	620	10	.	.	PUNCT
ejpam-4385	621	1	model	model	PROPN
ejpam-4385	621	2	assisted	assist	VERB
ejpam-4385	621	3	statistics	statistic	NOUN
ejpam-4385	621	4	and	and	CCONJ
ejpam-4385	621	5	applications	application	NOUN
ejpam-4385	621	6	,	,	PUNCT
ejpam-4385	621	7	12(4):321–334	12(4):321–334	PROPN
ejpam-4385	621	8	,	,	PUNCT
ejpam-4385	621	9	2017	2017	NUM
ejpam-4385	621	10	.	.	PUNCT
ejpam-4385	622	1	[	[	X
ejpam-4385	622	2	8	8	NUM
ejpam-4385	622	3	]	]	X
ejpam-4385	622	4	rogemar	rogemar	PROPN
ejpam-4385	622	5	s	s	PART
ejpam-4385	622	6	mamon	mamon	NOUN
ejpam-4385	622	7	.	.	PUNCT
ejpam-4385	623	1	three	three	NUM
ejpam-4385	623	2	ways	way	NOUN
ejpam-4385	623	3	to	to	PART
ejpam-4385	623	4	solve	solve	VERB
ejpam-4385	623	5	for	for	ADP
ejpam-4385	623	6	bond	bond	NOUN
ejpam-4385	623	7	prices	price	NOUN
ejpam-4385	623	8	in	in	ADP
ejpam-4385	623	9	the	the	DET
ejpam-4385	623	10	vasicek	vasicek	PROPN
ejpam-4385	623	11	model	model	NOUN
ejpam-4385	623	12	.	.	PUNCT
ejpam-4385	624	1	advances	advance	NOUN
ejpam-4385	624	2	in	in	ADP
ejpam-4385	624	3	decision	decision	NOUN
ejpam-4385	624	4	sciences	science	NOUN
ejpam-4385	624	5	,	,	PUNCT
ejpam-4385	624	6	8(1):1–14	8(1):1–14	PROPN
ejpam-4385	624	7	,	,	PUNCT
ejpam-4385	624	8	2004	2004	NUM
ejpam-4385	624	9	.	.	PUNCT
ejpam-4385	625	1	[	[	X
ejpam-4385	625	2	9	9	NUM
ejpam-4385	625	3	]	]	X
ejpam-4385	625	4	goran	goran	NOUN
ejpam-4385	625	5	peskir	peskir	NOUN
ejpam-4385	625	6	.	.	PUNCT
ejpam-4385	626	1	a	a	DET
ejpam-4385	626	2	change	change	NOUN
ejpam-4385	626	3	-	-	PUNCT
ejpam-4385	626	4	of	of	ADP
ejpam-4385	626	5	-	-	PUNCT
ejpam-4385	626	6	variable	variable	ADJ
ejpam-4385	626	7	formula	formula	NOUN
ejpam-4385	626	8	with	with	ADP
ejpam-4385	626	9	local	local	ADJ
ejpam-4385	626	10	time	time	NOUN
ejpam-4385	626	11	on	on	ADP
ejpam-4385	626	12	surfaces	surface	NOUN
ejpam-4385	626	13	.	.	PUNCT
ejpam-4385	627	1	in	in	ADP
ejpam-4385	627	2	séminaire	séminaire	PROPN
ejpam-4385	627	3	de	de	PROPN
ejpam-4385	627	4	probabilités	probabilités	PROPN
ejpam-4385	627	5	xl	xl	PROPN
ejpam-4385	627	6	,	,	PUNCT
ejpam-4385	627	7	pages	page	NOUN
ejpam-4385	627	8	70–96	70–96	NUM
ejpam-4385	627	9	.	.	PUNCT
ejpam-4385	627	10	springer	springer	NOUN
ejpam-4385	627	11	,	,	PUNCT
ejpam-4385	627	12	2007	2007	NUM
ejpam-4385	627	13	.	.	PUNCT
ejpam-4385	628	1	references	reference	NOUN
ejpam-4385	628	2	970	970	NUM
ejpam-4385	628	3	[	[	X
ejpam-4385	628	4	10	10	NUM
ejpam-4385	628	5	]	]	X
ejpam-4385	628	6	goran	goran	NOUN
ejpam-4385	628	7	peskir	peskir	PROPN
ejpam-4385	628	8	and	and	CCONJ
ejpam-4385	628	9	farman	farman	PROPN
ejpam-4385	628	10	samee	samee	PROPN
ejpam-4385	628	11	.	.	PUNCT
ejpam-4385	629	1	the	the	DET
ejpam-4385	629	2	british	british	ADJ
ejpam-4385	629	3	put	put	VERB
ejpam-4385	629	4	option	option	NOUN
ejpam-4385	629	5	.	.	PUNCT
ejpam-4385	630	1	applied	apply	VERB
ejpam-4385	630	2	mathematical	mathematical	ADJ
ejpam-4385	630	3	finance	finance	NOUN
ejpam-4385	630	4	,	,	PUNCT
ejpam-4385	630	5	18(6):537–563	18(6):537–563	PROPN
ejpam-4385	630	6	,	,	PUNCT
ejpam-4385	630	7	2011	2011	NUM
ejpam-4385	630	8	.	.	PUNCT
ejpam-4385	631	1	[	[	X
ejpam-4385	631	2	11	11	NUM
ejpam-4385	631	3	]	]	X
ejpam-4385	631	4	goran	goran	NOUN
ejpam-4385	631	5	peskir	peskir	PROPN
ejpam-4385	631	6	and	and	CCONJ
ejpam-4385	631	7	farman	farman	PROPN
ejpam-4385	631	8	samee	samee	PROPN
ejpam-4385	631	9	.	.	PUNCT
ejpam-4385	632	1	the	the	DET
ejpam-4385	632	2	british	british	ADJ
ejpam-4385	632	3	call	call	NOUN
ejpam-4385	632	4	option	option	NOUN
ejpam-4385	632	5	.	.	PUNCT
ejpam-4385	633	1	quantitative	quantitative	ADJ
ejpam-4385	633	2	finance	finance	NOUN
ejpam-4385	633	3	,	,	PUNCT
ejpam-4385	633	4	13(1):95–109	13(1):95–109	NUM
ejpam-4385	633	5	,	,	PUNCT
ejpam-4385	633	6	2013	2013	NUM
ejpam-4385	633	7	.	.	PUNCT
ejpam-4385	634	1	[	[	X
ejpam-4385	634	2	12	12	NUM
ejpam-4385	634	3	]	]	X
ejpam-4385	634	4	goran	goran	NOUN
ejpam-4385	634	5	peskir	peskir	PROPN
ejpam-4385	634	6	and	and	CCONJ
ejpam-4385	634	7	albert	albert	PROPN
ejpam-4385	634	8	shiryaev	shiryaev	PROPN
ejpam-4385	634	9	.	.	PUNCT
ejpam-4385	635	1	optimal	optimal	ADJ
ejpam-4385	635	2	stopping	stopping	NOUN
ejpam-4385	635	3	and	and	CCONJ
ejpam-4385	635	4	free	free	ADJ
ejpam-4385	635	5	-	-	PUNCT
ejpam-4385	635	6	boundary	boundary	NOUN
ejpam-4385	635	7	problems	problem	NOUN
ejpam-4385	635	8	.	.	PUNCT
ejpam-4385	636	1	springer	springer	NOUN
ejpam-4385	636	2	,	,	PUNCT
ejpam-4385	636	3	2006	2006	NUM
ejpam-4385	636	4	.	.	PUNCT
ejpam-4385	637	1	[	[	X
ejpam-4385	637	2	13	13	NUM
ejpam-4385	637	3	]	]	PUNCT
ejpam-4385	637	4	andras	andras	PROPN
ejpam-4385	637	5	vanyolos	vanyolo	NOUN
ejpam-4385	637	6	,	,	PUNCT
ejpam-4385	637	7	maxx	maxx	PROPN
ejpam-4385	637	8	cho	cho	PROPN
ejpam-4385	637	9	,	,	PUNCT
ejpam-4385	637	10	and	and	CCONJ
ejpam-4385	637	11	scott	scott	PROPN
ejpam-4385	637	12	alan	alan	PROPN
ejpam-4385	637	13	glasgow	glasgow	PROPN
ejpam-4385	637	14	.	.	PUNCT
ejpam-4385	638	1	probability	probability	NOUN
ejpam-4385	638	2	density	density	NOUN
ejpam-4385	638	3	of	of	ADP
ejpam-4385	638	4	the	the	DET
ejpam-4385	638	5	cir	cir	PROPN
ejpam-4385	638	6	model	model	PROPN
ejpam-4385	638	7	.	.	PUNCT
ejpam-4385	639	1	available	available	ADJ
ejpam-4385	639	2	at	at	ADP
ejpam-4385	639	3	ssrn	ssrn	NOUN
ejpam-4385	639	4	2508699	2508699	NUM
ejpam-4385	639	5	,	,	PUNCT
ejpam-4385	639	6	2014	2014	NUM
ejpam-4385	639	7	.	.	PUNCT
ejpam-4385	640	1	[	[	X
ejpam-4385	640	2	14	14	NUM
ejpam-4385	640	3	]	]	X
ejpam-4385	640	4	duc	duc	PROPN
ejpam-4385	640	5	hong	hong	PROPN
ejpam-4385	640	6	vo	vo	PROPN
ejpam-4385	640	7	,	,	PUNCT
ejpam-4385	640	8	son	son	NOUN
ejpam-4385	640	9	van	van	PROPN
ejpam-4385	640	10	huynh	huynh	PROPN
ejpam-4385	640	11	,	,	PUNCT
ejpam-4385	640	12	anh	anh	NOUN
ejpam-4385	640	13	the	the	DET
ejpam-4385	640	14	vo	vo	NOUN
ejpam-4385	640	15	,	,	PUNCT
ejpam-4385	640	16	and	and	CCONJ
ejpam-4385	640	17	dao	dao	VERB
ejpam-4385	640	18	thi	thi	VERB
ejpam-4385	640	19	-	-	PUNCT
ejpam-4385	640	20	thieu	thieu	NOUN
ejpam-4385	640	21	ha	ha	INTJ
ejpam-4385	640	22	.	.	PUNCT
ejpam-4385	641	1	the	the	DET
ejpam-4385	641	2	importance	importance	NOUN
ejpam-4385	641	3	of	of	ADP
ejpam-4385	641	4	the	the	DET
ejpam-4385	641	5	financial	financial	ADJ
ejpam-4385	641	6	derivatives	derivative	NOUN
ejpam-4385	641	7	markets	market	NOUN
ejpam-4385	641	8	to	to	ADP
ejpam-4385	641	9	economic	economic	ADJ
ejpam-4385	641	10	development	development	NOUN
ejpam-4385	641	11	in	in	ADP
ejpam-4385	641	12	the	the	DET
ejpam-4385	641	13	world	world	NOUN
ejpam-4385	641	14	’s	’s	PART
ejpam-4385	641	15	four	four	NUM
ejpam-4385	641	16	major	major	ADJ
ejpam-4385	641	17	economies	economy	NOUN
ejpam-4385	641	18	.	.	PUNCT
ejpam-4385	642	1	journal	journal	NOUN
ejpam-4385	642	2	of	of	ADP
ejpam-4385	642	3	risk	risk	NOUN
ejpam-4385	642	4	and	and	CCONJ
ejpam-4385	642	5	financial	financial	ADJ
ejpam-4385	642	6	management	management	NOUN
ejpam-4385	642	7	,	,	PUNCT
ejpam-4385	642	8	12(1):35	12(1):35	NUM
ejpam-4385	642	9	,	,	PUNCT
ejpam-4385	642	10	2019	2019	NUM
ejpam-4385	642	11	.	.	PUNCT
ejpam-4385	643	1	[	[	X
ejpam-4385	643	2	15	15	NUM
ejpam-4385	643	3	]	]	X
ejpam-4385	643	4	david	david	PROPN
ejpam-4385	643	5	d	d	PROPN
ejpam-4385	643	6	yao	yao	PROPN
ejpam-4385	643	7	,	,	PUNCT
ejpam-4385	643	8	qing	qing	PROPN
ejpam-4385	643	9	zhang	zhang	PROPN
ejpam-4385	643	10	,	,	PUNCT
ejpam-4385	643	11	and	and	CCONJ
ejpam-4385	643	12	xun	xun	PROPN
ejpam-4385	643	13	yu	yu	PROPN
ejpam-4385	643	14	zhou	zhou	PROPN
ejpam-4385	643	15	.	.	PUNCT
ejpam-4385	644	1	a	a	DET
ejpam-4385	644	2	regime	regime	NOUN
ejpam-4385	644	3	-	-	PUNCT
ejpam-4385	644	4	switching	switch	VERB
ejpam-4385	644	5	model	model	NOUN
ejpam-4385	644	6	for	for	ADP
ejpam-4385	644	7	european	european	ADJ
ejpam-4385	644	8	options	option	NOUN
ejpam-4385	644	9	.	.	PUNCT
ejpam-4385	645	1	in	in	ADP
ejpam-4385	645	2	stochastic	stochastic	ADJ
ejpam-4385	645	3	processes	process	NOUN
ejpam-4385	645	4	,	,	PUNCT
ejpam-4385	645	5	optimization	optimization	NOUN
ejpam-4385	645	6	,	,	PUNCT
ejpam-4385	645	7	and	and	CCONJ
ejpam-4385	645	8	control	control	NOUN
ejpam-4385	645	9	theory	theory	NOUN
ejpam-4385	645	10	:	:	PUNCT
ejpam-4385	645	11	applications	application	NOUN
ejpam-4385	645	12	in	in	ADP
ejpam-4385	645	13	financial	financial	ADJ
ejpam-4385	645	14	engineering	engineering	NOUN
ejpam-4385	645	15	,	,	PUNCT
ejpam-4385	645	16	queueing	queue	VERB
ejpam-4385	645	17	networks	network	NOUN
ejpam-4385	645	18	,	,	PUNCT
ejpam-4385	645	19	and	and	CCONJ
ejpam-4385	645	20	manufacturing	manufacturing	NOUN
ejpam-4385	645	21	systems	system	NOUN
ejpam-4385	645	22	,	,	PUNCT
ejpam-4385	645	23	pages	page	NOUN
ejpam-4385	645	24	281–300	281–300	NUM
ejpam-4385	645	25	.	.	PUNCT
ejpam-4385	645	26	springer	springer	NOUN
ejpam-4385	645	27	,	,	PUNCT
ejpam-4385	645	28	2006	2006	NUM
ejpam-4385	645	29	.	.	PUNCT