id	sid	tid	token	lemma	pos
ejpam-846	1	1	european	european	PROPN
ejpam-846	1	2	journal	journal	PROPN
ejpam-846	1	3	of	of	ADP
ejpam-846	1	4	pure	pure	ADJ
ejpam-846	1	5	and	and	CCONJ
ejpam-846	1	6	applied	apply	VERB
ejpam-846	1	7	mathematics	mathematic	NOUN
ejpam-846	1	8	vol	vol	NOUN
ejpam-846	1	9	.	.	PUNCT
ejpam-846	2	1	3	3	NUM
ejpam-846	2	2	,	,	PUNCT
ejpam-846	2	3	no	no	INTJ
ejpam-846	2	4	.	.	NOUN
ejpam-846	2	5	3	3	NUM
ejpam-846	2	6	,	,	PUNCT
ejpam-846	2	7	2010	2010	NUM
ejpam-846	2	8	,	,	PUNCT
ejpam-846	2	9	572	572	NUM
ejpam-846	2	10	-	-	SYM
ejpam-846	2	11	592	592	NUM
ejpam-846	2	12	issn	issn	PROPN
ejpam-846	2	13	1307	1307	NUM
ejpam-846	2	14	-	-	SYM
ejpam-846	2	15	5543	5543	NUM
ejpam-846	2	16	–	–	PUNCT
ejpam-846	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-846	2	18	special	special	ADJ
ejpam-846	2	19	issue	issue	NOUN
ejpam-846	2	20	on	on	ADP
ejpam-846	2	21	granger	granger	PROPN
ejpam-846	2	22	econometrics	econometric	NOUN
ejpam-846	2	23	and	and	CCONJ
ejpam-846	2	24	statistical	statistical	ADJ
ejpam-846	2	25	modeling	modeling	NOUN
ejpam-846	2	26	dedicated	dedicate	VERB
ejpam-846	2	27	to	to	ADP
ejpam-846	2	28	the	the	DET
ejpam-846	2	29	memory	memory	NOUN
ejpam-846	2	30	of	of	ADP
ejpam-846	2	31	prof	prof	NOUN
ejpam-846	2	32	.	.	PUNCT
ejpam-846	3	1	sir	sir	PROPN
ejpam-846	3	2	clive	clive	PROPN
ejpam-846	3	3	w.j	w.j	PROPN
ejpam-846	3	4	.	.	PROPN
ejpam-846	4	1	granger	granger	PROPN
ejpam-846	4	2	approximating	approximate	VERB
ejpam-846	4	3	expectation	expectation	NOUN
ejpam-846	4	4	functionals	functional	NOUN
ejpam-846	4	5	for	for	ADP
ejpam-846	4	6	financial	financial	ADJ
ejpam-846	4	7	optimization	optimization	NOUN
ejpam-846	4	8	n.c.p	n.c.p	PROPN
ejpam-846	4	9	.	.	PROPN
ejpam-846	4	10	edirisinghe	edirisinghe	PROPN
ejpam-846	4	11	department	department	PROPN
ejpam-846	4	12	of	of	ADP
ejpam-846	4	13	statistics	statistic	NOUN
ejpam-846	4	14	,	,	PUNCT
ejpam-846	4	15	operations	operation	NOUN
ejpam-846	4	16	and	and	CCONJ
ejpam-846	4	17	management	management	NOUN
ejpam-846	4	18	science	science	NOUN
ejpam-846	4	19	,	,	PUNCT
ejpam-846	4	20	college	college	NOUN
ejpam-846	4	21	of	of	ADP
ejpam-846	4	22	business	business	PROPN
ejpam-846	4	23	university	university	PROPN
ejpam-846	4	24	of	of	ADP
ejpam-846	4	25	tennessee	tennessee	PROPN
ejpam-846	4	26	,	,	PUNCT
ejpam-846	4	27	knoxville	knoxville	PROPN
ejpam-846	4	28	,	,	PUNCT
ejpam-846	4	29	tn	tn	PROPN
ejpam-846	4	30	37996	37996	NUM
ejpam-846	4	31	,	,	PUNCT
ejpam-846	4	32	usa	usa	PROPN
ejpam-846	4	33	.	.	PROPN
ejpam-846	4	34	abstract	abstract	PROPN
ejpam-846	4	35	.	.	PUNCT
ejpam-846	5	1	numerical	numerical	ADJ
ejpam-846	5	2	evaluation	evaluation	NOUN
ejpam-846	5	3	of	of	ADP
ejpam-846	5	4	the	the	DET
ejpam-846	5	5	expectation	expectation	NOUN
ejpam-846	5	6	of	of	ADP
ejpam-846	5	7	a	a	DET
ejpam-846	5	8	function	function	NOUN
ejpam-846	5	9	of	of	ADP
ejpam-846	5	10	a	a	DET
ejpam-846	5	11	random	random	ADJ
ejpam-846	5	12	vector	vector	NOUN
ejpam-846	5	13	is	be	AUX
ejpam-846	5	14	often	often	ADV
ejpam-846	5	15	difficult	difficult	ADJ
ejpam-846	5	16	because	because	SCONJ
ejpam-846	5	17	either	either	CCONJ
ejpam-846	5	18	the	the	DET
ejpam-846	5	19	knowledge	knowledge	NOUN
ejpam-846	5	20	of	of	ADP
ejpam-846	5	21	the	the	DET
ejpam-846	5	22	underlying	underlying	ADJ
ejpam-846	5	23	probability	probability	NOUN
ejpam-846	5	24	distribution	distribution	NOUN
ejpam-846	5	25	is	be	AUX
ejpam-846	5	26	not	not	PART
ejpam-846	5	27	complete	complete	ADJ
ejpam-846	5	28	,	,	PUNCT
ejpam-846	5	29	or	or	CCONJ
ejpam-846	5	30	the	the	DET
ejpam-846	5	31	probability	probability	NOUN
ejpam-846	5	32	space	space	NOUN
ejpam-846	5	33	is	be	AUX
ejpam-846	5	34	continuous	continuous	ADJ
ejpam-846	5	35	and	and	CCONJ
ejpam-846	5	36	each	each	DET
ejpam-846	5	37	function	function	NOUN
ejpam-846	5	38	evaluation	evaluation	NOUN
ejpam-846	5	39	is	be	AUX
ejpam-846	5	40	expensive	expensive	ADJ
ejpam-846	5	41	.	.	PUNCT
ejpam-846	6	1	such	such	ADJ
ejpam-846	6	2	difficulties	difficulty	NOUN
ejpam-846	6	3	often	often	ADV
ejpam-846	6	4	arise	arise	VERB
ejpam-846	6	5	in	in	ADP
ejpam-846	6	6	financial	financial	ADJ
ejpam-846	6	7	optimization	optimization	NOUN
ejpam-846	6	8	where	where	SCONJ
ejpam-846	6	9	a	a	DET
ejpam-846	6	10	risk	risk	NOUN
ejpam-846	6	11	measure	measure	NOUN
ejpam-846	6	12	is	be	AUX
ejpam-846	6	13	expressed	express	VERB
ejpam-846	6	14	as	as	ADP
ejpam-846	6	15	an	an	DET
ejpam-846	6	16	expectation	expectation	NOUN
ejpam-846	6	17	functional	functional	ADJ
ejpam-846	6	18	of	of	ADP
ejpam-846	6	19	random	random	ADJ
ejpam-846	6	20	(	(	PUNCT
ejpam-846	6	21	asset	asset	NOUN
ejpam-846	6	22	)	)	PUNCT
ejpam-846	6	23	returns	return	NOUN
ejpam-846	6	24	.	.	PUNCT
ejpam-846	7	1	not	not	PART
ejpam-846	7	2	only	only	ADV
ejpam-846	7	3	does	do	AUX
ejpam-846	7	4	the	the	DET
ejpam-846	7	5	latter	latter	ADJ
ejpam-846	7	6	expectation	expectation	NOUN
ejpam-846	7	7	depends	depend	VERB
ejpam-846	7	8	on	on	ADP
ejpam-846	7	9	investment	investment	NOUN
ejpam-846	7	10	positions	position	NOUN
ejpam-846	7	11	created	create	VERB
ejpam-846	7	12	in	in	ADP
ejpam-846	7	13	the	the	DET
ejpam-846	7	14	underlying	underlie	VERB
ejpam-846	7	15	assets	asset	NOUN
ejpam-846	7	16	,	,	PUNCT
ejpam-846	7	17	but	but	CCONJ
ejpam-846	7	18	also	also	ADV
ejpam-846	7	19	it	it	PRON
ejpam-846	7	20	requires	require	VERB
ejpam-846	7	21	the	the	DET
ejpam-846	7	22	solution	solution	NOUN
ejpam-846	7	23	of	of	ADP
ejpam-846	7	24	a	a	DET
ejpam-846	7	25	mathematical	mathematical	ADJ
ejpam-846	7	26	program	program	NOUN
ejpam-846	7	27	.	.	PUNCT
ejpam-846	8	1	first	first	ADV
ejpam-846	8	2	,	,	PUNCT
ejpam-846	8	3	the	the	DET
ejpam-846	8	4	basic	basic	ADJ
ejpam-846	8	5	results	result	NOUN
ejpam-846	8	6	from	from	ADP
ejpam-846	8	7	generalized	generalized	ADJ
ejpam-846	8	8	moment	moment	NOUN
ejpam-846	8	9	problems	problem	NOUN
ejpam-846	8	10	are	be	AUX
ejpam-846	8	11	presented	present	VERB
ejpam-846	8	12	to	to	PART
ejpam-846	8	13	establish	establish	VERB
ejpam-846	8	14	tightness	tightness	ADJ
ejpam-846	8	15	properties	property	NOUN
ejpam-846	8	16	of	of	ADP
ejpam-846	8	17	approximations	approximation	NOUN
ejpam-846	8	18	.	.	PUNCT
ejpam-846	9	1	then	then	ADV
ejpam-846	9	2	,	,	PUNCT
ejpam-846	9	3	first	first	ADJ
ejpam-846	9	4	and	and	CCONJ
ejpam-846	9	5	second	second	ADJ
ejpam-846	9	6	moment	moment	NOUN
ejpam-846	9	7	approximations	approximation	NOUN
ejpam-846	9	8	are	be	AUX
ejpam-846	9	9	presented	present	VERB
ejpam-846	9	10	for	for	ADP
ejpam-846	9	11	the	the	DET
ejpam-846	9	12	expectation	expectation	NOUN
ejpam-846	9	13	.	.	PUNCT
ejpam-846	10	1	these	these	DET
ejpam-846	10	2	results	result	NOUN
ejpam-846	10	3	are	be	AUX
ejpam-846	10	4	applied	apply	VERB
ejpam-846	10	5	within	within	ADP
ejpam-846	10	6	a	a	DET
ejpam-846	10	7	financial	financial	ADJ
ejpam-846	10	8	optimization	optimization	NOUN
ejpam-846	10	9	problem	problem	NOUN
ejpam-846	10	10	to	to	PART
ejpam-846	10	11	illustrate	illustrate	VERB
ejpam-846	10	12	the	the	DET
ejpam-846	10	13	efficiency	efficiency	NOUN
ejpam-846	10	14	of	of	ADP
ejpam-846	10	15	the	the	DET
ejpam-846	10	16	approximations	approximation	NOUN
ejpam-846	10	17	for	for	ADP
ejpam-846	10	18	determining	determine	VERB
ejpam-846	10	19	optimal	optimal	ADJ
ejpam-846	10	20	positions	position	NOUN
ejpam-846	10	21	in	in	ADP
ejpam-846	10	22	a	a	DET
ejpam-846	10	23	portfolio	portfolio	NOUN
ejpam-846	10	24	of	of	ADP
ejpam-846	10	25	the	the	DET
ejpam-846	10	26	standard	standard	NOUN
ejpam-846	10	27	and	and	CCONJ
ejpam-846	10	28	poors	poor	NOUN
ejpam-846	10	29	100	100	NUM
ejpam-846	10	30	stocks	stock	NOUN
ejpam-846	10	31	.	.	PUNCT
ejpam-846	11	1	2000	2000	NUM
ejpam-846	11	2	mathematics	mathematic	NOUN
ejpam-846	11	3	subject	subject	NOUN
ejpam-846	11	4	classifications	classification	NOUN
ejpam-846	11	5	:	:	PUNCT
ejpam-846	11	6	46n10	46n10	NUM
ejpam-846	11	7	,	,	PUNCT
ejpam-846	11	8	44a60	44a60	NUM
ejpam-846	11	9	,	,	PUNCT
ejpam-846	11	10	91g99	91g99	NUM
ejpam-846	11	11	key	key	ADJ
ejpam-846	11	12	words	word	NOUN
ejpam-846	11	13	and	and	CCONJ
ejpam-846	11	14	phrases	phrase	NOUN
ejpam-846	11	15	:	:	PUNCT
ejpam-846	11	16	approximating	approximate	VERB
ejpam-846	11	17	expectation	expectation	NOUN
ejpam-846	11	18	,	,	PUNCT
ejpam-846	11	19	lower	low	ADJ
ejpam-846	11	20	bounds	bound	NOUN
ejpam-846	11	21	,	,	PUNCT
ejpam-846	11	22	moment	moment	NOUN
ejpam-846	11	23	problems	problem	NOUN
ejpam-846	11	24	,	,	PUNCT
ejpam-846	11	25	portfolio	portfolio	NOUN
ejpam-846	11	26	optimization	optimization	NOUN
ejpam-846	11	27	.	.	PUNCT
ejpam-846	12	1	1	1	X
ejpam-846	12	2	.	.	X
ejpam-846	12	3	introduction	introduction	NOUN
ejpam-846	12	4	determining	determine	VERB
ejpam-846	12	5	the	the	DET
ejpam-846	12	6	expectation	expectation	NOUN
ejpam-846	12	7	of	of	ADP
ejpam-846	12	8	a	a	DET
ejpam-846	12	9	function	function	NOUN
ejpam-846	12	10	of	of	ADP
ejpam-846	12	11	a	a	DET
ejpam-846	12	12	random	random	ADJ
ejpam-846	12	13	vector	vector	NOUN
ejpam-846	12	14	arises	arise	VERB
ejpam-846	12	15	in	in	ADP
ejpam-846	12	16	many	many	ADJ
ejpam-846	12	17	applications	application	NOUN
ejpam-846	12	18	,	,	PUNCT
ejpam-846	12	19	including	include	VERB
ejpam-846	12	20	agriculture	agriculture	NOUN
ejpam-846	12	21	,	,	PUNCT
ejpam-846	12	22	economics	economic	NOUN
ejpam-846	12	23	,	,	PUNCT
ejpam-846	12	24	engineering	engineering	NOUN
ejpam-846	12	25	,	,	PUNCT
ejpam-846	12	26	and	and	CCONJ
ejpam-846	12	27	finance	finance	NOUN
ejpam-846	12	28	.	.	PUNCT
ejpam-846	13	1	numerical	numerical	ADJ
ejpam-846	13	2	evaluation	evaluation	NOUN
ejpam-846	13	3	of	of	ADP
ejpam-846	13	4	such	such	ADJ
ejpam-846	13	5	expectation	expectation	NOUN
ejpam-846	13	6	is	be	AUX
ejpam-846	13	7	often	often	ADV
ejpam-846	13	8	difficult	difficult	ADJ
ejpam-846	13	9	because	because	SCONJ
ejpam-846	13	10	either	either	CCONJ
ejpam-846	13	11	the	the	DET
ejpam-846	13	12	knowledge	knowledge	NOUN
ejpam-846	13	13	of	of	ADP
ejpam-846	13	14	the	the	DET
ejpam-846	13	15	underlying	underlying	ADJ
ejpam-846	13	16	probability	probability	NOUN
ejpam-846	13	17	distribution	distribution	NOUN
ejpam-846	13	18	is	be	AUX
ejpam-846	13	19	not	not	PART
ejpam-846	13	20	complete	complete	ADJ
ejpam-846	13	21	,	,	PUNCT
ejpam-846	13	22	or	or	CCONJ
ejpam-846	13	23	the	the	DET
ejpam-846	13	24	probability	probability	NOUN
ejpam-846	13	25	space	space	NOUN
ejpam-846	13	26	is	be	AUX
ejpam-846	13	27	continuous	continuous	ADJ
ejpam-846	13	28	and	and	CCONJ
ejpam-846	13	29	each	each	DET
ejpam-846	13	30	function	function	NOUN
ejpam-846	13	31	evaluation	evaluation	NOUN
ejpam-846	13	32	is	be	AUX
ejpam-846	13	33	expensive	expensive	ADJ
ejpam-846	13	34	.	.	PUNCT
ejpam-846	14	1	for	for	ADP
ejpam-846	14	2	instance	instance	NOUN
ejpam-846	14	3	,	,	PUNCT
ejpam-846	14	4	the	the	DET
ejpam-846	14	5	function	function	NOUN
ejpam-846	14	6	evaluation	evaluation	NOUN
ejpam-846	14	7	may	may	AUX
ejpam-846	14	8	involve	involve	VERB
ejpam-846	14	9	simulation	simulation	NOUN
ejpam-846	14	10	or	or	CCONJ
ejpam-846	14	11	solution	solution	NOUN
ejpam-846	14	12	of	of	ADP
ejpam-846	14	13	a	a	DET
ejpam-846	14	14	mathematical	mathematical	ADJ
ejpam-846	14	15	program	program	NOUN
ejpam-846	14	16	.	.	PUNCT
ejpam-846	15	1	these	these	DET
ejpam-846	15	2	difficulties	difficulty	NOUN
ejpam-846	15	3	are	be	AUX
ejpam-846	15	4	further	far	ADV
ejpam-846	15	5	compounded	compound	VERB
ejpam-846	15	6	when	when	SCONJ
ejpam-846	15	7	the	the	DET
ejpam-846	15	8	email	email	NOUN
ejpam-846	15	9	address	address	NOUN
ejpam-846	15	10	:	:	PUNCT
ejpam-846	15	11	chanaka@utk.edu	chanaka@utk.edu	PROPN
ejpam-846	15	12	(	(	PUNCT
ejpam-846	15	13	n.c.p	n.c.p	PROPN
ejpam-846	15	14	.	.	PROPN
ejpam-846	15	15	edirisinghe	edirisinghe	PROPN
ejpam-846	15	16	)	)	PUNCT
ejpam-846	15	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-846	15	18	572	572	NUM
ejpam-846	15	19	c⃝	c⃝	NOUN
ejpam-846	15	20	2010	2010	NUM
ejpam-846	15	21	ejpam	ejpam	VERB
ejpam-846	15	22	all	all	DET
ejpam-846	15	23	rights	right	NOUN
ejpam-846	15	24	reserved	reserve	VERB
ejpam-846	15	25	.	.	PUNCT
ejpam-846	16	1	edirisinghe	edirisinghe	PROPN
ejpam-846	16	2	/	/	SYM
ejpam-846	16	3	eur	eur	PROPN
ejpam-846	16	4	.	.	PUNCT
ejpam-846	17	1	j.	j.	PROPN
ejpam-846	17	2	pure	pure	PROPN
ejpam-846	17	3	appl	appl	PROPN
ejpam-846	17	4	.	.	PROPN
ejpam-846	17	5	math	math	PROPN
ejpam-846	17	6	,	,	PUNCT
ejpam-846	17	7	3	3	NUM
ejpam-846	17	8	(	(	PUNCT
ejpam-846	17	9	2010	2010	NUM
ejpam-846	17	10	)	)	PUNCT
ejpam-846	17	11	,	,	PUNCT
ejpam-846	17	12	572	572	NUM
ejpam-846	17	13	-	-	SYM
ejpam-846	17	14	592	592	NUM
ejpam-846	17	15	573	573	NUM
ejpam-846	17	16	underlying	underlie	VERB
ejpam-846	17	17	random	random	ADJ
ejpam-846	17	18	variables	variable	NOUN
ejpam-846	17	19	are	be	AUX
ejpam-846	17	20	stochastically	stochastically	ADV
ejpam-846	17	21	dependent	dependent	ADJ
ejpam-846	17	22	and	and	CCONJ
ejpam-846	17	23	such	such	DET
ejpam-846	17	24	an	an	DET
ejpam-846	17	25	expectation	expectation	NOUN
ejpam-846	17	26	functional	functional	NOUN
ejpam-846	17	27	is	be	AUX
ejpam-846	17	28	embedded	embed	VERB
ejpam-846	17	29	in	in	ADP
ejpam-846	17	30	an	an	DET
ejpam-846	17	31	(	(	PUNCT
ejpam-846	17	32	outer	outer	ADJ
ejpam-846	17	33	)	)	PUNCT
ejpam-846	17	34	decision	decision	NOUN
ejpam-846	17	35	optimization	optimization	NOUN
ejpam-846	17	36	problem	problem	NOUN
ejpam-846	17	37	.	.	PUNCT
ejpam-846	18	1	consequently	consequently	ADV
ejpam-846	18	2	,	,	PUNCT
ejpam-846	18	3	it	it	PRON
ejpam-846	18	4	may	may	AUX
ejpam-846	18	5	become	become	VERB
ejpam-846	18	6	necessary	necessary	ADJ
ejpam-846	18	7	to	to	PART
ejpam-846	18	8	evaluate	evaluate	VERB
ejpam-846	18	9	the	the	DET
ejpam-846	18	10	expectation	expectation	NOUN
ejpam-846	18	11	functional	functional	ADJ
ejpam-846	18	12	as	as	ADP
ejpam-846	18	13	many	many	ADJ
ejpam-846	18	14	times	time	NOUN
ejpam-846	18	15	as	as	SCONJ
ejpam-846	18	16	needed	need	VERB
ejpam-846	18	17	in	in	ADP
ejpam-846	18	18	an	an	DET
ejpam-846	18	19	iterative	iterative	NOUN
ejpam-846	18	20	search	search	NOUN
ejpam-846	18	21	designed	design	VERB
ejpam-846	18	22	to	to	PART
ejpam-846	18	23	determine	determine	VERB
ejpam-846	18	24	an	an	DET
ejpam-846	18	25	optimal	optimal	ADJ
ejpam-846	18	26	decision	decision	NOUN
ejpam-846	18	27	for	for	ADP
ejpam-846	18	28	the	the	DET
ejpam-846	18	29	problem	problem	NOUN
ejpam-846	18	30	at	at	ADP
ejpam-846	18	31	hand	hand	NOUN
ejpam-846	18	32	.	.	PUNCT
ejpam-846	19	1	multidimensional	multidimensional	ADJ
ejpam-846	19	2	numerical	numerical	ADJ
ejpam-846	19	3	integration	integration	NOUN
ejpam-846	19	4	as	as	ADP
ejpam-846	19	5	a	a	DET
ejpam-846	19	6	computational	computational	ADJ
ejpam-846	19	7	strategy	strategy	NOUN
ejpam-846	19	8	is	be	AUX
ejpam-846	19	9	prohibitively	prohibitively	ADV
ejpam-846	19	10	expensive	expensive	ADJ
ejpam-846	19	11	even	even	ADV
ejpam-846	19	12	for	for	ADP
ejpam-846	19	13	a	a	DET
ejpam-846	19	14	modest	modest	ADJ
ejpam-846	19	15	number	number	NOUN
ejpam-846	19	16	of	of	ADP
ejpam-846	19	17	random	random	ADJ
ejpam-846	19	18	variables	variable	NOUN
ejpam-846	19	19	.	.	PUNCT
ejpam-846	20	1	to	to	PART
ejpam-846	20	2	motivate	motivate	VERB
ejpam-846	20	3	,	,	PUNCT
ejpam-846	20	4	consider	consider	VERB
ejpam-846	20	5	the	the	DET
ejpam-846	20	6	following	follow	VERB
ejpam-846	20	7	financial	financial	ADJ
ejpam-846	20	8	optimization	optimization	NOUN
ejpam-846	20	9	problem	problem	NOUN
ejpam-846	20	10	.	.	PUNCT
ejpam-846	21	1	a	a	DET
ejpam-846	21	2	portfolio	portfolio	NOUN
ejpam-846	21	3	manager	manager	NOUN
ejpam-846	21	4	wishes	wish	VERB
ejpam-846	21	5	to	to	PART
ejpam-846	21	6	determine	determine	VERB
ejpam-846	21	7	a	a	DET
ejpam-846	21	8	set	set	NOUN
ejpam-846	21	9	of	of	ADP
ejpam-846	21	10	(	(	PUNCT
ejpam-846	21	11	risky	risky	ADJ
ejpam-846	21	12	)	)	PUNCT
ejpam-846	21	13	assets	asset	NOUN
ejpam-846	21	14	,	,	PUNCT
ejpam-846	21	15	such	such	ADJ
ejpam-846	21	16	as	as	ADP
ejpam-846	21	17	stocks	stock	NOUN
ejpam-846	21	18	,	,	PUNCT
ejpam-846	21	19	for	for	ADP
ejpam-846	21	20	investment	investment	NOUN
ejpam-846	21	21	for	for	ADP
ejpam-846	21	22	a	a	DET
ejpam-846	21	23	certain	certain	ADJ
ejpam-846	21	24	future	future	ADJ
ejpam-846	21	25	period	period	NOUN
ejpam-846	21	26	during	during	ADP
ejpam-846	21	27	which	which	PRON
ejpam-846	21	28	asset	asset	NOUN
ejpam-846	21	29	returns	return	NOUN
ejpam-846	21	30	are	be	AUX
ejpam-846	21	31	uncertain	uncertain	ADJ
ejpam-846	21	32	.	.	PUNCT
ejpam-846	22	1	having	having	AUX
ejpam-846	22	2	created	create	VERB
ejpam-846	22	3	the	the	DET
ejpam-846	22	4	portfolio	portfolio	NOUN
ejpam-846	22	5	positions	position	NOUN
ejpam-846	22	6	,	,	PUNCT
ejpam-846	22	7	and	and	CCONJ
ejpam-846	22	8	upon	upon	SCONJ
ejpam-846	22	9	observing	observe	VERB
ejpam-846	22	10	the	the	DET
ejpam-846	22	11	realized	realize	VERB
ejpam-846	22	12	asset	asset	NOUN
ejpam-846	22	13	returns	return	NOUN
ejpam-846	22	14	,	,	PUNCT
ejpam-846	22	15	the	the	DET
ejpam-846	22	16	portfolio	portfolio	NOUN
ejpam-846	22	17	manager	manager	NOUN
ejpam-846	22	18	may	may	AUX
ejpam-846	22	19	revise	revise	VERB
ejpam-846	22	20	(	(	PUNCT
ejpam-846	22	21	or	or	CCONJ
ejpam-846	22	22	rebalance	rebalance	NOUN
ejpam-846	22	23	)	)	PUNCT
ejpam-846	22	24	her	her	PRON
ejpam-846	22	25	portfolio	portfolio	NOUN
ejpam-846	22	26	in	in	ADP
ejpam-846	22	27	order	order	NOUN
ejpam-846	22	28	to	to	PART
ejpam-846	22	29	control	control	VERB
ejpam-846	22	30	the	the	DET
ejpam-846	22	31	expected	expect	VERB
ejpam-846	22	32	deviation	deviation	NOUN
ejpam-846	22	33	of	of	ADP
ejpam-846	22	34	portfolio	portfolio	NOUN
ejpam-846	22	35	value	value	NOUN
ejpam-846	22	36	from	from	ADP
ejpam-846	22	37	a	a	DET
ejpam-846	22	38	prescribed	prescribed	ADJ
ejpam-846	22	39	wealth	wealth	NOUN
ejpam-846	22	40	target	target	NOUN
ejpam-846	22	41	.	.	PUNCT
ejpam-846	23	1	in	in	ADP
ejpam-846	23	2	this	this	DET
ejpam-846	23	3	context	context	NOUN
ejpam-846	23	4	,	,	PUNCT
ejpam-846	23	5	the	the	DET
ejpam-846	23	6	portfolio	portfolio	NOUN
ejpam-846	23	7	manager	manager	NOUN
ejpam-846	23	8	wishes	wish	VERB
ejpam-846	23	9	to	to	PART
ejpam-846	23	10	pick	pick	VERB
ejpam-846	23	11	an	an	DET
ejpam-846	23	12	initial	initial	ADJ
ejpam-846	23	13	portfolio	portfolio	NOUN
ejpam-846	23	14	that	that	PRON
ejpam-846	23	15	would	would	AUX
ejpam-846	23	16	hedge	hedge	VERB
ejpam-846	23	17	well	well	ADV
ejpam-846	23	18	against	against	ADP
ejpam-846	23	19	all	all	DET
ejpam-846	23	20	possible	possible	ADJ
ejpam-846	23	21	realizations	realization	NOUN
ejpam-846	23	22	of	of	ADP
ejpam-846	23	23	random	random	ADJ
ejpam-846	23	24	asset	asset	NOUN
ejpam-846	23	25	returns	return	NOUN
ejpam-846	23	26	with	with	ADP
ejpam-846	23	27	respect	respect	NOUN
ejpam-846	23	28	to	to	ADP
ejpam-846	23	29	a	a	DET
ejpam-846	23	30	desired	desire	VERB
ejpam-846	23	31	portfolio	portfolio	NOUN
ejpam-846	23	32	return	return	NOUN
ejpam-846	23	33	and	and	CCONJ
ejpam-846	23	34	any	any	DET
ejpam-846	23	35	risk	risk	NOUN
ejpam-846	23	36	thereof	thereof	ADV
ejpam-846	23	37	.	.	PUNCT
ejpam-846	24	1	such	such	ADJ
ejpam-846	24	2	decision	decision	NOUN
ejpam-846	24	3	problems	problem	NOUN
ejpam-846	24	4	can	can	AUX
ejpam-846	24	5	be	be	AUX
ejpam-846	24	6	typically	typically	ADV
ejpam-846	24	7	formulated	formulate	VERB
ejpam-846	24	8	as	as	ADP
ejpam-846	24	9	two	two	NUM
ejpam-846	24	10	-	-	PUNCT
ejpam-846	24	11	stage	stage	NOUN
ejpam-846	24	12	stochastic	stochastic	ADJ
ejpam-846	24	13	optimization	optimization	NOUN
ejpam-846	24	14	models	model	NOUN
ejpam-846	24	15	,	,	PUNCT
ejpam-846	24	16	e.g.	e.g.	ADV
ejpam-846	24	17	see	see	VERB
ejpam-846	24	18	edirisinghe	edirisinghe	NOUN
ejpam-846	24	19	[	[	X
ejpam-846	24	20	8	8	NUM
ejpam-846	24	21	]	]	PUNCT
ejpam-846	24	22	,	,	PUNCT
ejpam-846	24	23	kall	kall	PROPN
ejpam-846	25	1	[	[	X
ejpam-846	25	2	11	11	NUM
ejpam-846	25	3	]	]	PUNCT
ejpam-846	25	4	,	,	PUNCT
ejpam-846	25	5	wets	wet	VERB
ejpam-846	25	6	[	[	PUNCT
ejpam-846	25	7	20	20	NUM
ejpam-846	25	8	]	]	PUNCT
ejpam-846	25	9	,	,	PUNCT
ejpam-846	25	10	in	in	ADP
ejpam-846	25	11	which	which	PRON
ejpam-846	25	12	an	an	DET
ejpam-846	25	13	optimized	optimize	VERB
ejpam-846	25	14	current	current	ADJ
ejpam-846	25	15	allocation	allocation	NOUN
ejpam-846	25	16	is	be	AUX
ejpam-846	25	17	made	make	VERB
ejpam-846	25	18	to	to	PART
ejpam-846	25	19	maximize	maximize	VERB
ejpam-846	25	20	the	the	DET
ejpam-846	25	21	portfolio	portfolio	NOUN
ejpam-846	25	22	return	return	NOUN
ejpam-846	25	23	,	,	PUNCT
ejpam-846	25	24	less	less	ADV
ejpam-846	25	25	an	an	DET
ejpam-846	25	26	appropriately	appropriately	ADV
ejpam-846	25	27	measured	measure	VERB
ejpam-846	25	28	risk	risk	NOUN
ejpam-846	25	29	associated	associate	VERB
ejpam-846	25	30	with	with	ADP
ejpam-846	25	31	the	the	DET
ejpam-846	25	32	allocation	allocation	NOUN
ejpam-846	25	33	,	,	PUNCT
ejpam-846	25	34	subject	subject	ADJ
ejpam-846	25	35	to	to	ADP
ejpam-846	25	36	policy	policy	NOUN
ejpam-846	25	37	and	and	CCONJ
ejpam-846	25	38	other	other	ADJ
ejpam-846	25	39	constraints	constraint	NOUN
ejpam-846	25	40	.	.	PUNCT
ejpam-846	26	1	let	let	VERB
ejpam-846	26	2	x	x	PRON
ejpam-846	26	3	denote	denote	VERB
ejpam-846	26	4	the	the	DET
ejpam-846	26	5	vector	vector	NOUN
ejpam-846	26	6	of	of	ADP
ejpam-846	26	7	(	(	PUNCT
ejpam-846	26	8	anticipatory	anticipatory	ADJ
ejpam-846	26	9	)	)	PUNCT
ejpam-846	26	10	allocative	allocative	ADJ
ejpam-846	26	11	decisions	decision	NOUN
ejpam-846	26	12	,	,	PUNCT
ejpam-846	26	13	which	which	PRON
ejpam-846	26	14	yields	yield	VERB
ejpam-846	26	15	an	an	DET
ejpam-846	26	16	(	(	PUNCT
ejpam-846	26	17	expected	expect	VERB
ejpam-846	26	18	)	)	PUNCT
ejpam-846	26	19	profit	profit	NOUN
ejpam-846	26	20	function	function	NOUN
ejpam-846	26	21	c(x	c(x	NOUN
ejpam-846	26	22	)	)	PUNCT
ejpam-846	26	23	,	,	PUNCT
ejpam-846	26	24	associated	associate	VERB
ejpam-846	26	25	with	with	ADP
ejpam-846	26	26	a	a	DET
ejpam-846	26	27	given	give	VERB
ejpam-846	26	28	risk	risk	NOUN
ejpam-846	26	29	function	function	NOUN
ejpam-846	26	30	ψ(x	ψ(x	NOUN
ejpam-846	26	31	)	)	PUNCT
ejpam-846	26	32	.	.	PUNCT
ejpam-846	27	1	consider	consider	VERB
ejpam-846	27	2	the	the	DET
ejpam-846	27	3	following	follow	VERB
ejpam-846	27	4	model	model	NOUN
ejpam-846	27	5	:	:	PUNCT
ejpam-846	27	6	z∗	z∗	NOUN
ejpam-846	27	7	:	:	PUNCT
ejpam-846	27	8	=	=	SYM
ejpam-846	27	9	max	max	PROPN
ejpam-846	27	10	x	x	SYM
ejpam-846	27	11	c(x)−	c(x)−	PROPN
ejpam-846	27	12	λ	λ	PROPN
ejpam-846	27	13	ψ(x	ψ(x	PROPN
ejpam-846	27	14	)	)	PUNCT
ejpam-846	27	15	s.t	s.t	PROPN
ejpam-846	27	16	.	.	PUNCT
ejpam-846	27	17	ax	ax	NOUN
ejpam-846	27	18	=	=	SYM
ejpam-846	27	19	b	b	PROPN
ejpam-846	27	20	x	x	X
ejpam-846	27	21	≥	≥	NOUN
ejpam-846	27	22	0	0	NUM
ejpam-846	27	23	,	,	PUNCT
ejpam-846	27	24	(	(	PUNCT
ejpam-846	27	25	1	1	X
ejpam-846	27	26	)	)	PUNCT
ejpam-846	27	27	where	where	SCONJ
ejpam-846	27	28	λ	λ	PROPN
ejpam-846	27	29	≥	≥	X
ejpam-846	27	30	0	0	NUM
ejpam-846	27	31	is	be	AUX
ejpam-846	27	32	a	a	DET
ejpam-846	27	33	risk	risk	NOUN
ejpam-846	27	34	-	-	PUNCT
ejpam-846	27	35	aversion	aversion	NOUN
ejpam-846	27	36	parameter	parameter	NOUN
ejpam-846	27	37	.	.	PUNCT
ejpam-846	28	1	upon	upon	SCONJ
ejpam-846	28	2	realization	realization	NOUN
ejpam-846	28	3	of	of	ADP
ejpam-846	28	4	the	the	DET
ejpam-846	28	5	random	random	ADJ
ejpam-846	28	6	vector	vector	NOUN
ejpam-846	28	7	ξ	ξ	PROPN
ejpam-846	28	8	,	,	PUNCT
ejpam-846	28	9	the	the	DET
ejpam-846	28	10	specific	specific	ADJ
ejpam-846	28	11	risk	risk	NOUN
ejpam-846	28	12	consequence	consequence	NOUN
ejpam-846	28	13	ϕ(x	ϕ(x	PROPN
ejpam-846	28	14	,	,	PUNCT
ejpam-846	28	15	ξ	ξ	X
ejpam-846	28	16	)	)	PUNCT
ejpam-846	28	17	is	be	AUX
ejpam-846	28	18	determined	determine	VERB
ejpam-846	28	19	under	under	ADP
ejpam-846	28	20	adaptive	adaptive	ADJ
ejpam-846	28	21	decisions	decision	NOUN
ejpam-846	28	22	y	y	PROPN
ejpam-846	28	23	(	(	PUNCT
ejpam-846	28	24	such	such	ADJ
ejpam-846	28	25	as	as	ADP
ejpam-846	28	26	portfolio	portfolio	NOUN
ejpam-846	28	27	rebalancing	rebalancing	NOUN
ejpam-846	28	28	or	or	CCONJ
ejpam-846	28	29	financing	financing	NOUN
ejpam-846	28	30	missed	miss	VERB
ejpam-846	28	31	wealth	wealth	NOUN
ejpam-846	28	32	targets	target	NOUN
ejpam-846	28	33	)	)	PUNCT
ejpam-846	28	34	,	,	PUNCT
ejpam-846	28	35	and	and	CCONJ
ejpam-846	28	36	it	it	PRON
ejpam-846	28	37	is	be	AUX
ejpam-846	28	38	modeled	model	VERB
ejpam-846	28	39	by	by	ADP
ejpam-846	28	40	ϕ(x	ϕ(x	PROPN
ejpam-846	28	41	,	,	PUNCT
ejpam-846	28	42	ξ	ξ	NOUN
ejpam-846	28	43	)	)	PUNCT
ejpam-846	28	44	:	:	PUNCT
ejpam-846	29	1	=	=	SYM
ejpam-846	29	2	min	min	PROPN
ejpam-846	29	3	y	y	PROPN
ejpam-846	29	4	q(y	q(y	PROPN
ejpam-846	29	5	)	)	PUNCT
ejpam-846	29	6	s.t	s.t	PROPN
ejpam-846	29	7	.	.	PROPN
ejpam-846	29	8	wy	wy	PROPN
ejpam-846	29	9	=	=	PROPN
ejpam-846	29	10	h(ξ)−	h(ξ)−	PROPN
ejpam-846	29	11	t	t	PROPN
ejpam-846	29	12	(	(	PUNCT
ejpam-846	29	13	ξ)x	ξ)x	PROPN
ejpam-846	29	14	y	y	NUM
ejpam-846	29	15	≥	≥	PROPN
ejpam-846	29	16	0	0	NUM
ejpam-846	29	17	.	.	PUNCT
ejpam-846	30	1	(	(	PUNCT
ejpam-846	30	2	2	2	X
ejpam-846	30	3	)	)	PUNCT
ejpam-846	30	4	note	note	NOUN
ejpam-846	30	5	that	that	SCONJ
ejpam-846	30	6	a	a	DET
ejpam-846	30	7	random	random	ADJ
ejpam-846	30	8	matrix	matrix	NOUN
ejpam-846	30	9	t	t	NOUN
ejpam-846	30	10	transforms	transform	VERB
ejpam-846	30	11	the	the	DET
ejpam-846	30	12	decisions	decision	NOUN
ejpam-846	30	13	x	x	PUNCT
ejpam-846	30	14	into	into	ADP
ejpam-846	30	15	risk	risk	NOUN
ejpam-846	30	16	constraints	constraint	NOUN
ejpam-846	30	17	to	to	PART
ejpam-846	30	18	measure	measure	VERB
ejpam-846	30	19	against	against	ADP
ejpam-846	30	20	the	the	DET
ejpam-846	30	21	observed	observed	ADJ
ejpam-846	30	22	state	state	NOUN
ejpam-846	30	23	of	of	ADP
ejpam-846	30	24	nature	nature	NOUN
ejpam-846	30	25	(	(	PUNCT
ejpam-846	30	26	vector	vector	NOUN
ejpam-846	30	27	)	)	PUNCT
ejpam-846	30	28	h.	h.	NOUN
ejpam-846	31	1	then	then	ADV
ejpam-846	31	2	,	,	PUNCT
ejpam-846	31	3	the	the	DET
ejpam-846	31	4	risk	risk	NOUN
ejpam-846	31	5	function	function	NOUN
ejpam-846	31	6	is	be	AUX
ejpam-846	31	7	given	give	VERB
ejpam-846	31	8	by	by	ADP
ejpam-846	31	9	ψ(x	ψ(x	NOUN
ejpam-846	31	10	)	)	PUNCT
ejpam-846	31	11	=	=	PUNCT
ejpam-846	31	12	e[ϕ(x	e[ϕ(x	NOUN
ejpam-846	31	13	,	,	PUNCT
ejpam-846	31	14	ξ	ξ	NOUN
ejpam-846	31	15	)	)	PUNCT
ejpam-846	31	16	]	]	PUNCT
ejpam-846	31	17	,	,	PUNCT
ejpam-846	31	18	where	where	SCONJ
ejpam-846	31	19	e	e	X
ejpam-846	31	20	[	[	NOUN
ejpam-846	31	21	.	.	X
ejpam-846	31	22	]	]	PUNCT
ejpam-846	32	1	≡	≡	PROPN
ejpam-846	32	2	ep	ep	PROPN
ejpam-846	32	3	tr	tr	X
ejpam-846	33	1	[	[	X
ejpam-846	33	2	.	.	X
ejpam-846	33	3	]	]	PUNCT
ejpam-846	33	4	represents	represent	VERB
ejpam-846	33	5	the	the	DET
ejpam-846	33	6	mathematical	mathematical	ADJ
ejpam-846	33	7	expectation	expectation	NOUN
ejpam-846	33	8	with	with	ADP
ejpam-846	33	9	respect	respect	NOUN
ejpam-846	33	10	to	to	ADP
ejpam-846	33	11	the	the	DET
ejpam-846	33	12	true	true	ADJ
ejpam-846	33	13	probability	probability	NOUN
ejpam-846	33	14	measure	measure	NOUN
ejpam-846	33	15	p	p	NOUN
ejpam-846	33	16	tr	tr	VERB
ejpam-846	33	17	on	on	ADP
ejpam-846	33	18	ξ	ξ	PROPN
ejpam-846	33	19	,	,	PUNCT
ejpam-846	33	20	the	the	DET
ejpam-846	33	21	domain	domain	NOUN
ejpam-846	33	22	of	of	ADP
ejpam-846	33	23	the	the	DET
ejpam-846	33	24	random	random	ADJ
ejpam-846	33	25	k	k	NOUN
ejpam-846	33	26	-	-	NOUN
ejpam-846	33	27	vector	vector	NOUN
ejpam-846	33	28	ξ	ξ	PROPN
ejpam-846	33	29	.	.	PUNCT
ejpam-846	34	1	p	p	NOUN
ejpam-846	34	2	tr	tr	VERB
ejpam-846	34	3	is	be	AUX
ejpam-846	34	4	assumed	assume	VERB
ejpam-846	34	5	to	to	PART
ejpam-846	34	6	be	be	AUX
ejpam-846	34	7	nondegenerate	nondegenerate	ADJ
ejpam-846	34	8	,	,	PUNCT
ejpam-846	34	9	and	and	CCONJ
ejpam-846	34	10	ξ	ξ	PROPN
ejpam-846	34	11	is	be	AUX
ejpam-846	34	12	assumed	assume	VERB
ejpam-846	34	13	to	to	PART
ejpam-846	34	14	be	be	AUX
ejpam-846	34	15	a	a	DET
ejpam-846	34	16	convex	convex	NOUN
ejpam-846	34	17	subset	subset	VERB
ejpam-846	34	18	in	in	ADP
ejpam-846	34	19	ℜk	ℜk	PROPN
ejpam-846	34	20	.	.	PUNCT
ejpam-846	35	1	the	the	DET
ejpam-846	35	2	matrices	matrix	NOUN
ejpam-846	35	3	a	a	DET
ejpam-846	35	4	(	(	PUNCT
ejpam-846	35	5	∈	∈	PROPN
ejpam-846	35	6	ℜm1×n1	ℜm1×n1	NOUN
ejpam-846	35	7	)	)	PUNCT
ejpam-846	35	8	andw	andw	NOUN
ejpam-846	35	9	(	(	PUNCT
ejpam-846	35	10	∈	∈	PROPN
ejpam-846	35	11	ℜm2×n2	ℜm2×n2	NOUN
ejpam-846	35	12	)	)	PUNCT
ejpam-846	35	13	are	be	AUX
ejpam-846	35	14	deterministic	deterministic	ADJ
ejpam-846	35	15	,	,	PUNCT
ejpam-846	35	16	while	while	SCONJ
ejpam-846	35	17	the	the	DET
ejpam-846	35	18	matrix	matrix	NOUN
ejpam-846	35	19	t	t	NOUN
ejpam-846	35	20	:	:	PUNCT
ejpam-846	35	21	ξ	ξ	X
ejpam-846	35	22	→	→	PUNCT
ejpam-846	35	23	ℜm2×n1	ℜm2×n1	NOUN
ejpam-846	35	24	and	and	CCONJ
ejpam-846	35	25	the	the	DET
ejpam-846	35	26	right	right	ADJ
ejpam-846	35	27	-	-	PUNCT
ejpam-846	35	28	hand	hand	NOUN
ejpam-846	35	29	side	side	NOUN
ejpam-846	35	30	h	h	NOUN
ejpam-846	35	31	:	:	PUNCT
ejpam-846	35	32	ξ	ξ	X
ejpam-846	35	33	→	→	SYM
ejpam-846	35	34	ℜm2	ℜm2	NOUN
ejpam-846	35	35	are	be	AUX
ejpam-846	35	36	linear	linear	PROPN
ejpam-846	35	37	affine	affine	NOUN
ejpam-846	35	38	in	in	ADP
ejpam-846	35	39	the	the	DET
ejpam-846	35	40	random	random	ADJ
ejpam-846	35	41	vector	vector	NOUN
ejpam-846	35	42	ξ	ξ	PROPN
ejpam-846	35	43	.	.	PUNCT
ejpam-846	36	1	the	the	DET
ejpam-846	36	2	objective	objective	ADJ
ejpam-846	36	3	functions	function	NOUN
ejpam-846	36	4	c	c	X
ejpam-846	36	5	(	(	PUNCT
ejpam-846	36	6	.	.	PUNCT
ejpam-846	36	7	)	)	PUNCT
ejpam-846	37	1	and	and	CCONJ
ejpam-846	37	2	q	q	X
ejpam-846	37	3	(	(	PUNCT
ejpam-846	37	4	.	.	PUNCT
ejpam-846	37	5	)	)	PUNCT
ejpam-846	37	6	are	be	AUX
ejpam-846	37	7	concave	concave	ADJ
ejpam-846	37	8	and	and	CCONJ
ejpam-846	37	9	convex	convex	PROPN
ejpam-846	37	10	,	,	PUNCT
ejpam-846	37	11	respectively	respectively	ADV
ejpam-846	37	12	.	.	PUNCT
ejpam-846	38	1	the	the	DET
ejpam-846	38	2	model	model	NOUN
ejpam-846	38	3	in	in	ADP
ejpam-846	38	4	(	(	PUNCT
ejpam-846	38	5	1)-(2	1)-(2	NUM
ejpam-846	38	6	)	)	PUNCT
ejpam-846	38	7	admits	admit	VERB
ejpam-846	38	8	several	several	ADJ
ejpam-846	38	9	practical	practical	ADJ
ejpam-846	38	10	investment	investment	NOUN
ejpam-846	38	11	decision	decision	NOUN
ejpam-846	38	12	-	-	PUNCT
ejpam-846	38	13	making	make	VERB
ejpam-846	38	14	situations	situation	NOUN
ejpam-846	38	15	and	and	CCONJ
ejpam-846	38	16	a	a	DET
ejpam-846	38	17	variety	variety	NOUN
ejpam-846	38	18	of	of	ADP
ejpam-846	38	19	risk	risk	NOUN
ejpam-846	38	20	descriptions	description	NOUN
ejpam-846	38	21	.	.	PUNCT
ejpam-846	39	1	also	also	ADV
ejpam-846	39	2	,	,	PUNCT
ejpam-846	39	3	note	note	VERB
ejpam-846	39	4	that	that	SCONJ
ejpam-846	39	5	depending	depend	VERB
ejpam-846	39	6	on	on	ADP
ejpam-846	39	7	the	the	DET
ejpam-846	39	8	measure	measure	NOUN
ejpam-846	39	9	of	of	ADP
ejpam-846	39	10	risk	risk	NOUN
ejpam-846	39	11	assessment	assessment	NOUN
ejpam-846	39	12	,	,	PUNCT
ejpam-846	39	13	the	the	DET
ejpam-846	39	14	optimization	optimization	NOUN
ejpam-846	39	15	in	in	ADP
ejpam-846	39	16	(	(	PUNCT
ejpam-846	39	17	2	2	NUM
ejpam-846	39	18	)	)	PUNCT
ejpam-846	39	19	may	may	AUX
ejpam-846	39	20	become	become	VERB
ejpam-846	39	21	fictitious	fictitious	ADJ
ejpam-846	39	22	.	.	PUNCT
ejpam-846	40	1	as	as	ADP
ejpam-846	40	2	an	an	DET
ejpam-846	40	3	example	example	NOUN
ejpam-846	40	4	,	,	PUNCT
ejpam-846	40	5	consider	consider	VERB
ejpam-846	40	6	the	the	DET
ejpam-846	40	7	edirisinghe	edirisinghe	PROPN
ejpam-846	40	8	/	/	SYM
ejpam-846	40	9	eur	eur	PROPN
ejpam-846	40	10	.	.	PUNCT
ejpam-846	41	1	j.	j.	PROPN
ejpam-846	41	2	pure	pure	PROPN
ejpam-846	41	3	appl	appl	PROPN
ejpam-846	41	4	.	.	PROPN
ejpam-846	41	5	math	math	PROPN
ejpam-846	41	6	,	,	PUNCT
ejpam-846	41	7	3	3	NUM
ejpam-846	41	8	(	(	PUNCT
ejpam-846	41	9	2010	2010	NUM
ejpam-846	41	10	)	)	PUNCT
ejpam-846	41	11	,	,	PUNCT
ejpam-846	41	12	572	572	NUM
ejpam-846	41	13	-	-	SYM
ejpam-846	41	14	592	592	NUM
ejpam-846	41	15	574	574	NUM
ejpam-846	41	16	case	case	NOUN
ejpam-846	41	17	when	when	SCONJ
ejpam-846	41	18	w	w	PROPN
ejpam-846	41	19	=	=	VERB
ejpam-846	41	20	i	i	PROPN
ejpam-846	41	21	,	,	PUNCT
ejpam-846	41	22	h	h	PROPN
ejpam-846	41	23	=	=	SYM
ejpam-846	41	24	0	0	NUM
ejpam-846	41	25	,	,	PUNCT
ejpam-846	41	26	t	t	NOUN
ejpam-846	41	27	=	=	SYM
ejpam-846	41	28	diag(ξ1	diag(ξ1	ADJ
ejpam-846	41	29	−	−	PROPN
ejpam-846	41	30	e[ξ1	e[ξ1	NOUN
ejpam-846	41	31	]	]	X
ejpam-846	41	32	,	,	PUNCT
ejpam-846	41	33	.	.	PUNCT
ejpam-846	41	34	.	.	PUNCT
ejpam-846	42	1	.	.	PUNCT
ejpam-846	43	1	,	,	PUNCT
ejpam-846	43	2	ξk	ξk	ADP
ejpam-846	43	3	−	−	PROPN
ejpam-846	43	4	e[ξk	e[ξk	PROPN
ejpam-846	43	5	]	]	PUNCT
ejpam-846	43	6	)	)	PUNCT
ejpam-846	43	7	,	,	PUNCT
ejpam-846	43	8	and	and	CCONJ
ejpam-846	43	9	q(y	q(y	PROPN
ejpam-846	43	10	)	)	PUNCT
ejpam-846	43	11	=	=	PUNCT
ejpam-846	43	12	(	(	PUNCT
ejpam-846	43	13	∑n2	∑n2	PROPN
ejpam-846	43	14	j=1	j=1	PROPN
ejpam-846	43	15	yj	yj	PROPN
ejpam-846	43	16	)	)	PUNCT
ejpam-846	43	17	2	2	NUM
ejpam-846	43	18	.	.	PUNCT
ejpam-846	44	1	then	then	ADV
ejpam-846	44	2	,	,	PUNCT
ejpam-846	44	3	ϕ(x	ϕ(x	PROPN
ejpam-846	44	4	,	,	PUNCT
ejpam-846	44	5	ξ	ξ	X
ejpam-846	44	6	)	)	PUNCT
ejpam-846	44	7	=	=	SYM
ejpam-846	44	8	x′(ξ	x′(ξ	PUNCT
ejpam-846	45	1	−	−	NOUN
ejpam-846	45	2	e[ξ])(ξ	e[ξ])(ξ	PUNCT
ejpam-846	45	3	−	−	PROPN
ejpam-846	45	4	e[ξ])′x	e[ξ])′x	PROPN
ejpam-846	45	5	,	,	PUNCT
ejpam-846	45	6	where	where	SCONJ
ejpam-846	45	7	prime	prime	ADJ
ejpam-846	45	8	denotes	denote	NOUN
ejpam-846	45	9	transposition	transposition	NOUN
ejpam-846	45	10	of	of	ADP
ejpam-846	45	11	a	a	DET
ejpam-846	45	12	vector	vector	NOUN
ejpam-846	45	13	.	.	PUNCT
ejpam-846	46	1	thus	thus	ADV
ejpam-846	46	2	,	,	PUNCT
ejpam-846	46	3	it	it	PRON
ejpam-846	46	4	follows	follow	VERB
ejpam-846	46	5	that	that	SCONJ
ejpam-846	46	6	the	the	DET
ejpam-846	46	7	risk	risk	NOUN
ejpam-846	46	8	function	function	NOUN
ejpam-846	46	9	is	be	AUX
ejpam-846	46	10	ψ(x	ψ(x	NOUN
ejpam-846	46	11	)	)	PUNCT
ejpam-846	47	1	=	=	SYM
ejpam-846	47	2	x′mx	x′mx	PROPN
ejpam-846	47	3	,	,	PUNCT
ejpam-846	47	4	wherem	wherem	PROPN
ejpam-846	47	5	is	be	AUX
ejpam-846	47	6	the	the	DET
ejpam-846	47	7	variance	variance	NOUN
ejpam-846	47	8	-	-	PUNCT
ejpam-846	47	9	covariance	covariance	NOUN
ejpam-846	47	10	matrix	matrix	NOUN
ejpam-846	47	11	of	of	ADP
ejpam-846	47	12	ξ	ξ	PROPN
ejpam-846	47	13	.	.	PUNCT
ejpam-846	48	1	in	in	ADP
ejpam-846	48	2	this	this	DET
ejpam-846	48	3	special	special	ADJ
ejpam-846	48	4	case	case	NOUN
ejpam-846	48	5	,	,	PUNCT
ejpam-846	48	6	hence	hence	ADV
ejpam-846	48	7	,	,	PUNCT
ejpam-846	48	8	the	the	DET
ejpam-846	48	9	model	model	NOUN
ejpam-846	48	10	in	in	ADP
ejpam-846	48	11	(	(	PUNCT
ejpam-846	48	12	1	1	X
ejpam-846	48	13	)	)	PUNCT
ejpam-846	48	14	achieves	achieve	VERB
ejpam-846	48	15	a	a	DET
ejpam-846	48	16	mean	mean	ADJ
ejpam-846	48	17	-	-	PUNCT
ejpam-846	48	18	variance	variance	NOUN
ejpam-846	48	19	trade	trade	NOUN
ejpam-846	48	20	off	off	ADP
ejpam-846	48	21	in	in	ADP
ejpam-846	48	22	asset	asset	NOUN
ejpam-846	48	23	selection	selection	NOUN
ejpam-846	48	24	,	,	PUNCT
ejpam-846	48	25	see	see	VERB
ejpam-846	48	26	markowitz	markowitz	PROPN
ejpam-846	48	27	[	[	X
ejpam-846	48	28	15	15	NUM
ejpam-846	48	29	]	]	PUNCT
ejpam-846	48	30	.	.	PUNCT
ejpam-846	49	1	in	in	ADP
ejpam-846	49	2	general	general	ADJ
ejpam-846	49	3	,	,	PUNCT
ejpam-846	49	4	the	the	DET
ejpam-846	49	5	optimization	optimization	NOUN
ejpam-846	49	6	in	in	ADP
ejpam-846	49	7	(	(	PUNCT
ejpam-846	49	8	2	2	X
ejpam-846	49	9	)	)	PUNCT
ejpam-846	49	10	must	must	AUX
ejpam-846	49	11	be	be	AUX
ejpam-846	49	12	carried	carry	VERB
ejpam-846	49	13	out	out	ADP
ejpam-846	49	14	and	and	CCONJ
ejpam-846	49	15	the	the	DET
ejpam-846	49	16	expectation	expectation	NOUN
ejpam-846	49	17	risk	risk	NOUN
ejpam-846	49	18	functional	functional	ADJ
ejpam-846	49	19	is	be	AUX
ejpam-846	49	20	difficult	difficult	ADJ
ejpam-846	49	21	to	to	PART
ejpam-846	49	22	evaluate	evaluate	VERB
ejpam-846	49	23	.	.	PUNCT
ejpam-846	50	1	it	it	PRON
ejpam-846	50	2	is	be	AUX
ejpam-846	50	3	assumed	assume	VERB
ejpam-846	50	4	that	that	SCONJ
ejpam-846	50	5	the	the	DET
ejpam-846	50	6	feasible	feasible	ADJ
ejpam-846	50	7	set	set	NOUN
ejpam-846	50	8	x	x	SYM
ejpam-846	50	9	of	of	ADP
ejpam-846	50	10	(	(	PUNCT
ejpam-846	50	11	1	1	NUM
ejpam-846	50	12	)	)	PUNCT
ejpam-846	50	13	is	be	AUX
ejpam-846	50	14	nonempty	nonempty	ADJ
ejpam-846	50	15	,	,	PUNCT
ejpam-846	50	16	i.e.	i.e.	X
ejpam-846	50	17	,	,	PUNCT
ejpam-846	50	18	x	x	X
ejpam-846	50	19	:	:	PUNCT
ejpam-846	50	20	=	=	SYM
ejpam-846	50	21	{	{	PUNCT
ejpam-846	50	22	x	x	PUNCT
ejpam-846	50	23	∈	∈	PROPN
ejpam-846	50	24	ℜn1	ℜn1	NOUN
ejpam-846	50	25	:	:	PUNCT
ejpam-846	50	26	ax	ax	NOUN
ejpam-846	50	27	=	=	SYM
ejpam-846	50	28	b	b	PROPN
ejpam-846	50	29	,	,	PUNCT
ejpam-846	50	30	x	x	X
ejpam-846	50	31	≥	≥	NOUN
ejpam-846	50	32	0	0	NUM
ejpam-846	50	33	}	}	PUNCT
ejpam-846	50	34	̸=	̸=	PROPN
ejpam-846	50	35	∅.	∅.	ADV
ejpam-846	50	36	(	(	PUNCT
ejpam-846	50	37	3	3	NUM
ejpam-846	50	38	)	)	PUNCT
ejpam-846	50	39	also	also	ADV
ejpam-846	50	40	,	,	PUNCT
ejpam-846	50	41	it	it	PRON
ejpam-846	50	42	is	be	AUX
ejpam-846	50	43	assumed	assume	VERB
ejpam-846	50	44	that	that	SCONJ
ejpam-846	50	45	the	the	DET
ejpam-846	50	46	risk	risk	NOUN
ejpam-846	50	47	-	-	PUNCT
ejpam-846	50	48	defining	define	VERB
ejpam-846	50	49	(	(	PUNCT
ejpam-846	50	50	second	second	ADJ
ejpam-846	50	51	stage	stage	NOUN
ejpam-846	50	52	)	)	PUNCT
ejpam-846	50	53	problem	problem	NOUN
ejpam-846	50	54	(	(	PUNCT
ejpam-846	50	55	2	2	X
ejpam-846	50	56	)	)	PUNCT
ejpam-846	50	57	is	be	AUX
ejpam-846	50	58	feasible	feasible	ADJ
ejpam-846	50	59	and	and	CCONJ
ejpam-846	50	60	bounded	bound	VERB
ejpam-846	50	61	on	on	ADP
ejpam-846	50	62	ξ	ξ	PROPN
ejpam-846	50	63	for	for	ADP
ejpam-846	50	64	x	x	SYM
ejpam-846	50	65	∈	∈	PROPN
ejpam-846	50	66	x.	x.	NOUN
ejpam-846	50	67	thus	thus	ADV
ejpam-846	50	68	,	,	PUNCT
ejpam-846	50	69	ϕ	ϕ	PROPN
ejpam-846	50	70	is	be	AUX
ejpam-846	50	71	a	a	DET
ejpam-846	50	72	(	(	PUNCT
ejpam-846	50	73	proper	proper	ADJ
ejpam-846	50	74	)	)	PUNCT
ejpam-846	50	75	convex	convex	NOUN
ejpam-846	50	76	function	function	NOUN
ejpam-846	50	77	in	in	ADP
ejpam-846	50	78	ξ	ξ	PROPN
ejpam-846	50	79	and	and	CCONJ
ejpam-846	50	80	x	x	SYM
ejpam-846	50	81	,	,	PUNCT
ejpam-846	50	82	separately	separately	ADV
ejpam-846	50	83	.	.	PUNCT
ejpam-846	51	1	since	since	SCONJ
ejpam-846	51	2	integration	integration	NOUN
ejpam-846	51	3	with	with	ADP
ejpam-846	51	4	respect	respect	NOUN
ejpam-846	51	5	to	to	ADP
ejpam-846	51	6	a	a	DET
ejpam-846	51	7	probability	probability	NOUN
ejpam-846	51	8	measure	measure	NOUN
ejpam-846	51	9	preserves	preserve	VERB
ejpam-846	51	10	order	order	NOUN
ejpam-846	51	11	,	,	PUNCT
ejpam-846	51	12	the	the	DET
ejpam-846	51	13	risk	risk	NOUN
ejpam-846	51	14	function	function	NOUN
ejpam-846	51	15	ψ(x	ψ(x	NOUN
ejpam-846	51	16	)	)	PUNCT
ejpam-846	51	17	is	be	AUX
ejpam-846	51	18	convex	convex	ADJ
ejpam-846	51	19	on	on	ADP
ejpam-846	51	20	x	x	X
ejpam-846	51	21	,	,	PUNCT
ejpam-846	51	22	see	see	VERB
ejpam-846	51	23	wets	wet	VERB
ejpam-846	51	24	[	[	X
ejpam-846	51	25	19	19	NUM
ejpam-846	51	26	]	]	PUNCT
ejpam-846	51	27	.	.	PUNCT
ejpam-846	52	1	it	it	PRON
ejpam-846	52	2	is	be	AUX
ejpam-846	52	3	generally	generally	ADV
ejpam-846	52	4	accepted	accept	VERB
ejpam-846	52	5	that	that	SCONJ
ejpam-846	52	6	econometric	econometric	ADJ
ejpam-846	52	7	modeling	modeling	NOUN
ejpam-846	52	8	of	of	ADP
ejpam-846	52	9	financial	financial	ADJ
ejpam-846	52	10	time	time	NOUN
ejpam-846	52	11	series	series	NOUN
ejpam-846	52	12	is	be	AUX
ejpam-846	52	13	of	of	ADP
ejpam-846	52	14	paramount	paramount	ADJ
ejpam-846	52	15	importance	importance	NOUN
ejpam-846	52	16	for	for	ADP
ejpam-846	52	17	successful	successful	ADJ
ejpam-846	52	18	investment	investment	NOUN
ejpam-846	52	19	decision	decision	NOUN
ejpam-846	52	20	making	make	VERB
ejpam-846	52	21	in	in	ADP
ejpam-846	52	22	the	the	DET
ejpam-846	52	23	stock	stock	NOUN
ejpam-846	52	24	markets	market	NOUN
ejpam-846	52	25	.	.	PUNCT
ejpam-846	53	1	financial	financial	ADJ
ejpam-846	53	2	time	time	NOUN
ejpam-846	53	3	series	series	PROPN
ejpam-846	53	4	are	be	AUX
ejpam-846	53	5	often	often	ADV
ejpam-846	53	6	co	co	ADJ
ejpam-846	53	7	-	-	VERB
ejpam-846	53	8	integrated	integrated	ADJ
ejpam-846	53	9	and	and	CCONJ
ejpam-846	53	10	this	this	DET
ejpam-846	53	11	phenomenon	phenomenon	NOUN
ejpam-846	53	12	is	be	AUX
ejpam-846	53	13	useful	useful	ADJ
ejpam-846	53	14	in	in	ADP
ejpam-846	53	15	constructing	construct	VERB
ejpam-846	53	16	tests	test	NOUN
ejpam-846	53	17	of	of	ADP
ejpam-846	53	18	stock	stock	NOUN
ejpam-846	53	19	market	market	NOUN
ejpam-846	53	20	volatility	volatility	NOUN
ejpam-846	53	21	.	.	PUNCT
ejpam-846	54	1	the	the	DET
ejpam-846	54	2	implications	implication	NOUN
ejpam-846	54	3	of	of	ADP
ejpam-846	54	4	excess	excess	ADJ
ejpam-846	54	5	volatility	volatility	NOUN
ejpam-846	54	6	resulting	result	VERB
ejpam-846	54	7	from	from	ADP
ejpam-846	54	8	granger	granger	PROPN
ejpam-846	54	9	’s	’s	PART
ejpam-846	54	10	co	co	NOUN
ejpam-846	54	11	-	-	NOUN
ejpam-846	54	12	integration	integration	NOUN
ejpam-846	54	13	approach	approach	NOUN
ejpam-846	54	14	is	be	AUX
ejpam-846	54	15	highly	highly	ADV
ejpam-846	54	16	valuable	valuable	ADJ
ejpam-846	54	17	to	to	ADP
ejpam-846	54	18	financial	financial	ADJ
ejpam-846	54	19	managers	manager	NOUN
ejpam-846	54	20	.	.	PUNCT
ejpam-846	55	1	rather	rather	ADV
ejpam-846	55	2	than	than	ADP
ejpam-846	55	3	focusing	focus	VERB
ejpam-846	55	4	on	on	ADP
ejpam-846	55	5	time	time	NOUN
ejpam-846	55	6	series	series	PROPN
ejpam-846	55	7	modeling	modeling	PROPN
ejpam-846	55	8	,	,	PUNCT
ejpam-846	55	9	this	this	DET
ejpam-846	55	10	paper	paper	NOUN
ejpam-846	55	11	aims	aim	VERB
ejpam-846	55	12	at	at	ADP
ejpam-846	55	13	controlling	control	VERB
ejpam-846	55	14	risks	risk	NOUN
ejpam-846	55	15	directly	directly	ADV
ejpam-846	55	16	via	via	ADP
ejpam-846	55	17	portfolio	portfolio	NOUN
ejpam-846	55	18	optimization	optimization	NOUN
ejpam-846	55	19	,	,	PUNCT
ejpam-846	55	20	recognizing	recognize	VERB
ejpam-846	55	21	that	that	SCONJ
ejpam-846	55	22	scenarios	scenario	NOUN
ejpam-846	55	23	of	of	ADP
ejpam-846	55	24	the	the	DET
ejpam-846	55	25	future	future	NOUN
ejpam-846	55	26	can	can	AUX
ejpam-846	55	27	not	not	PART
ejpam-846	55	28	be	be	AUX
ejpam-846	55	29	known	know	VERB
ejpam-846	55	30	with	with	ADP
ejpam-846	55	31	certainty	certainty	PROPN
ejpam-846	55	32	.	.	PUNCT
ejpam-846	56	1	this	this	PRON
ejpam-846	56	2	is	be	AUX
ejpam-846	56	3	done	do	VERB
ejpam-846	56	4	through	through	ADP
ejpam-846	56	5	incorporating	incorporate	VERB
ejpam-846	56	6	risk	risk	NOUN
ejpam-846	56	7	functions	function	NOUN
ejpam-846	56	8	,	,	PUNCT
ejpam-846	56	9	of	of	ADP
ejpam-846	56	10	type	type	NOUN
ejpam-846	56	11	ψ(x	ψ(x	NOUN
ejpam-846	56	12	)	)	PUNCT
ejpam-846	56	13	,	,	PUNCT
ejpam-846	56	14	that	that	PRON
ejpam-846	56	15	involve	involve	VERB
ejpam-846	56	16	computing	compute	VERB
ejpam-846	56	17	expectations	expectation	NOUN
ejpam-846	56	18	in	in	ADP
ejpam-846	56	19	high	high	ADJ
ejpam-846	56	20	dimensions	dimension	NOUN
ejpam-846	56	21	.	.	PUNCT
ejpam-846	57	1	the	the	DET
ejpam-846	57	2	concept	concept	NOUN
ejpam-846	57	3	of	of	ADP
ejpam-846	57	4	approximating	approximate	VERB
ejpam-846	57	5	expectation	expectation	NOUN
ejpam-846	57	6	functions	function	NOUN
ejpam-846	57	7	using	use	VERB
ejpam-846	57	8	general	general	ADJ
ejpam-846	57	9	moment	moment	NOUN
ejpam-846	57	10	problems	problem	NOUN
ejpam-846	57	11	is	be	AUX
ejpam-846	57	12	presented	present	VERB
ejpam-846	57	13	in	in	ADP
ejpam-846	57	14	section	section	NOUN
ejpam-846	57	15	2	2	NUM
ejpam-846	57	16	,	,	PUNCT
ejpam-846	57	17	where	where	SCONJ
ejpam-846	57	18	the	the	DET
ejpam-846	57	19	case	case	NOUN
ejpam-846	57	20	of	of	ADP
ejpam-846	57	21	using	use	VERB
ejpam-846	57	22	only	only	ADJ
ejpam-846	57	23	first	first	ADJ
ejpam-846	57	24	moments	moment	NOUN
ejpam-846	57	25	is	be	AUX
ejpam-846	57	26	also	also	ADV
ejpam-846	57	27	considered	consider	VERB
ejpam-846	57	28	.	.	PUNCT
ejpam-846	58	1	in	in	ADP
ejpam-846	58	2	section	section	NOUN
ejpam-846	58	3	3	3	NUM
ejpam-846	58	4	,	,	PUNCT
ejpam-846	58	5	approximations	approximation	NOUN
ejpam-846	58	6	using	use	VERB
ejpam-846	58	7	both	both	CCONJ
ejpam-846	58	8	first	first	ADJ
ejpam-846	58	9	and	and	CCONJ
ejpam-846	58	10	second	second	ADJ
ejpam-846	58	11	moments	moment	NOUN
ejpam-846	58	12	(	(	PUNCT
ejpam-846	58	13	including	include	VERB
ejpam-846	58	14	covariances	covariance	NOUN
ejpam-846	58	15	)	)	PUNCT
ejpam-846	58	16	are	be	AUX
ejpam-846	58	17	developed	develop	VERB
ejpam-846	58	18	using	use	VERB
ejpam-846	58	19	the	the	DET
ejpam-846	58	20	underling	underling	NOUN
ejpam-846	58	21	moment	moment	NOUN
ejpam-846	58	22	problem	problem	NOUN
ejpam-846	58	23	.	.	PUNCT
ejpam-846	59	1	the	the	DET
ejpam-846	59	2	portfolio	portfolio	NOUN
ejpam-846	59	3	optimization	optimization	NOUN
ejpam-846	59	4	model	model	NOUN
ejpam-846	59	5	used	use	VERB
ejpam-846	59	6	for	for	ADP
ejpam-846	59	7	demonstrating	demonstrate	VERB
ejpam-846	59	8	the	the	DET
ejpam-846	59	9	approximations	approximation	NOUN
ejpam-846	59	10	is	be	AUX
ejpam-846	59	11	in	in	ADP
ejpam-846	59	12	section	section	NOUN
ejpam-846	59	13	4	4	NUM
ejpam-846	59	14	.	.	PUNCT
ejpam-846	59	15	section	section	NOUN
ejpam-846	59	16	5	5	NUM
ejpam-846	59	17	reports	report	VERB
ejpam-846	59	18	the	the	DET
ejpam-846	59	19	results	result	NOUN
ejpam-846	59	20	from	from	ADP
ejpam-846	59	21	portfolio	portfolio	NOUN
ejpam-846	59	22	analysis	analysis	NOUN
ejpam-846	59	23	while	while	SCONJ
ejpam-846	59	24	conclusions	conclusion	NOUN
ejpam-846	59	25	are	be	AUX
ejpam-846	59	26	in	in	ADP
ejpam-846	59	27	section	section	NOUN
ejpam-846	59	28	6	6	NUM
ejpam-846	59	29	.	.	NOUN
ejpam-846	59	30	2	2	NUM
ejpam-846	59	31	.	.	X
ejpam-846	59	32	approximating	approximate	VERB
ejpam-846	59	33	the	the	DET
ejpam-846	59	34	expectation	expectation	NOUN
ejpam-846	59	35	when	when	SCONJ
ejpam-846	59	36	ξ	ξ	PROPN
ejpam-846	59	37	has	have	VERB
ejpam-846	59	38	a	a	DET
ejpam-846	59	39	large	large	ADJ
ejpam-846	59	40	number	number	NOUN
ejpam-846	59	41	k	k	NOUN
ejpam-846	59	42	of	of	ADP
ejpam-846	59	43	random	random	ADJ
ejpam-846	59	44	components	component	NOUN
ejpam-846	59	45	that	that	PRON
ejpam-846	59	46	are	be	AUX
ejpam-846	59	47	possibly	possibly	ADV
ejpam-846	59	48	stochastically	stochastically	ADV
ejpam-846	59	49	dependent	dependent	ADJ
ejpam-846	59	50	,	,	PUNCT
ejpam-846	59	51	solution	solution	NOUN
ejpam-846	59	52	of	of	ADP
ejpam-846	59	53	the	the	DET
ejpam-846	59	54	model	model	NOUN
ejpam-846	59	55	(	(	PUNCT
ejpam-846	59	56	1	1	X
ejpam-846	59	57	)	)	PUNCT
ejpam-846	59	58	is	be	AUX
ejpam-846	59	59	computationally	computationally	ADV
ejpam-846	59	60	tedious	tedious	ADJ
ejpam-846	59	61	,	,	PUNCT
ejpam-846	59	62	and	and	CCONJ
ejpam-846	59	63	thus	thus	ADV
ejpam-846	59	64	,	,	PUNCT
ejpam-846	59	65	approximating	approximate	VERB
ejpam-846	59	66	the	the	DET
ejpam-846	59	67	expectation	expectation	NOUN
ejpam-846	59	68	of	of	ADP
ejpam-846	59	69	the	the	DET
ejpam-846	59	70	risks	risk	NOUN
ejpam-846	59	71	is	be	AUX
ejpam-846	59	72	a	a	DET
ejpam-846	59	73	critical	critical	ADJ
ejpam-846	59	74	component	component	NOUN
ejpam-846	59	75	in	in	ADP
ejpam-846	59	76	the	the	DET
ejpam-846	59	77	numerical	numerical	ADJ
ejpam-846	59	78	solution	solution	NOUN
ejpam-846	59	79	.	.	PUNCT
ejpam-846	60	1	the	the	DET
ejpam-846	60	2	basic	basic	ADJ
ejpam-846	60	3	approach	approach	NOUN
ejpam-846	60	4	is	be	AUX
ejpam-846	60	5	to	to	PART
ejpam-846	60	6	determine	determine	VERB
ejpam-846	60	7	a	a	DET
ejpam-846	60	8	lower	low	ADJ
ejpam-846	60	9	bound	bind	VERB
ejpam-846	60	10	on	on	ADP
ejpam-846	60	11	ψ(x	ψ(x	NUM
ejpam-846	60	12	)	)	PUNCT
ejpam-846	60	13	,	,	PUNCT
ejpam-846	60	14	say	say	VERB
ejpam-846	60	15	ψl(x	ψl(x	NOUN
ejpam-846	60	16	)	)	PUNCT
ejpam-846	60	17	,	,	PUNCT
ejpam-846	60	18	that	that	PRON
ejpam-846	60	19	is	be	AUX
ejpam-846	60	20	easily	easily	ADV
ejpam-846	60	21	computable	computable	ADJ
ejpam-846	60	22	,	,	PUNCT
ejpam-846	60	23	for	for	ADP
ejpam-846	60	24	example	example	NOUN
ejpam-846	60	25	,	,	PUNCT
ejpam-846	60	26	without	without	ADP
ejpam-846	60	27	the	the	DET
ejpam-846	60	28	need	need	NOUN
ejpam-846	60	29	for	for	ADP
ejpam-846	60	30	numerical	numerical	ADJ
ejpam-846	60	31	integration	integration	NOUN
ejpam-846	60	32	w.r.t	w.r.t	VERB
ejpam-846	60	33	.	.	PUNCT
ejpam-846	61	1	the	the	DET
ejpam-846	61	2	probability	probability	NOUN
ejpam-846	61	3	measure	measure	NOUN
ejpam-846	61	4	p	p	NOUN
ejpam-846	61	5	tr	tr	VERB
ejpam-846	61	6	.	.	PUNCT
ejpam-846	61	7	then	then	ADV
ejpam-846	61	8	,	,	PUNCT
ejpam-846	61	9	(	(	PUNCT
ejpam-846	61	10	1	1	X
ejpam-846	61	11	)	)	PUNCT
ejpam-846	61	12	is	be	AUX
ejpam-846	61	13	approximated	approximate	VERB
ejpam-846	61	14	with	with	ADP
ejpam-846	61	15	ψl	ψl	NOUN
ejpam-846	61	16	in	in	ADP
ejpam-846	61	17	place	place	NOUN
ejpam-846	61	18	of	of	ADP
ejpam-846	61	19	ψ	ψ	NOUN
ejpam-846	61	20	,	,	PUNCT
ejpam-846	61	21	i.e.	i.e.	X
ejpam-846	61	22	,	,	PUNCT
ejpam-846	61	23	zl	zl	ADJ
ejpam-846	61	24	:	:	PUNCT
ejpam-846	61	25	=	=	SYM
ejpam-846	61	26	max	max	PROPN
ejpam-846	61	27	x∈x	x∈x	PROPN
ejpam-846	61	28	{	{	PUNCT
ejpam-846	61	29	c(x)−	c(x)−	PROPN
ejpam-846	61	30	λ	λ	PROPN
ejpam-846	61	31	ψl(x	ψl(x	NUM
ejpam-846	61	32	)	)	PUNCT
ejpam-846	61	33	}	}	PUNCT
ejpam-846	61	34	,	,	PUNCT
ejpam-846	61	35	(	(	PUNCT
ejpam-846	61	36	4	4	X
ejpam-846	61	37	)	)	PUNCT
ejpam-846	61	38	the	the	DET
ejpam-846	61	39	solution	solution	NOUN
ejpam-846	61	40	of	of	ADP
ejpam-846	61	41	which	which	PRON
ejpam-846	61	42	yields	yield	VERB
ejpam-846	61	43	an	an	DET
ejpam-846	61	44	optimal	optimal	ADJ
ejpam-846	61	45	solution	solution	NOUN
ejpam-846	61	46	x∗l	x∗l	NUM
ejpam-846	61	47	that	that	PRON
ejpam-846	61	48	can	can	AUX
ejpam-846	61	49	serve	serve	VERB
ejpam-846	61	50	as	as	ADP
ejpam-846	61	51	a	a	DET
ejpam-846	61	52	near	near	ADV
ejpam-846	61	53	-	-	PUNCT
ejpam-846	61	54	optimal	optimal	ADJ
ejpam-846	61	55	decision	decision	NOUN
ejpam-846	61	56	.	.	PUNCT
ejpam-846	62	1	for	for	ADP
ejpam-846	62	2	this	this	DET
ejpam-846	62	3	reason	reason	NOUN
ejpam-846	62	4	,	,	PUNCT
ejpam-846	62	5	ψl	ψl	PROPN
ejpam-846	62	6	is	be	AUX
ejpam-846	62	7	required	require	VERB
ejpam-846	62	8	to	to	PART
ejpam-846	62	9	be	be	AUX
ejpam-846	62	10	a	a	DET
ejpam-846	62	11	high	high	ADJ
ejpam-846	62	12	-	-	PUNCT
ejpam-846	62	13	quality	quality	NOUN
ejpam-846	62	14	approximation	approximation	NOUN
ejpam-846	62	15	for	for	ADP
ejpam-846	62	16	ψ	ψ	X
ejpam-846	62	17	.	.	PUNCT
ejpam-846	63	1	in	in	ADP
ejpam-846	63	2	fact	fact	NOUN
ejpam-846	63	3	,	,	PUNCT
ejpam-846	63	4	edirisinghe	edirisinghe	PROPN
ejpam-846	63	5	/	/	SYM
ejpam-846	63	6	eur	eur	PROPN
ejpam-846	63	7	.	.	PUNCT
ejpam-846	64	1	j.	j.	PROPN
ejpam-846	64	2	pure	pure	PROPN
ejpam-846	64	3	appl	appl	PROPN
ejpam-846	64	4	.	.	PROPN
ejpam-846	64	5	math	math	PROPN
ejpam-846	64	6	,	,	PUNCT
ejpam-846	64	7	3	3	NUM
ejpam-846	64	8	(	(	PUNCT
ejpam-846	64	9	2010	2010	NUM
ejpam-846	64	10	)	)	PUNCT
ejpam-846	64	11	,	,	PUNCT
ejpam-846	64	12	572	572	NUM
ejpam-846	64	13	-	-	SYM
ejpam-846	64	14	592	592	NUM
ejpam-846	64	15	575	575	NUM
ejpam-846	64	16	the	the	DET
ejpam-846	64	17	lower	low	ADJ
ejpam-846	64	18	and	and	CCONJ
ejpam-846	64	19	upper	upper	ADJ
ejpam-846	64	20	bounds	bound	NOUN
ejpam-846	64	21	resulting	result	VERB
ejpam-846	64	22	from	from	ADP
ejpam-846	64	23	the	the	DET
ejpam-846	64	24	use	use	NOUN
ejpam-846	64	25	of	of	ADP
ejpam-846	64	26	ψl(x	ψl(x	NOUN
ejpam-846	64	27	)	)	PUNCT
ejpam-846	64	28	,	,	PUNCT
ejpam-846	64	29	as	as	SCONJ
ejpam-846	64	30	given	give	VERB
ejpam-846	64	31	by	by	ADP
ejpam-846	64	32	,	,	PUNCT
ejpam-846	64	33	zl	zl	X
ejpam-846	64	34	≥	≥	NOUN
ejpam-846	64	35	z∗	z∗	X
ejpam-846	64	36	≥	≥	NOUN
ejpam-846	64	37	c(x∗l)−	c(x∗l)−	PROPN
ejpam-846	64	38	λψ(x∗l	λψ(x∗l	CCONJ
ejpam-846	64	39	)	)	PUNCT
ejpam-846	64	40	(	(	PUNCT
ejpam-846	64	41	5	5	X
ejpam-846	64	42	)	)	PUNCT
ejpam-846	64	43	may	may	AUX
ejpam-846	64	44	be	be	AUX
ejpam-846	64	45	used	use	VERB
ejpam-846	64	46	to	to	PART
ejpam-846	64	47	verify	verify	VERB
ejpam-846	64	48	the	the	DET
ejpam-846	64	49	quality	quality	NOUN
ejpam-846	64	50	of	of	ADP
ejpam-846	64	51	the	the	DET
ejpam-846	64	52	computed	computed	ADJ
ejpam-846	64	53	allocation	allocation	NOUN
ejpam-846	64	54	x∗l	x∗l	PROPN
ejpam-846	64	55	.	.	PUNCT
ejpam-846	65	1	the	the	DET
ejpam-846	65	2	lower	lower	ADV
ejpam-846	65	3	bound	bind	VERB
ejpam-846	65	4	in	in	ADP
ejpam-846	65	5	(	(	PUNCT
ejpam-846	65	6	5	5	NUM
ejpam-846	65	7	)	)	PUNCT
ejpam-846	65	8	requires	require	VERB
ejpam-846	65	9	computing	compute	VERB
ejpam-846	65	10	the	the	DET
ejpam-846	65	11	expected	expect	VERB
ejpam-846	65	12	risk	risk	NOUN
ejpam-846	65	13	function	function	NOUN
ejpam-846	65	14	once	once	ADV
ejpam-846	65	15	;	;	PUNCT
ejpam-846	65	16	however	however	ADV
ejpam-846	65	17	,	,	PUNCT
ejpam-846	65	18	if	if	SCONJ
ejpam-846	65	19	even	even	ADV
ejpam-846	65	20	that	that	PRON
ejpam-846	65	21	is	be	AUX
ejpam-846	65	22	complicated	complicated	ADJ
ejpam-846	65	23	,	,	PUNCT
ejpam-846	65	24	one	one	PRON
ejpam-846	65	25	may	may	AUX
ejpam-846	65	26	use	use	VERB
ejpam-846	65	27	an	an	DET
ejpam-846	65	28	upper	upper	ADJ
ejpam-846	65	29	bounding	bounding	NOUN
ejpam-846	65	30	function	function	NOUN
ejpam-846	65	31	ψu(x	ψu(x	VERB
ejpam-846	65	32	)	)	PUNCT
ejpam-846	65	33	on	on	ADP
ejpam-846	65	34	the	the	DET
ejpam-846	65	35	expected	expect	VERB
ejpam-846	65	36	risk	risk	NOUN
ejpam-846	65	37	function	function	NOUN
ejpam-846	65	38	,	,	PUNCT
ejpam-846	65	39	so	so	SCONJ
ejpam-846	65	40	that	that	SCONJ
ejpam-846	65	41	the	the	DET
ejpam-846	65	42	quality	quality	NOUN
ejpam-846	65	43	of	of	ADP
ejpam-846	65	44	the	the	DET
ejpam-846	65	45	computed	compute	VERB
ejpam-846	65	46	allocation	allocation	NOUN
ejpam-846	65	47	may	may	AUX
ejpam-846	65	48	be	be	AUX
ejpam-846	65	49	measured	measure	VERB
ejpam-846	65	50	with	with	ADP
ejpam-846	65	51	respect	respect	NOUN
ejpam-846	65	52	to	to	ADP
ejpam-846	65	53	the	the	DET
ejpam-846	65	54	relative	relative	ADJ
ejpam-846	65	55	gap	gap	NOUN
ejpam-846	65	56	,	,	PUNCT
ejpam-846	65	57	given	give	VERB
ejpam-846	65	58	by	by	ADP
ejpam-846	65	59	[	[	X
ejpam-846	65	60	ψu(x	ψu(x	NOUN
ejpam-846	65	61	∗	∗	NOUN
ejpam-846	65	62	l)−	l)−	PROPN
ejpam-846	65	63	ψl(x	ψl(x	NOUN
ejpam-846	65	64	∗	∗	NOUN
ejpam-846	65	65	l)]/|zl|	l)]/|zl|	PROPN
ejpam-846	65	66	.	.	PUNCT
ejpam-846	66	1	in	in	ADP
ejpam-846	66	2	this	this	DET
ejpam-846	66	3	sense	sense	NOUN
ejpam-846	66	4	,	,	PUNCT
ejpam-846	66	5	the	the	DET
ejpam-846	66	6	lower	low	ADJ
ejpam-846	66	7	approximation	approximation	NOUN
ejpam-846	66	8	is	be	AUX
ejpam-846	66	9	quite	quite	ADV
ejpam-846	66	10	important	important	ADJ
ejpam-846	66	11	and	and	CCONJ
ejpam-846	66	12	it	it	PRON
ejpam-846	66	13	is	be	AUX
ejpam-846	66	14	the	the	DET
ejpam-846	66	15	central	central	ADJ
ejpam-846	66	16	focus	focus	NOUN
ejpam-846	66	17	here	here	ADV
ejpam-846	66	18	.	.	PUNCT
ejpam-846	67	1	we	we	PRON
ejpam-846	67	2	will	will	AUX
ejpam-846	67	3	utilize	utilize	VERB
ejpam-846	67	4	first	first	ADJ
ejpam-846	67	5	and	and	CCONJ
ejpam-846	67	6	second	second	ADJ
ejpam-846	67	7	moment	moment	NOUN
ejpam-846	67	8	information	information	NOUN
ejpam-846	67	9	of	of	ADP
ejpam-846	67	10	p	p	NOUN
ejpam-846	67	11	tr	tr	VERB
ejpam-846	67	12	for	for	ADP
ejpam-846	67	13	this	this	DET
ejpam-846	67	14	purpose	purpose	NOUN
ejpam-846	67	15	,	,	PUNCT
ejpam-846	67	16	and	and	CCONJ
ejpam-846	67	17	then	then	ADV
ejpam-846	67	18	demonstrate	demonstrate	VERB
ejpam-846	67	19	the	the	DET
ejpam-846	67	20	quality	quality	NOUN
ejpam-846	67	21	of	of	ADP
ejpam-846	67	22	these	these	DET
ejpam-846	67	23	approximations	approximation	NOUN
ejpam-846	67	24	in	in	ADP
ejpam-846	67	25	the	the	DET
ejpam-846	67	26	financial	financial	ADJ
ejpam-846	67	27	portfolio	portfolio	NOUN
ejpam-846	67	28	application	application	NOUN
ejpam-846	67	29	later	later	ADV
ejpam-846	67	30	.	.	PUNCT
ejpam-846	68	1	2.1	2.1	NUM
ejpam-846	68	2	.	.	PUNCT
ejpam-846	68	3	generalized	generalize	VERB
ejpam-846	68	4	moment	moment	NOUN
ejpam-846	68	5	problems	problem	NOUN
ejpam-846	68	6	while	while	SCONJ
ejpam-846	68	7	there	there	PRON
ejpam-846	68	8	exist	exist	VERB
ejpam-846	68	9	varying	vary	VERB
ejpam-846	68	10	approaches	approach	NOUN
ejpam-846	68	11	for	for	ADP
ejpam-846	68	12	constructing	construct	VERB
ejpam-846	68	13	approximations	approximation	NOUN
ejpam-846	68	14	on	on	ADP
ejpam-846	68	15	ψ(x	ψ(x	NUM
ejpam-846	68	16	)	)	PUNCT
ejpam-846	68	17	,	,	PUNCT
ejpam-846	68	18	one	one	NOUN
ejpam-846	68	19	that	that	PRON
ejpam-846	68	20	has	have	AUX
ejpam-846	68	21	received	receive	VERB
ejpam-846	68	22	most	most	ADJ
ejpam-846	68	23	attention	attention	NOUN
ejpam-846	68	24	is	be	AUX
ejpam-846	68	25	the	the	DET
ejpam-846	68	26	bounds	bound	NOUN
ejpam-846	68	27	using	use	VERB
ejpam-846	68	28	a	a	DET
ejpam-846	68	29	given	give	VERB
ejpam-846	68	30	set	set	NOUN
ejpam-846	68	31	of	of	ADP
ejpam-846	68	32	moment	moment	NOUN
ejpam-846	68	33	information	information	NOUN
ejpam-846	68	34	of	of	ADP
ejpam-846	68	35	the	the	DET
ejpam-846	68	36	underlying	underlying	ADJ
ejpam-846	68	37	probability	probability	NOUN
ejpam-846	68	38	distribution	distribution	NOUN
ejpam-846	68	39	,	,	PUNCT
ejpam-846	68	40	termed	term	VERB
ejpam-846	68	41	the	the	DET
ejpam-846	68	42	generalized	generalized	ADJ
ejpam-846	68	43	moment	moment	NOUN
ejpam-846	68	44	problem	problem	NOUN
ejpam-846	68	45	(	(	PUNCT
ejpam-846	68	46	gmp	gmp	PROPN
ejpam-846	68	47	)	)	PUNCT
ejpam-846	68	48	.	.	PUNCT
ejpam-846	69	1	since	since	SCONJ
ejpam-846	69	2	the	the	DET
ejpam-846	69	3	gmp	gmp	PROPN
ejpam-846	69	4	is	be	AUX
ejpam-846	69	5	based	base	VERB
ejpam-846	69	6	on	on	ADP
ejpam-846	69	7	an	an	DET
ejpam-846	69	8	optimizing	optimizing	NOUN
ejpam-846	69	9	criterion	criterion	NOUN
ejpam-846	69	10	,	,	PUNCT
ejpam-846	69	11	often	often	ADV
ejpam-846	69	12	the	the	DET
ejpam-846	69	13	gmp	gmp	PROPN
ejpam-846	69	14	is	be	AUX
ejpam-846	69	15	used	use	VERB
ejpam-846	69	16	as	as	ADP
ejpam-846	69	17	the	the	DET
ejpam-846	69	18	yardstick	yardstick	NOUN
ejpam-846	69	19	of	of	ADP
ejpam-846	69	20	bound	bind	VERB
ejpam-846	69	21	tightness	tightness	NOUN
ejpam-846	69	22	.	.	PUNCT
ejpam-846	70	1	we	we	PRON
ejpam-846	70	2	shall	shall	AUX
ejpam-846	70	3	review	review	VERB
ejpam-846	70	4	this	this	DET
ejpam-846	70	5	important	important	ADJ
ejpam-846	70	6	class	class	NOUN
ejpam-846	70	7	of	of	ADP
ejpam-846	70	8	problems	problem	NOUN
ejpam-846	70	9	first	first	ADV
ejpam-846	70	10	.	.	PUNCT
ejpam-846	71	1	for	for	ADP
ejpam-846	71	2	ξ	ξ	PROPN
ejpam-846	71	3	being	be	AUX
ejpam-846	71	4	a	a	DET
ejpam-846	71	5	random	random	ADJ
ejpam-846	71	6	vector	vector	NOUN
ejpam-846	71	7	mapping	mapping	NOUN
ejpam-846	71	8	a	a	DET
ejpam-846	71	9	measurable	measurable	ADJ
ejpam-846	71	10	space	space	NOUN
ejpam-846	71	11	(	(	PUNCT
ejpam-846	71	12	ξ	ξ	PROPN
ejpam-846	71	13	,	,	PUNCT
ejpam-846	71	14	b	b	NOUN
ejpam-846	71	15	)	)	PUNCT
ejpam-846	71	16	to	to	ADP
ejpam-846	71	17	ℜk	ℜk	PROPN
ejpam-846	71	18	,	,	PUNCT
ejpam-846	71	19	with	with	ADP
ejpam-846	71	20	b	b	PROPN
ejpam-846	71	21	the	the	DET
ejpam-846	71	22	borel	borel	PROPN
ejpam-846	71	23	sigma	sigma	VERB
ejpam-846	71	24	field	field	NOUN
ejpam-846	71	25	of	of	ADP
ejpam-846	71	26	events	event	NOUN
ejpam-846	71	27	in	in	ADP
ejpam-846	71	28	ξ(⊂	ξ(⊂	PROPN
ejpam-846	71	29	ℜk	ℜk	PROPN
ejpam-846	71	30	)	)	PUNCT
ejpam-846	71	31	,	,	PUNCT
ejpam-846	71	32	let	let	VERB
ejpam-846	71	33	fi	fi	NOUN
ejpam-846	71	34	:	:	PUNCT
ejpam-846	71	35	ξ	ξ	X
ejpam-846	71	36	→	→	SYM
ejpam-846	71	37	ℜ	ℜ	PROPN
ejpam-846	71	38	,	,	PUNCT
ejpam-846	71	39	for	for	ADP
ejpam-846	71	40	i	i	PROPN
ejpam-846	71	41	=	=	NOUN
ejpam-846	71	42	1	1	NUM
ejpam-846	71	43	,	,	PUNCT
ejpam-846	71	44	.	.	PUNCT
ejpam-846	71	45	.	.	PUNCT
ejpam-846	72	1	.	.	PUNCT
ejpam-846	73	1	,	,	PUNCT
ejpam-846	73	2	n	n	X
ejpam-846	73	3	,	,	PUNCT
ejpam-846	73	4	be	be	AUX
ejpam-846	73	5	finite	finite	ADJ
ejpam-846	73	6	measurable	measurable	ADJ
ejpam-846	73	7	functions	function	NOUN
ejpam-846	73	8	.	.	PUNCT
ejpam-846	74	1	suppose	suppose	VERB
ejpam-846	74	2	the	the	DET
ejpam-846	74	3	knowledge	knowledge	NOUN
ejpam-846	74	4	of	of	ADP
ejpam-846	74	5	the	the	DET
ejpam-846	74	6	true	true	ADJ
ejpam-846	74	7	probability	probability	NOUN
ejpam-846	74	8	distribution	distribution	NOUN
ejpam-846	74	9	p	p	NOUN
ejpam-846	74	10	tr	tr	VERB
ejpam-846	74	11	is	be	AUX
ejpam-846	74	12	available	available	ADJ
ejpam-846	74	13	through	through	ADP
ejpam-846	74	14	the	the	DET
ejpam-846	74	15	moments	moment	NOUN
ejpam-846	75	1	µi	µi	INTJ
ejpam-846	75	2	:	:	PUNCT
ejpam-846	75	3	=	=	SYM
ejpam-846	75	4	e[fi(ξ	e[fi(ξ	PROPN
ejpam-846	75	5	)	)	PUNCT
ejpam-846	75	6	]	]	PUNCT
ejpam-846	76	1	for	for	ADP
ejpam-846	76	2	i	i	PROPN
ejpam-846	76	3	=	=	NOUN
ejpam-846	76	4	1	1	NUM
ejpam-846	76	5	,	,	PUNCT
ejpam-846	76	6	.	.	PUNCT
ejpam-846	76	7	.	.	PUNCT
ejpam-846	76	8	.	.	PUNCT
ejpam-846	77	1	,	,	PUNCT
ejpam-846	77	2	n	n	X
ejpam-846	77	3	.	.	PUNCT
ejpam-846	78	1	given	give	VERB
ejpam-846	78	2	the	the	DET
ejpam-846	78	3	vector	vector	NOUN
ejpam-846	78	4	µ	µ	X
ejpam-846	78	5	∈	∈	NOUN
ejpam-846	79	1	ℜn	ℜn	PROPN
ejpam-846	79	2	,	,	PUNCT
ejpam-846	79	3	a	a	DET
ejpam-846	79	4	“	"	PUNCT
ejpam-846	79	5	tight	tight	ADJ
ejpam-846	79	6	”	"	PUNCT
ejpam-846	79	7	lower	low	ADJ
ejpam-846	79	8	bound	bind	VERB
ejpam-846	79	9	on	on	ADP
ejpam-846	79	10	the	the	DET
ejpam-846	79	11	expectation	expectation	NOUN
ejpam-846	79	12	ψ(x	ψ(x	NOUN
ejpam-846	79	13	)	)	PUNCT
ejpam-846	79	14	=	=	PUNCT
ejpam-846	79	15	e[ϕ(x	e[ϕ(x	NOUN
ejpam-846	79	16	,	,	PUNCT
ejpam-846	79	17	ξ	ξ	NOUN
ejpam-846	79	18	)	)	PUNCT
ejpam-846	79	19	]	]	PUNCT
ejpam-846	79	20	is	be	AUX
ejpam-846	79	21	determined	determine	VERB
ejpam-846	79	22	by	by	ADP
ejpam-846	79	23	solving	solve	VERB
ejpam-846	79	24	the	the	DET
ejpam-846	79	25	general	general	ADJ
ejpam-846	79	26	moment	moment	NOUN
ejpam-846	79	27	problem	problem	NOUN
ejpam-846	79	28	(	(	PUNCT
ejpam-846	79	29	gmp	gmp	PROPN
ejpam-846	79	30	):	):	PUNCT
ejpam-846	79	31	φ(x	φ(x	PROPN
ejpam-846	79	32	)	)	PUNCT
ejpam-846	79	33	:	:	PUNCT
ejpam-846	80	1	=	=	NUM
ejpam-846	80	2	inf	inf	PROPN
ejpam-846	80	3	p∈p	p∈p	NOUN
ejpam-846	80	4	{	{	PUNCT
ejpam-846	80	5	∫	∫	PROPN
ejpam-846	80	6	ξ	ξ	X
ejpam-846	80	7	ϕ(x	ϕ(x	PROPN
ejpam-846	80	8	,	,	PUNCT
ejpam-846	80	9	ξ)p	ξ)p	ADJ
ejpam-846	80	10	(	(	PUNCT
ejpam-846	80	11	dξ	dξ	PROPN
ejpam-846	80	12	)	)	PUNCT
ejpam-846	80	13	:	:	PUNCT
ejpam-846	80	14	∫	∫	PROPN
ejpam-846	80	15	ξ	ξ	X
ejpam-846	80	16	fi(ξ)p	fi(ξ)p	PROPN
ejpam-846	80	17	(	(	PUNCT
ejpam-846	80	18	dξ	dξ	PROPN
ejpam-846	80	19	)	)	PUNCT
ejpam-846	80	20	=	=	SYM
ejpam-846	80	21	µi	µi	PROPN
ejpam-846	80	22	,	,	PUNCT
ejpam-846	80	23	i	i	PRON
ejpam-846	80	24	=	=	NOUN
ejpam-846	80	25	1	1	NUM
ejpam-846	80	26	,	,	PUNCT
ejpam-846	80	27	.	.	PUNCT
ejpam-846	80	28	.	.	PUNCT
ejpam-846	80	29	.	.	PUNCT
ejpam-846	80	30	,	,	PUNCT
ejpam-846	80	31	n	n	CCONJ
ejpam-846	80	32	}	}	PUNCT
ejpam-846	80	33	,	,	PUNCT
ejpam-846	80	34	(	(	PUNCT
ejpam-846	80	35	6	6	NUM
ejpam-846	80	36	)	)	PUNCT
ejpam-846	80	37	where	where	SCONJ
ejpam-846	80	38	p	p	NOUN
ejpam-846	80	39	denotes	denote	VERB
ejpam-846	80	40	the	the	DET
ejpam-846	80	41	set	set	NOUN
ejpam-846	80	42	of	of	ADP
ejpam-846	80	43	all	all	DET
ejpam-846	80	44	probability	probability	NOUN
ejpam-846	80	45	measures	measure	NOUN
ejpam-846	80	46	on	on	ADP
ejpam-846	80	47	(	(	PUNCT
ejpam-846	80	48	ξ	ξ	PROPN
ejpam-846	80	49	,	,	PUNCT
ejpam-846	80	50	b	b	NOUN
ejpam-846	80	51	)	)	PUNCT
ejpam-846	80	52	.	.	PUNCT
ejpam-846	81	1	since	since	SCONJ
ejpam-846	81	2	the	the	DET
ejpam-846	81	3	true	true	ADJ
ejpam-846	81	4	measure	measure	NOUN
ejpam-846	81	5	p	p	NOUN
ejpam-846	81	6	tr	tr	VERB
ejpam-846	81	7	satisfies	satisfy	VERB
ejpam-846	81	8	the	the	DET
ejpam-846	81	9	conditions	condition	NOUN
ejpam-846	81	10	in	in	ADP
ejpam-846	81	11	(	(	PUNCT
ejpam-846	81	12	6	6	NUM
ejpam-846	81	13	)	)	PUNCT
ejpam-846	82	1	,	,	PUNCT
ejpam-846	82	2	it	it	PRON
ejpam-846	82	3	follows	follow	VERB
ejpam-846	82	4	that	that	SCONJ
ejpam-846	82	5	ψ(x	ψ(x	NOUN
ejpam-846	82	6	)	)	PUNCT
ejpam-846	82	7	≥	≥	NOUN
ejpam-846	82	8	φ(x	φ(x	NOUN
ejpam-846	82	9	)	)	PUNCT
ejpam-846	82	10	.	.	PUNCT
ejpam-846	83	1	conditions	condition	NOUN
ejpam-846	83	2	for	for	ADP
ejpam-846	83	3	the	the	DET
ejpam-846	83	4	existence	existence	NOUN
ejpam-846	83	5	of	of	ADP
ejpam-846	83	6	a	a	DET
ejpam-846	83	7	probability	probability	NOUN
ejpam-846	83	8	measure	measure	NOUN
ejpam-846	83	9	that	that	PRON
ejpam-846	83	10	solves	solve	VERB
ejpam-846	83	11	the	the	DET
ejpam-846	83	12	gmp	gmp	PROPN
ejpam-846	83	13	is	be	AUX
ejpam-846	83	14	derived	derive	VERB
ejpam-846	83	15	in	in	ADP
ejpam-846	83	16	kemperman	kemperman	PROPN
ejpam-846	83	17	[	[	X
ejpam-846	83	18	14	14	NUM
ejpam-846	83	19	]	]	PUNCT
ejpam-846	83	20	.	.	PUNCT
ejpam-846	84	1	the	the	DET
ejpam-846	84	2	set	set	NOUN
ejpam-846	84	3	of	of	ADP
ejpam-846	84	4	probability	probability	NOUN
ejpam-846	84	5	measures	measure	NOUN
ejpam-846	84	6	feasible	feasible	ADJ
ejpam-846	84	7	in	in	ADP
ejpam-846	84	8	gmp	gmp	PROPN
ejpam-846	84	9	has	have	AUX
ejpam-846	84	10	been	be	AUX
ejpam-846	84	11	studied	study	VERB
ejpam-846	84	12	extensively	extensively	ADV
ejpam-846	84	13	.	.	PUNCT
ejpam-846	85	1	for	for	ADP
ejpam-846	85	2	instance	instance	NOUN
ejpam-846	85	3	,	,	PUNCT
ejpam-846	85	4	extreme	extreme	ADJ
ejpam-846	85	5	points	point	NOUN
ejpam-846	85	6	of	of	ADP
ejpam-846	85	7	the	the	DET
ejpam-846	85	8	set	set	NOUN
ejpam-846	85	9	of	of	ADP
ejpam-846	85	10	admissible	admissible	ADJ
ejpam-846	85	11	probability	probability	NOUN
ejpam-846	85	12	measures	measure	NOUN
ejpam-846	85	13	of	of	ADP
ejpam-846	85	14	gmp	gmp	PROPN
ejpam-846	85	15	are	be	AUX
ejpam-846	85	16	discrete	discrete	ADJ
ejpam-846	85	17	measures	measure	NOUN
ejpam-846	85	18	involving	involve	VERB
ejpam-846	85	19	no	no	DET
ejpam-846	85	20	more	more	ADJ
ejpam-846	85	21	than	than	ADP
ejpam-846	85	22	n+1	n+1	NUM
ejpam-846	85	23	atoms	atom	NOUN
ejpam-846	85	24	,	,	PUNCT
ejpam-846	85	25	see	see	VERB
ejpam-846	85	26	karr	karr	PROPN
ejpam-846	86	1	[	[	X
ejpam-846	86	2	13	13	NUM
ejpam-846	86	3	]	]	PUNCT
ejpam-846	86	4	.	.	PUNCT
ejpam-846	87	1	hence	hence	ADV
ejpam-846	87	2	,	,	PUNCT
ejpam-846	87	3	the	the	DET
ejpam-846	87	4	optimizing	optimizing	NOUN
ejpam-846	87	5	measure	measure	NOUN
ejpam-846	87	6	in	in	ADP
ejpam-846	87	7	(	(	PUNCT
ejpam-846	87	8	6	6	NUM
ejpam-846	87	9	)	)	PUNCT
ejpam-846	87	10	is	be	AUX
ejpam-846	87	11	a	a	DET
ejpam-846	87	12	discrete	discrete	ADJ
ejpam-846	87	13	measure	measure	NOUN
ejpam-846	87	14	with	with	ADP
ejpam-846	87	15	cardinality	cardinality	NOUN
ejpam-846	87	16	at	at	ADP
ejpam-846	87	17	most	most	ADJ
ejpam-846	87	18	n	n	DET
ejpam-846	87	19	+1	+1	PROPN
ejpam-846	87	20	.	.	PUNCT
ejpam-846	88	1	however	however	ADV
ejpam-846	88	2	,	,	PUNCT
ejpam-846	88	3	determination	determination	NOUN
ejpam-846	88	4	of	of	ADP
ejpam-846	88	5	this	this	DET
ejpam-846	88	6	discrete	discrete	ADJ
ejpam-846	88	7	measure	measure	NOUN
ejpam-846	88	8	is	be	AUX
ejpam-846	88	9	difficult	difficult	ADJ
ejpam-846	88	10	,	,	PUNCT
ejpam-846	88	11	and	and	CCONJ
ejpam-846	88	12	it	it	PRON
ejpam-846	88	13	may	may	AUX
ejpam-846	88	14	generally	generally	ADV
ejpam-846	88	15	involve	involve	VERB
ejpam-846	88	16	nonconvex	nonconvex	NOUN
ejpam-846	88	17	optimization	optimization	NOUN
ejpam-846	88	18	,	,	PUNCT
ejpam-846	88	19	see	see	VERB
ejpam-846	88	20	birge	birge	NOUN
ejpam-846	88	21	and	and	CCONJ
ejpam-846	88	22	wets	wet	VERB
ejpam-846	88	23	[	[	PUNCT
ejpam-846	88	24	2	2	NUM
ejpam-846	88	25	]	]	PUNCT
ejpam-846	88	26	.	.	PUNCT
ejpam-846	89	1	instead	instead	ADV
ejpam-846	89	2	,	,	PUNCT
ejpam-846	89	3	one	one	PRON
ejpam-846	89	4	may	may	AUX
ejpam-846	89	5	attempt	attempt	VERB
ejpam-846	89	6	to	to	PART
ejpam-846	89	7	solve	solve	VERB
ejpam-846	89	8	the	the	DET
ejpam-846	89	9	semi	semi	ADJ
ejpam-846	89	10	-	-	ADJ
ejpam-846	89	11	infinite	infinite	ADJ
ejpam-846	89	12	dual	dual	ADJ
ejpam-846	89	13	problem	problem	NOUN
ejpam-846	89	14	of	of	ADP
ejpam-846	89	15	the	the	DET
ejpam-846	89	16	gmp	gmp	PROPN
ejpam-846	89	17	,	,	PUNCT
ejpam-846	89	18	given	give	VERB
ejpam-846	89	19	by	by	ADP
ejpam-846	89	20	φ∗(x	φ∗(x	NOUN
ejpam-846	89	21	)	)	PUNCT
ejpam-846	89	22	:	:	PUNCT
ejpam-846	89	23	=	=	SYM
ejpam-846	89	24	sup	sup	X
ejpam-846	89	25	π∈ℜn+1	π∈ℜn+1	PUNCT
ejpam-846	89	26	{	{	PUNCT
ejpam-846	89	27	π0	π0	NOUN
ejpam-846	89	28	+	+	CCONJ
ejpam-846	89	29	n∑	n∑	ADJ
ejpam-846	89	30	i=1	i=1	PROPN
ejpam-846	89	31	µiπi	µiπi	NOUN
ejpam-846	89	32	:	:	PUNCT
ejpam-846	89	33	π0	π0	NOUN
ejpam-846	90	1	+	+	CCONJ
ejpam-846	90	2	n∑	n∑	ADJ
ejpam-846	90	3	i=1	i=1	PRON
ejpam-846	91	1	fi(ξ)πi	fi(ξ)πi	ADJ
ejpam-846	91	2	≤	≤	PUNCT
ejpam-846	91	3	ϕ(x	ϕ(x	PROPN
ejpam-846	91	4	,	,	PUNCT
ejpam-846	91	5	ξ	ξ	NOUN
ejpam-846	91	6	)	)	PUNCT
ejpam-846	91	7	,	,	PUNCT
ejpam-846	91	8	ξ	ξ	PROPN
ejpam-846	91	9	∈	∈	PROPN
ejpam-846	91	10	ξ	ξ	X
ejpam-846	91	11	}	}	PUNCT
ejpam-846	91	12	.	.	PUNCT
ejpam-846	92	1	(	(	PUNCT
ejpam-846	92	2	7	7	X
ejpam-846	92	3	)	)	PUNCT
ejpam-846	92	4	edirisinghe	edirisinghe	NOUN
ejpam-846	92	5	/	/	SYM
ejpam-846	92	6	eur	eur	PROPN
ejpam-846	92	7	.	.	PUNCT
ejpam-846	93	1	j.	j.	PROPN
ejpam-846	93	2	pure	pure	PROPN
ejpam-846	93	3	appl	appl	PROPN
ejpam-846	93	4	.	.	PROPN
ejpam-846	93	5	math	math	PROPN
ejpam-846	93	6	,	,	PUNCT
ejpam-846	93	7	3	3	NUM
ejpam-846	93	8	(	(	PUNCT
ejpam-846	93	9	2010	2010	NUM
ejpam-846	93	10	)	)	PUNCT
ejpam-846	93	11	,	,	PUNCT
ejpam-846	93	12	572	572	NUM
ejpam-846	93	13	-	-	SYM
ejpam-846	93	14	592	592	NUM
ejpam-846	93	15	576	576	NUM
ejpam-846	93	16	kall	kall	X
ejpam-846	94	1	[	[	X
ejpam-846	94	2	12	12	NUM
ejpam-846	94	3	]	]	PUNCT
ejpam-846	94	4	investigates	investigate	VERB
ejpam-846	94	5	this	this	DET
ejpam-846	94	6	duality	duality	NOUN
ejpam-846	94	7	relationship	relationship	NOUN
ejpam-846	94	8	in	in	ADP
ejpam-846	94	9	the	the	DET
ejpam-846	94	10	context	context	NOUN
ejpam-846	94	11	of	of	ADP
ejpam-846	94	12	general	general	ADJ
ejpam-846	94	13	moment	moment	NOUN
ejpam-846	94	14	problems	problem	NOUN
ejpam-846	94	15	.	.	PUNCT
ejpam-846	95	1	for	for	ADP
ejpam-846	95	2	a	a	DET
ejpam-846	95	3	more	more	ADV
ejpam-846	95	4	general	general	ADJ
ejpam-846	95	5	treatment	treatment	NOUN
ejpam-846	95	6	of	of	ADP
ejpam-846	95	7	duality	duality	NOUN
ejpam-846	95	8	theory	theory	NOUN
ejpam-846	95	9	for	for	ADP
ejpam-846	95	10	semi	semi	ADJ
ejpam-846	95	11	-	-	ADJ
ejpam-846	95	12	infinite	infinite	ADJ
ejpam-846	95	13	linear	linear	NOUN
ejpam-846	95	14	programs	program	NOUN
ejpam-846	95	15	,	,	PUNCT
ejpam-846	95	16	see	see	VERB
ejpam-846	95	17	glashoff	glashoff	NOUN
ejpam-846	95	18	and	and	CCONJ
ejpam-846	95	19	gustafson	gustafson	PROPN
ejpam-846	96	1	[	[	X
ejpam-846	96	2	9	9	NUM
ejpam-846	96	3	]	]	PUNCT
ejpam-846	96	4	.	.	PUNCT
ejpam-846	97	1	weak	weak	ADJ
ejpam-846	97	2	duality	duality	NOUN
ejpam-846	97	3	holds	hold	VERB
ejpam-846	97	4	for	for	ADP
ejpam-846	97	5	(	(	PUNCT
ejpam-846	97	6	6	6	NUM
ejpam-846	97	7	)	)	PUNCT
ejpam-846	97	8	and	and	CCONJ
ejpam-846	97	9	(	(	PUNCT
ejpam-846	97	10	7	7	NUM
ejpam-846	97	11	)	)	PUNCT
ejpam-846	97	12	,	,	PUNCT
ejpam-846	97	13	i.e.	i.e.	X
ejpam-846	97	14	,	,	PUNCT
ejpam-846	97	15	proposition	proposition	NOUN
ejpam-846	97	16	1	1	NUM
ejpam-846	97	17	.	.	PUNCT
ejpam-846	97	18	φ(x	φ(x	NOUN
ejpam-846	97	19	)	)	PUNCT
ejpam-846	97	20	≥	≥	NOUN
ejpam-846	97	21	φ∗(x	φ∗(x	NOUN
ejpam-846	97	22	)	)	PUNCT
ejpam-846	97	23	.	.	PUNCT
ejpam-846	98	1	proof	proof	NOUN
ejpam-846	98	2	.	.	PUNCT
ejpam-846	99	1	when	when	SCONJ
ejpam-846	99	2	(	(	PUNCT
ejpam-846	99	3	6	6	NUM
ejpam-846	99	4	)	)	PUNCT
ejpam-846	99	5	is	be	AUX
ejpam-846	99	6	infeasible	infeasible	ADJ
ejpam-846	99	7	,	,	PUNCT
ejpam-846	99	8	we	we	PRON
ejpam-846	99	9	set	set	VERB
ejpam-846	99	10	φ(x	φ(x	NOUN
ejpam-846	99	11	)	)	PUNCT
ejpam-846	99	12	=	=	PUNCT
ejpam-846	100	1	+	+	PUNCT
ejpam-846	100	2	∞	∞	NUM
ejpam-846	100	3	and	and	CCONJ
ejpam-846	100	4	if	if	SCONJ
ejpam-846	100	5	(	(	PUNCT
ejpam-846	100	6	7	7	X
ejpam-846	100	7	)	)	PUNCT
ejpam-846	100	8	is	be	AUX
ejpam-846	100	9	infeasible	infeasible	ADJ
ejpam-846	100	10	,	,	PUNCT
ejpam-846	100	11	we	we	PRON
ejpam-846	100	12	set	set	VERB
ejpam-846	100	13	φ∗(x	φ∗(x	NOUN
ejpam-846	100	14	)	)	PUNCT
ejpam-846	100	15	=	=	PUNCT
ejpam-846	100	16	−∞	−∞	NOUN
ejpam-846	100	17	,	,	PUNCT
ejpam-846	100	18	and	and	CCONJ
ejpam-846	100	19	then	then	ADV
ejpam-846	100	20	the	the	DET
ejpam-846	100	21	proposition	proposition	NOUN
ejpam-846	100	22	is	be	AUX
ejpam-846	100	23	held	hold	VERB
ejpam-846	100	24	trivially	trivially	ADV
ejpam-846	100	25	.	.	PUNCT
ejpam-846	101	1	otherwise	otherwise	ADV
ejpam-846	101	2	,	,	PUNCT
ejpam-846	101	3	for	for	ADP
ejpam-846	101	4	some	some	DET
ejpam-846	101	5	probability	probability	NOUN
ejpam-846	101	6	measure	measure	NOUN
ejpam-846	101	7	p	p	NOUN
ejpam-846	101	8	feasible	feasible	ADJ
ejpam-846	101	9	in	in	ADP
ejpam-846	101	10	(	(	PUNCT
ejpam-846	101	11	6	6	NUM
ejpam-846	101	12	)	)	PUNCT
ejpam-846	101	13	and	and	CCONJ
ejpam-846	101	14	for	for	ADP
ejpam-846	101	15	any	any	DET
ejpam-846	101	16	vector	vector	NOUN
ejpam-846	101	17	(	(	PUNCT
ejpam-846	101	18	π0	π0	NOUN
ejpam-846	101	19	,	,	PUNCT
ejpam-846	101	20	π1	π1	NOUN
ejpam-846	101	21	,	,	PUNCT
ejpam-846	101	22	.	.	PUNCT
ejpam-846	101	23	.	.	PUNCT
ejpam-846	101	24	.	.	PUNCT
ejpam-846	102	1	,	,	PUNCT
ejpam-846	102	2	πn	πn	X
ejpam-846	102	3	)	)	PUNCT
ejpam-846	102	4	feasible	feasible	ADJ
ejpam-846	102	5	in	in	ADP
ejpam-846	102	6	(	(	PUNCT
ejpam-846	102	7	7	7	NUM
ejpam-846	102	8	)	)	PUNCT
ejpam-846	102	9	,	,	PUNCT
ejpam-846	102	10	π0	π0	NOUN
ejpam-846	102	11	+	+	CCONJ
ejpam-846	102	12	n∑	n∑	ADJ
ejpam-846	102	13	i=1	i=1	PROPN
ejpam-846	102	14	µiπi	µiπi	NOUN
ejpam-846	102	15	=	=	SYM
ejpam-846	102	16	∫	∫	PROPN
ejpam-846	103	1	ξ	ξ	X
ejpam-846	103	2	p	p	X
ejpam-846	103	3	(	(	PUNCT
ejpam-846	103	4	dξ)π0	dξ)π0	X
ejpam-846	103	5	+	+	CCONJ
ejpam-846	103	6	n∑	n∑	ADJ
ejpam-846	103	7	i=1	i=1	PROPN
ejpam-846	103	8	(	(	PUNCT
ejpam-846	103	9	∫	∫	PROPN
ejpam-846	103	10	ξ	ξ	X
ejpam-846	103	11	fi(ξ)p	fi(ξ)p	PROPN
ejpam-846	103	12	(	(	PUNCT
ejpam-846	103	13	dξ))πi	dξ))πi	NOUN
ejpam-846	103	14	=	=	PUNCT
ejpam-846	103	15	∫	∫	PROPN
ejpam-846	103	16	ξ	ξ	X
ejpam-846	104	1	[	[	X
ejpam-846	104	2	π0	π0	NOUN
ejpam-846	104	3	+	+	CCONJ
ejpam-846	104	4	n∑	n∑	PROPN
ejpam-846	104	5	i=1	i=1	PROPN
ejpam-846	104	6	fi(ξ)πi]p	fi(ξ)πi]p	PROPN
ejpam-846	104	7	(	(	PUNCT
ejpam-846	104	8	dξ	dξ	PROPN
ejpam-846	104	9	)	)	PUNCT
ejpam-846	104	10	≤	≤	NUM
ejpam-846	104	11	∫	∫	PROPN
ejpam-846	104	12	ξ	ξ	X
ejpam-846	104	13	ϕ(x	ϕ(x	PROPN
ejpam-846	104	14	,	,	PUNCT
ejpam-846	104	15	ξ)p	ξ)p	ADJ
ejpam-846	104	16	(	(	PUNCT
ejpam-846	104	17	dξ	dξ	PROPN
ejpam-846	104	18	)	)	PUNCT
ejpam-846	104	19	.	.	PUNCT
ejpam-846	105	1	(	(	PUNCT
ejpam-846	105	2	8)	8)	NUM
ejpam-846	105	3	hence	hence	ADV
ejpam-846	105	4	,	,	PUNCT
ejpam-846	105	5	any	any	DET
ejpam-846	105	6	feasible	feasible	ADJ
ejpam-846	105	7	solution	solution	NOUN
ejpam-846	105	8	of	of	ADP
ejpam-846	105	9	(	(	PUNCT
ejpam-846	105	10	7	7	NUM
ejpam-846	105	11	)	)	PUNCT
ejpam-846	105	12	generates	generate	VERB
ejpam-846	105	13	a	a	DET
ejpam-846	105	14	lower	low	ADJ
ejpam-846	105	15	bound	bind	VERB
ejpam-846	105	16	on	on	ADP
ejpam-846	105	17	ψ(x	ψ(x	NUM
ejpam-846	105	18	)	)	PUNCT
ejpam-846	105	19	;	;	PUNCT
ejpam-846	105	20	however	however	ADV
ejpam-846	105	21	,	,	PUNCT
ejpam-846	105	22	the	the	DET
ejpam-846	105	23	intent	intent	NOUN
ejpam-846	105	24	is	be	AUX
ejpam-846	105	25	to	to	PART
ejpam-846	105	26	generate	generate	VERB
ejpam-846	105	27	the	the	DET
ejpam-846	105	28	best	well	ADV
ejpam-846	105	29	lower	lower	ADV
ejpam-846	105	30	bound	bind	VERB
ejpam-846	105	31	by	by	ADP
ejpam-846	105	32	solving	solve	VERB
ejpam-846	105	33	(	(	PUNCT
ejpam-846	105	34	7	7	NUM
ejpam-846	105	35	)	)	PUNCT
ejpam-846	105	36	.	.	PUNCT
ejpam-846	106	1	moreover	moreover	ADV
ejpam-846	106	2	,	,	PUNCT
ejpam-846	106	3	if	if	SCONJ
ejpam-846	106	4	φ(x	φ(x	NOUN
ejpam-846	106	5	)	)	PUNCT
ejpam-846	106	6	=	=	SYM
ejpam-846	106	7	φ∗(x	φ∗(x	PROPN
ejpam-846	106	8	)	)	PUNCT
ejpam-846	106	9	,	,	PUNCT
ejpam-846	106	10	then	then	ADV
ejpam-846	106	11	the	the	DET
ejpam-846	106	12	computed	compute	VERB
ejpam-846	106	13	lower	lower	ADV
ejpam-846	106	14	bound	bind	VERB
ejpam-846	106	15	is	be	AUX
ejpam-846	106	16	declared	declare	VERB
ejpam-846	106	17	tight	tight	ADJ
ejpam-846	106	18	w.r.t	w.r.t	NOUN
ejpam-846	106	19	to	to	ADP
ejpam-846	106	20	the	the	DET
ejpam-846	106	21	gmp	gmp	PROPN
ejpam-846	106	22	.	.	PUNCT
ejpam-846	107	1	the	the	DET
ejpam-846	107	2	latter	latter	ADJ
ejpam-846	107	3	strong	strong	ADJ
ejpam-846	107	4	duality	duality	NOUN
ejpam-846	107	5	can	can	AUX
ejpam-846	107	6	be	be	AUX
ejpam-846	107	7	assured	assure	VERB
ejpam-846	107	8	under	under	ADP
ejpam-846	107	9	mild	mild	ADJ
ejpam-846	107	10	conditions	condition	NOUN
ejpam-846	107	11	,	,	PUNCT
ejpam-846	107	12	as	as	SCONJ
ejpam-846	107	13	given	give	VERB
ejpam-846	107	14	below	below	ADV
ejpam-846	107	15	.	.	PUNCT
ejpam-846	108	1	proposition	proposition	NOUN
ejpam-846	108	2	2	2	NUM
ejpam-846	108	3	.	.	PUNCT
ejpam-846	108	4	φ(x	φ(x	NOUN
ejpam-846	108	5	)	)	PUNCT
ejpam-846	108	6	=	=	SYM
ejpam-846	108	7	φ∗(x	φ∗(x	PROPN
ejpam-846	108	8	)	)	PUNCT
ejpam-846	108	9	holds	hold	VERB
ejpam-846	108	10	if	if	SCONJ
ejpam-846	108	11	(	(	PUNCT
ejpam-846	108	12	i	i	NOUN
ejpam-846	108	13	)	)	PUNCT
ejpam-846	108	14	fi	fi	NOUN
ejpam-846	108	15	,	,	PUNCT
ejpam-846	108	16	i	i	NOUN
ejpam-846	108	17	=	=	NOUN
ejpam-846	108	18	1	1	NUM
ejpam-846	108	19	,	,	PUNCT
ejpam-846	108	20	.	.	PUNCT
ejpam-846	108	21	.	.	PUNCT
ejpam-846	109	1	.	.	PUNCT
ejpam-846	110	1	,	,	PUNCT
ejpam-846	110	2	n	n	CCONJ
ejpam-846	110	3	,	,	PUNCT
ejpam-846	110	4	are	be	AUX
ejpam-846	110	5	continuous	continuous	ADJ
ejpam-846	110	6	,	,	PUNCT
ejpam-846	110	7	and	and	CCONJ
ejpam-846	110	8	(	(	PUNCT
ejpam-846	110	9	ii	ii	NOUN
ejpam-846	110	10	)	)	PUNCT
ejpam-846	110	11	ξ	ξ	PROPN
ejpam-846	110	12	is	be	AUX
ejpam-846	110	13	compact	compact	ADJ
ejpam-846	110	14	.	.	PUNCT
ejpam-846	111	1	proof	proof	NOUN
ejpam-846	111	2	.	.	PUNCT
ejpam-846	112	1	see	see	VERB
ejpam-846	112	2	glashoff	glashoff	NOUN
ejpam-846	112	3	and	and	CCONJ
ejpam-846	112	4	gustafson	gustafson	PROPN
ejpam-846	113	1	[	[	X
ejpam-846	113	2	9	9	NUM
ejpam-846	113	3	,	,	PUNCT
ejpam-846	113	4	p.79	p.79	ADP
ejpam-846	113	5	]	]	PUNCT
ejpam-846	113	6	,	,	PUNCT
ejpam-846	113	7	kall	kall	PROPN
ejpam-846	114	1	[	[	X
ejpam-846	114	2	12	12	NUM
ejpam-846	114	3	,	,	PUNCT
ejpam-846	114	4	theorem	theorem	VERB
ejpam-846	114	5	4	4	NUM
ejpam-846	114	6	]	]	PUNCT
ejpam-846	114	7	.	.	PUNCT
ejpam-846	115	1	however	however	ADV
ejpam-846	115	2	,	,	PUNCT
ejpam-846	115	3	when	when	SCONJ
ejpam-846	115	4	ξ	ξ	PROPN
ejpam-846	115	5	is	be	AUX
ejpam-846	115	6	unbounded	unbounde	VERB
ejpam-846	115	7	,	,	PUNCT
ejpam-846	115	8	a	a	DET
ejpam-846	115	9	certain	certain	ADJ
ejpam-846	115	10	interior	interior	ADJ
ejpam-846	115	11	-	-	PUNCT
ejpam-846	115	12	type	type	NOUN
ejpam-846	115	13	condition	condition	NOUN
ejpam-846	115	14	is	be	AUX
ejpam-846	115	15	required	require	VERB
ejpam-846	115	16	to	to	PART
ejpam-846	115	17	ensure	ensure	VERB
ejpam-846	115	18	strong	strong	ADJ
ejpam-846	115	19	duality	duality	NOUN
ejpam-846	115	20	.	.	PUNCT
ejpam-846	116	1	define	define	VERB
ejpam-846	116	2	m	m	PROPN
ejpam-846	116	3	as	as	ADP
ejpam-846	116	4	the	the	DET
ejpam-846	116	5	convex	convex	PROPN
ejpam-846	116	6	hull	hull	NOUN
ejpam-846	116	7	of	of	ADP
ejpam-846	116	8	the	the	DET
ejpam-846	116	9	moment	moment	NOUN
ejpam-846	116	10	conditions	condition	NOUN
ejpam-846	116	11	fi(ξ	fi(ξ	NOUN
ejpam-846	116	12	)	)	PUNCT
ejpam-846	116	13	,	,	PUNCT
ejpam-846	116	14	i	i	PRON
ejpam-846	116	15	=	=	NOUN
ejpam-846	116	16	1	1	NUM
ejpam-846	116	17	,	,	PUNCT
ejpam-846	116	18	.	.	PUNCT
ejpam-846	116	19	.	.	PUNCT
ejpam-846	117	1	.	.	PUNCT
ejpam-846	118	1	,	,	PUNCT
ejpam-846	118	2	n	n	PROPN
ejpam-846	118	3	for	for	ADP
ejpam-846	118	4	ξ	ξ	PROPN
ejpam-846	118	5	∈	∈	PROPN
ejpam-846	118	6	ξ	ξ	PROPN
ejpam-846	118	7	,	,	PUNCT
ejpam-846	118	8	i.e.	i.e.	X
ejpam-846	118	9	,	,	PUNCT
ejpam-846	118	10	m	m	VERB
ejpam-846	118	11	:	:	PUNCT
ejpam-846	118	12	=	=	SYM
ejpam-846	118	13	co	co	X
ejpam-846	118	14	{	{	PUNCT
ejpam-846	118	15	(	(	PUNCT
ejpam-846	118	16	f1(ξ	f1(ξ	NOUN
ejpam-846	118	17	)	)	PUNCT
ejpam-846	118	18	,	,	PUNCT
ejpam-846	118	19	.	.	PUNCT
ejpam-846	118	20	.	.	PUNCT
ejpam-846	119	1	.	.	PUNCT
ejpam-846	120	1	,	,	PUNCT
ejpam-846	120	2	fn	fn	NOUN
ejpam-846	120	3	(	(	PUNCT
ejpam-846	120	4	ξ	ξ	NOUN
ejpam-846	120	5	)	)	PUNCT
ejpam-846	120	6	)	)	PUNCT
ejpam-846	120	7	:	:	PUNCT
ejpam-846	121	1	ξ	ξ	X
ejpam-846	121	2	∈	∈	PROPN
ejpam-846	121	3	ξ	ξ	NOUN
ejpam-846	121	4	}	}	PUNCT
ejpam-846	121	5	.	.	PUNCT
ejpam-846	122	1	(	(	PUNCT
ejpam-846	122	2	9	9	X
ejpam-846	122	3	)	)	PUNCT
ejpam-846	122	4	proposition	proposition	NOUN
ejpam-846	122	5	3	3	NUM
ejpam-846	122	6	.	.	PUNCT
ejpam-846	123	1	the	the	DET
ejpam-846	123	2	semi	semi	ADJ
ejpam-846	123	3	-	-	ADJ
ejpam-846	123	4	infinite	infinite	ADJ
ejpam-846	123	5	dual	dual	ADJ
ejpam-846	123	6	(	(	PUNCT
ejpam-846	123	7	7	7	NUM
ejpam-846	123	8	)	)	PUNCT
ejpam-846	123	9	is	be	AUX
ejpam-846	123	10	solvable	solvable	ADJ
ejpam-846	123	11	and	and	CCONJ
ejpam-846	123	12	φ(x	φ(x	NOUN
ejpam-846	123	13	)	)	PUNCT
ejpam-846	123	14	=	=	SYM
ejpam-846	123	15	φ∗(x	φ∗(x	PROPN
ejpam-846	123	16	)	)	PUNCT
ejpam-846	123	17	holds	hold	VERB
ejpam-846	123	18	if	if	SCONJ
ejpam-846	123	19	(	(	PUNCT
ejpam-846	123	20	i	i	NOUN
ejpam-846	123	21	)	)	PUNCT
ejpam-846	123	22	(	(	PUNCT
ejpam-846	123	23	7	7	X
ejpam-846	123	24	)	)	PUNCT
ejpam-846	123	25	is	be	AUX
ejpam-846	123	26	feasible	feasible	ADJ
ejpam-846	123	27	,	,	PUNCT
ejpam-846	123	28	and	and	CCONJ
ejpam-846	123	29	(	(	PUNCT
ejpam-846	123	30	ii	ii	NOUN
ejpam-846	123	31	)	)	PUNCT
ejpam-846	123	32	the	the	DET
ejpam-846	123	33	n	n	CCONJ
ejpam-846	123	34	-dimensional	-dimensional	ADJ
ejpam-846	123	35	point	point	NOUN
ejpam-846	123	36	µ	µ	X
ejpam-846	123	37	∈	∈	NOUN
ejpam-846	123	38	int(m	int(m	NOUN
ejpam-846	123	39	)	)	PUNCT
ejpam-846	123	40	,	,	PUNCT
ejpam-846	123	41	the	the	DET
ejpam-846	123	42	interior	interior	NOUN
ejpam-846	123	43	of	of	ADP
ejpam-846	123	44	the	the	DET
ejpam-846	123	45	set	set	ADJ
ejpam-846	123	46	m.	m.	NOUN
ejpam-846	123	47	proof	proof	NOUN
ejpam-846	123	48	.	.	PUNCT
ejpam-846	124	1	see	see	VERB
ejpam-846	124	2	glashoff	glashoff	NOUN
ejpam-846	124	3	and	and	CCONJ
ejpam-846	124	4	gustafson	gustafson	PROPN
ejpam-846	125	1	[	[	X
ejpam-846	125	2	9	9	NUM
ejpam-846	125	3	,	,	PUNCT
ejpam-846	125	4	p.79	p.79	ADP
ejpam-846	125	5	]	]	PUNCT
ejpam-846	125	6	,	,	PUNCT
ejpam-846	125	7	kall	kall	PROPN
ejpam-846	126	1	[	[	X
ejpam-846	126	2	12	12	NUM
ejpam-846	126	3	,	,	PUNCT
ejpam-846	126	4	theorem	theorem	VERB
ejpam-846	126	5	4	4	NUM
ejpam-846	126	6	]	]	PUNCT
ejpam-846	126	7	.	.	PUNCT
ejpam-846	127	1	while	while	SCONJ
ejpam-846	127	2	existence	existence	NOUN
ejpam-846	127	3	of	of	ADP
ejpam-846	127	4	solutions	solution	NOUN
ejpam-846	127	5	and	and	CCONJ
ejpam-846	127	6	strong	strong	ADJ
ejpam-846	127	7	duality	duality	NOUN
ejpam-846	127	8	are	be	AUX
ejpam-846	127	9	claimed	claim	VERB
ejpam-846	127	10	as	as	ADP
ejpam-846	127	11	above	above	ADV
ejpam-846	127	12	,	,	PUNCT
ejpam-846	127	13	an	an	DET
ejpam-846	127	14	explicit	explicit	ADJ
ejpam-846	127	15	expression	expression	NOUN
ejpam-846	127	16	of	of	ADP
ejpam-846	127	17	the	the	DET
ejpam-846	127	18	solution	solution	NOUN
ejpam-846	127	19	is	be	AUX
ejpam-846	127	20	not	not	PART
ejpam-846	127	21	easy	easy	ADJ
ejpam-846	127	22	for	for	ADP
ejpam-846	127	23	arbitrary	arbitrary	ADJ
ejpam-846	127	24	moment	moment	NOUN
ejpam-846	127	25	functions	function	NOUN
ejpam-846	127	26	fi	fi	NOUN
ejpam-846	127	27	.	.	PUNCT
ejpam-846	128	1	also	also	ADV
ejpam-846	128	2	,	,	PUNCT
ejpam-846	128	3	note	note	VERB
ejpam-846	128	4	that	that	SCONJ
ejpam-846	128	5	the	the	DET
ejpam-846	128	6	above	above	ADJ
ejpam-846	128	7	results	result	NOUN
ejpam-846	128	8	do	do	AUX
ejpam-846	128	9	not	not	PART
ejpam-846	128	10	require	require	VERB
ejpam-846	128	11	any	any	DET
ejpam-846	128	12	functional	functional	ADJ
ejpam-846	128	13	properties	property	NOUN
ejpam-846	128	14	of	of	ADP
ejpam-846	128	15	ϕ.	ϕ.	PROPN
ejpam-846	128	16	however	however	ADV
ejpam-846	128	17	,	,	PUNCT
ejpam-846	128	18	in	in	ADP
ejpam-846	128	19	our	our	PRON
ejpam-846	128	20	case	case	NOUN
ejpam-846	128	21	,	,	PUNCT
ejpam-846	128	22	using	use	VERB
ejpam-846	128	23	the	the	DET
ejpam-846	128	24	convexity	convexity	NOUN
ejpam-846	128	25	of	of	ADP
ejpam-846	128	26	ϕ	ϕ	NOUN
ejpam-846	128	27	in	in	ADP
ejpam-846	128	28	ξ	ξ	PROPN
ejpam-846	128	29	,	,	PUNCT
ejpam-846	128	30	the	the	DET
ejpam-846	128	31	semi	semi	ADJ
ejpam-846	128	32	-	-	ADJ
ejpam-846	128	33	infinite	infinite	ADJ
ejpam-846	128	34	dual	dual	ADJ
ejpam-846	128	35	optimal	optimal	ADJ
ejpam-846	128	36	solution	solution	NOUN
ejpam-846	128	37	can	can	AUX
ejpam-846	128	38	be	be	AUX
ejpam-846	128	39	expressed	express	VERB
ejpam-846	128	40	in	in	ADP
ejpam-846	128	41	closed	closed	ADJ
ejpam-846	128	42	-	-	PUNCT
ejpam-846	128	43	form	form	NOUN
ejpam-846	128	44	under	under	ADP
ejpam-846	128	45	first	first	ADJ
ejpam-846	128	46	moment	moment	NOUN
ejpam-846	128	47	conditions	condition	NOUN
ejpam-846	128	48	.	.	PUNCT
ejpam-846	129	1	edirisinghe	edirisinghe	PROPN
ejpam-846	129	2	/	/	SYM
ejpam-846	129	3	eur	eur	PROPN
ejpam-846	129	4	.	.	PUNCT
ejpam-846	130	1	j.	j.	PROPN
ejpam-846	130	2	pure	pure	PROPN
ejpam-846	130	3	appl	appl	PROPN
ejpam-846	130	4	.	.	PROPN
ejpam-846	130	5	math	math	PROPN
ejpam-846	130	6	,	,	PUNCT
ejpam-846	130	7	3	3	NUM
ejpam-846	130	8	(	(	PUNCT
ejpam-846	130	9	2010	2010	NUM
ejpam-846	130	10	)	)	PUNCT
ejpam-846	130	11	,	,	PUNCT
ejpam-846	130	12	572	572	NUM
ejpam-846	130	13	-	-	SYM
ejpam-846	130	14	592	592	NUM
ejpam-846	130	15	577	577	NUM
ejpam-846	130	16	2.2	2.2	NUM
ejpam-846	130	17	.	.	PUNCT
ejpam-846	131	1	first	first	ADJ
ejpam-846	131	2	moment	moment	NOUN
ejpam-846	131	3	approximation	approximation	NOUN
ejpam-846	131	4	consider	consider	VERB
ejpam-846	131	5	the	the	DET
ejpam-846	131	6	gmp	gmp	PROPN
ejpam-846	131	7	in	in	ADP
ejpam-846	131	8	(	(	PUNCT
ejpam-846	131	9	6	6	NUM
ejpam-846	131	10	)	)	PUNCT
ejpam-846	131	11	using	use	VERB
ejpam-846	131	12	only	only	ADV
ejpam-846	131	13	the	the	DET
ejpam-846	131	14	first	first	ADJ
ejpam-846	131	15	moments	moment	NOUN
ejpam-846	131	16	ξ̄	ξ̄	ADJ
ejpam-846	131	17	=	=	SYM
ejpam-846	131	18	e[ξ	e[ξ	NOUN
ejpam-846	131	19	]	]	PUNCT
ejpam-846	131	20	,	,	PUNCT
ejpam-846	131	21	i.e.	i.e.	X
ejpam-846	131	22	,	,	PUNCT
ejpam-846	131	23	φ1(x	φ1(x	NOUN
ejpam-846	131	24	)	)	PUNCT
ejpam-846	131	25	=	=	SYM
ejpam-846	131	26	inf	inf	PROPN
ejpam-846	131	27	p∈p	p∈p	NOUN
ejpam-846	131	28	{	{	PUNCT
ejpam-846	131	29	∫	∫	PROPN
ejpam-846	131	30	ξ	ξ	X
ejpam-846	131	31	ϕ(x	ϕ(x	PROPN
ejpam-846	131	32	,	,	PUNCT
ejpam-846	131	33	ξ)p	ξ)p	ADJ
ejpam-846	131	34	(	(	PUNCT
ejpam-846	131	35	dξ	dξ	PROPN
ejpam-846	131	36	)	)	PUNCT
ejpam-846	131	37	:	:	PUNCT
ejpam-846	131	38	∫	∫	PROPN
ejpam-846	132	1	ξ	ξ	X
ejpam-846	132	2	ξp	ξp	PROPN
ejpam-846	132	3	(	(	PUNCT
ejpam-846	132	4	dξ	dξ	PROPN
ejpam-846	132	5	)	)	PUNCT
ejpam-846	132	6	=	=	PUNCT
ejpam-846	132	7	ξ̄	ξ̄	ADJ
ejpam-846	132	8	}	}	PUNCT
ejpam-846	132	9	.	.	PUNCT
ejpam-846	133	1	(	(	PUNCT
ejpam-846	133	2	10	10	X
ejpam-846	133	3	)	)	PUNCT
ejpam-846	133	4	defining	define	VERB
ejpam-846	133	5	the	the	DET
ejpam-846	133	6	graph	graph	NOUN
ejpam-846	133	7	g(x	g(x	NOUN
ejpam-846	133	8	)	)	PUNCT
ejpam-846	134	1	:	:	PUNCT
ejpam-846	134	2	=	=	SYM
ejpam-846	134	3	{	{	PUNCT
ejpam-846	134	4	(	(	PUNCT
ejpam-846	134	5	ξ	ξ	PROPN
ejpam-846	134	6	,	,	PUNCT
ejpam-846	134	7	ϕ(x	ϕ(x	PROPN
ejpam-846	134	8	,	,	PUNCT
ejpam-846	134	9	ξ	ξ	NOUN
ejpam-846	134	10	)	)	PUNCT
ejpam-846	134	11	)	)	PUNCT
ejpam-846	134	12	:	:	PUNCT
ejpam-846	134	13	ξ	ξ	X
ejpam-846	134	14	∈	∈	PROPN
ejpam-846	134	15	ξ	ξ	PROPN
ejpam-846	134	16	}	}	PUNCT
ejpam-846	134	17	,	,	PUNCT
ejpam-846	134	18	(	(	PUNCT
ejpam-846	134	19	11	11	X
ejpam-846	134	20	)	)	PUNCT
ejpam-846	134	21	let	let	VERB
ejpam-846	134	22	z(x	z(x	NOUN
ejpam-846	134	23	)	)	PUNCT
ejpam-846	134	24	=	=	SYM
ejpam-846	134	25	cog(x	cog(x	X
ejpam-846	134	26	)	)	PUNCT
ejpam-846	134	27	,	,	PUNCT
ejpam-846	134	28	the	the	DET
ejpam-846	134	29	convex	convex	PROPN
ejpam-846	134	30	hull	hull	NOUN
ejpam-846	134	31	of	of	ADP
ejpam-846	134	32	g	g	NOUN
ejpam-846	134	33	,	,	PUNCT
ejpam-846	134	34	which	which	PRON
ejpam-846	134	35	is	be	AUX
ejpam-846	134	36	closed	close	VERB
ejpam-846	134	37	since	since	SCONJ
ejpam-846	134	38	ϕ	ϕ	NOUN
ejpam-846	134	39	is	be	AUX
ejpam-846	134	40	continuous	continuous	ADJ
ejpam-846	134	41	in	in	ADP
ejpam-846	134	42	ξ	ξ	PROPN
ejpam-846	134	43	.	.	PUNCT
ejpam-846	135	1	then	then	ADV
ejpam-846	135	2	(	(	PUNCT
ejpam-846	135	3	10	10	NUM
ejpam-846	135	4	)	)	PUNCT
ejpam-846	135	5	is	be	AUX
ejpam-846	135	6	equivalent	equivalent	ADJ
ejpam-846	135	7	to	to	ADP
ejpam-846	135	8	φ1(x	φ1(x	NOUN
ejpam-846	135	9	)	)	PUNCT
ejpam-846	135	10	=	=	SYM
ejpam-846	135	11	inf	inf	PROPN
ejpam-846	135	12	z	z	NOUN
ejpam-846	135	13	{	{	PUNCT
ejpam-846	135	14	zk+1	zk+1	NUM
ejpam-846	135	15	∈	∈	PROPN
ejpam-846	135	16	ℜ	ℜ	PROPN
ejpam-846	135	17	:	:	PUNCT
ejpam-846	135	18	(	(	PUNCT
ejpam-846	135	19	z1	z1	NOUN
ejpam-846	135	20	,	,	PUNCT
ejpam-846	135	21	.	.	PUNCT
ejpam-846	135	22	.	.	PUNCT
ejpam-846	136	1	.	.	PUNCT
ejpam-846	137	1	,	,	PUNCT
ejpam-846	137	2	zk+1	zk+1	X
ejpam-846	137	3	)	)	PUNCT
ejpam-846	137	4	∈	∈	NOUN
ejpam-846	137	5	z(x	z(x	NUM
ejpam-846	137	6	)	)	PUNCT
ejpam-846	137	7	,	,	PUNCT
ejpam-846	137	8	zk	zk	PROPN
ejpam-846	137	9	=	=	SYM
ejpam-846	137	10	ξ̄k	ξ̄k	PROPN
ejpam-846	137	11	,	,	PUNCT
ejpam-846	137	12	k	k	NOUN
ejpam-846	137	13	=	=	SYM
ejpam-846	137	14	1	1	NUM
ejpam-846	137	15	,	,	PUNCT
ejpam-846	137	16	.	.	PUNCT
ejpam-846	137	17	.	.	PUNCT
ejpam-846	138	1	.	.	PUNCT
ejpam-846	139	1	,	,	PUNCT
ejpam-846	139	2	k	k	NOUN
ejpam-846	139	3	}	}	PUNCT
ejpam-846	139	4	.	.	PUNCT
ejpam-846	140	1	(	(	PUNCT
ejpam-846	140	2	12	12	NUM
ejpam-846	140	3	)	)	PUNCT
ejpam-846	140	4	define	define	VERB
ejpam-846	140	5	the	the	DET
ejpam-846	140	6	epigraph	epigraph	NOUN
ejpam-846	140	7	of	of	ADP
ejpam-846	140	8	ϕ(x	ϕ(x	PROPN
ejpam-846	140	9	,	,	PUNCT
ejpam-846	140	10	ξ	ξ	X
ejpam-846	140	11	)	)	PUNCT
ejpam-846	140	12	by	by	ADP
ejpam-846	140	13	the	the	DET
ejpam-846	140	14	set	set	NOUN
ejpam-846	140	15	eϕ(x	eϕ(x	PUNCT
ejpam-846	140	16	)	)	PUNCT
ejpam-846	140	17	,	,	PUNCT
ejpam-846	140	18	i.e.	i.e.	X
ejpam-846	140	19	,	,	PUNCT
ejpam-846	140	20	eϕ(x	eϕ(x	PUNCT
ejpam-846	140	21	)	)	PUNCT
ejpam-846	140	22	:	:	PUNCT
ejpam-846	141	1	=	=	SYM
ejpam-846	141	2	{	{	PUNCT
ejpam-846	141	3	(	(	PUNCT
ejpam-846	141	4	ξ1	ξ1	NOUN
ejpam-846	141	5	,	,	PUNCT
ejpam-846	141	6	.	.	PUNCT
ejpam-846	141	7	.	.	PUNCT
ejpam-846	141	8	.	.	PUNCT
ejpam-846	142	1	,	,	PUNCT
ejpam-846	143	1	ξk	ξk	ADP
ejpam-846	143	2	,	,	PUNCT
ejpam-846	143	3	zk+1	zk+1	NUM
ejpam-846	143	4	)	)	PUNCT
ejpam-846	143	5	:	:	PUNCT
ejpam-846	143	6	zk+1	zk+1	NUM
ejpam-846	143	7	≥	≥	X
ejpam-846	143	8	ϕ(x	ϕ(x	PROPN
ejpam-846	143	9	,	,	PUNCT
ejpam-846	143	10	ξ	ξ	NOUN
ejpam-846	143	11	)	)	PUNCT
ejpam-846	143	12	,	,	PUNCT
ejpam-846	143	13	ξ	ξ	PROPN
ejpam-846	143	14	∈	∈	PROPN
ejpam-846	143	15	ξ	ξ	NOUN
ejpam-846	143	16	}	}	PUNCT
ejpam-846	143	17	.	.	PUNCT
ejpam-846	144	1	(	(	PUNCT
ejpam-846	144	2	13	13	NUM
ejpam-846	144	3	)	)	PUNCT
ejpam-846	144	4	proposition	proposition	NOUN
ejpam-846	144	5	4	4	NUM
ejpam-846	144	6	.	.	NOUN
ejpam-846	144	7	z(x	z(x	NUM
ejpam-846	144	8	)	)	PUNCT
ejpam-846	144	9	⊆	⊆	NUM
ejpam-846	144	10	eϕ(x	eϕ(x	X
ejpam-846	144	11	)	)	PUNCT
ejpam-846	144	12	.	.	PUNCT
ejpam-846	145	1	proof	proof	NOUN
ejpam-846	145	2	.	.	PUNCT
ejpam-846	146	1	consider	consider	VERB
ejpam-846	146	2	an	an	DET
ejpam-846	146	3	arbitrary	arbitrary	ADJ
ejpam-846	146	4	point	point	NOUN
ejpam-846	146	5	ẑ	ẑ	NUM
ejpam-846	146	6	∈	∈	PROPN
ejpam-846	146	7	z(x	z(x	NUM
ejpam-846	146	8	)	)	PUNCT
ejpam-846	146	9	.	.	PUNCT
ejpam-846	147	1	since	since	SCONJ
ejpam-846	147	2	z(x	z(x	NUM
ejpam-846	147	3	)	)	PUNCT
ejpam-846	147	4	=	=	PUNCT
ejpam-846	147	5	co	co	X
ejpam-846	147	6	g(x	g(x	NOUN
ejpam-846	147	7	)	)	PUNCT
ejpam-846	147	8	,	,	PUNCT
ejpam-846	147	9	there	there	PRON
ejpam-846	147	10	exist	exist	VERB
ejpam-846	147	11	a	a	DET
ejpam-846	147	12	set	set	NOUN
ejpam-846	147	13	of	of	ADP
ejpam-846	147	14	i	i	PRON
ejpam-846	147	15	points	point	VERB
ejpam-846	147	16	(	(	PUNCT
ejpam-846	147	17	ξi	ξi	NOUN
ejpam-846	147	18	,	,	PUNCT
ejpam-846	147	19	ϕ(x	ϕ(x	NOUN
ejpam-846	147	20	,	,	PUNCT
ejpam-846	147	21	ξi	ξi	NOUN
ejpam-846	147	22	)	)	PUNCT
ejpam-846	147	23	)	)	PUNCT
ejpam-846	147	24	,	,	PUNCT
ejpam-846	147	25	where	where	SCONJ
ejpam-846	147	26	ξi	ξi	PROPN
ejpam-846	147	27	∈	∈	PROPN
ejpam-846	147	28	ξ	ξ	PROPN
ejpam-846	147	29	,	,	PUNCT
ejpam-846	147	30	and	and	CCONJ
ejpam-846	147	31	nonnegative	nonnegative	ADJ
ejpam-846	147	32	multipliers	multiplier	NOUN
ejpam-846	147	33	λi	λi	ADP
ejpam-846	147	34	,	,	PUNCT
ejpam-846	147	35	i	i	NOUN
ejpam-846	147	36	=	=	NOUN
ejpam-846	147	37	1	1	NUM
ejpam-846	147	38	,	,	PUNCT
ejpam-846	147	39	.	.	PUNCT
ejpam-846	147	40	.	.	PUNCT
ejpam-846	148	1	.	.	PUNCT
ejpam-846	149	1	,	,	PUNCT
ejpam-846	149	2	i	i	PRON
ejpam-846	149	3	,	,	PUNCT
ejpam-846	149	4	such	such	ADJ
ejpam-846	149	5	that	that	SCONJ
ejpam-846	149	6	ẑk	ẑk	X
ejpam-846	149	7	=	=	SYM
ejpam-846	150	1	i∑	i∑	PROPN
ejpam-846	151	1	i=1	i=1	PRON
ejpam-846	151	2	λiξ	λiξ	NOUN
ejpam-846	151	3	i	i	PRON
ejpam-846	151	4	k	k	NOUN
ejpam-846	151	5	,	,	PUNCT
ejpam-846	151	6	k	k	NOUN
ejpam-846	152	1	=	=	SYM
ejpam-846	153	1	1	1	NUM
ejpam-846	153	2	,	,	PUNCT
ejpam-846	153	3	.	.	PUNCT
ejpam-846	153	4	.	.	PUNCT
ejpam-846	153	5	.	.	PUNCT
ejpam-846	154	1	,	,	PUNCT
ejpam-846	154	2	k	k	NOUN
ejpam-846	154	3	,	,	PUNCT
ejpam-846	154	4	ẑk+1	ẑk+1	PROPN
ejpam-846	154	5	=	=	SYM
ejpam-846	154	6	i∑	i∑	PROPN
ejpam-846	154	7	i=1	i=1	PROPN
ejpam-846	154	8	λiϕ(x	λiϕ(x	PROPN
ejpam-846	154	9	,	,	PUNCT
ejpam-846	154	10	ξ	ξ	PROPN
ejpam-846	154	11	i	i	PROPN
ejpam-846	154	12	)	)	PUNCT
ejpam-846	154	13	,	,	PUNCT
ejpam-846	154	14	i∑	i∑	PROPN
ejpam-846	154	15	i=1	i=1	X
ejpam-846	154	16	λi	λi	X
ejpam-846	154	17	=	=	ADJ
ejpam-846	154	18	1	1	NUM
ejpam-846	154	19	.	.	PUNCT
ejpam-846	155	1	(	(	PUNCT
ejpam-846	155	2	14	14	NUM
ejpam-846	155	3	)	)	PUNCT
ejpam-846	155	4	since	since	SCONJ
ejpam-846	155	5	ϕ	ϕ	NOUN
ejpam-846	155	6	is	be	AUX
ejpam-846	155	7	convex	convex	ADJ
ejpam-846	155	8	in	in	ADP
ejpam-846	155	9	ξ	ξ	PROPN
ejpam-846	155	10	,	,	PUNCT
ejpam-846	155	11	(	(	PUNCT
ejpam-846	155	12	14	14	NUM
ejpam-846	155	13	)	)	PUNCT
ejpam-846	155	14	implies	imply	VERB
ejpam-846	155	15	∑i	∑i	PROPN
ejpam-846	155	16	i=1	i=1	PROPN
ejpam-846	155	17	λiϕ(x	λiϕ(x	PROPN
ejpam-846	155	18	,	,	PUNCT
ejpam-846	155	19	ξ	ξ	PROPN
ejpam-846	155	20	i	i	PROPN
ejpam-846	155	21	)	)	PUNCT
ejpam-846	155	22	≥	≥	NOUN
ejpam-846	155	23	ϕ(x	ϕ(x	NOUN
ejpam-846	155	24	,	,	PUNCT
ejpam-846	155	25	ẑ1	ẑ1	NOUN
ejpam-846	155	26	,	,	PUNCT
ejpam-846	155	27	.	.	PUNCT
ejpam-846	155	28	.	.	PUNCT
ejpam-846	156	1	.	.	PUNCT
ejpam-846	157	1	,	,	PUNCT
ejpam-846	157	2	ẑk	ẑk	X
ejpam-846	157	3	)	)	PUNCT
ejpam-846	157	4	,	,	PUNCT
ejpam-846	157	5	and	and	CCONJ
ejpam-846	157	6	thus	thus	ADV
ejpam-846	157	7	,	,	PUNCT
ejpam-846	157	8	it	it	PRON
ejpam-846	157	9	follows	follow	VERB
ejpam-846	157	10	that	that	SCONJ
ejpam-846	157	11	ẑk+1	ẑk+1	PROPN
ejpam-846	157	12	≥	≥	X
ejpam-846	157	13	ϕ(x	ϕ(x	PROPN
ejpam-846	157	14	,	,	PUNCT
ejpam-846	157	15	ẑ1	ẑ1	NOUN
ejpam-846	157	16	,	,	PUNCT
ejpam-846	157	17	.	.	PUNCT
ejpam-846	157	18	.	.	PUNCT
ejpam-846	158	1	.	.	PUNCT
ejpam-846	159	1	,	,	PUNCT
ejpam-846	159	2	ẑk	ẑk	X
ejpam-846	159	3	)	)	PUNCT
ejpam-846	159	4	.	.	PUNCT
ejpam-846	160	1	moreover	moreover	ADV
ejpam-846	160	2	,	,	PUNCT
ejpam-846	160	3	ξi	ξi	PROPN
ejpam-846	160	4	∈	∈	PROPN
ejpam-846	160	5	ξ	ξ	PROPN
ejpam-846	160	6	implies	imply	VERB
ejpam-846	160	7	that	that	SCONJ
ejpam-846	160	8	(	(	PUNCT
ejpam-846	160	9	ẑ1	ẑ1	NOUN
ejpam-846	160	10	,	,	PUNCT
ejpam-846	160	11	.	.	PUNCT
ejpam-846	160	12	.	.	PUNCT
ejpam-846	161	1	.	.	PUNCT
ejpam-846	162	1	,	,	PUNCT
ejpam-846	162	2	ẑk	ẑk	X
ejpam-846	162	3	)	)	PUNCT
ejpam-846	162	4	∈	∈	PROPN
ejpam-846	163	1	ξ	ξ	X
ejpam-846	163	2	due	due	ADP
ejpam-846	163	3	to	to	ADP
ejpam-846	163	4	the	the	DET
ejpam-846	163	5	convexity	convexity	NOUN
ejpam-846	163	6	of	of	ADP
ejpam-846	163	7	ξ	ξ	PROPN
ejpam-846	163	8	.	.	PUNCT
ejpam-846	164	1	thus	thus	ADV
ejpam-846	164	2	,	,	PUNCT
ejpam-846	164	3	ẑ	ẑ	PROPN
ejpam-846	164	4	∈	∈	PROPN
ejpam-846	164	5	eϕ(x	eϕ(x	PUNCT
ejpam-846	164	6	)	)	PUNCT
ejpam-846	164	7	,	,	PUNCT
ejpam-846	164	8	completing	complete	VERB
ejpam-846	164	9	the	the	DET
ejpam-846	164	10	proof	proof	NOUN
ejpam-846	164	11	.	.	PUNCT
ejpam-846	165	1	proposition	proposition	NOUN
ejpam-846	165	2	5	5	NUM
ejpam-846	165	3	.	.	PUNCT
ejpam-846	165	4	φ1(x	φ1(x	NOUN
ejpam-846	165	5	)	)	PUNCT
ejpam-846	165	6	=	=	SYM
ejpam-846	165	7	ϕ(x	ϕ(x	NOUN
ejpam-846	165	8	,	,	PUNCT
ejpam-846	165	9	ξ̄	ξ̄	ADJ
ejpam-846	165	10	)	)	PUNCT
ejpam-846	165	11	.	.	PUNCT
ejpam-846	166	1	proof	proof	NOUN
ejpam-846	166	2	.	.	PUNCT
ejpam-846	167	1	since	since	SCONJ
ejpam-846	167	2	z(x	z(x	NUM
ejpam-846	167	3	)	)	PUNCT
ejpam-846	167	4	⊆	⊆	NUM
ejpam-846	167	5	eϕ(x	eϕ(x	X
ejpam-846	167	6	)	)	PUNCT
ejpam-846	167	7	holds	hold	VERB
ejpam-846	167	8	due	due	ADJ
ejpam-846	167	9	to	to	ADP
ejpam-846	167	10	proposition	proposition	NOUN
ejpam-846	167	11	4	4	NUM
ejpam-846	167	12	,	,	PUNCT
ejpam-846	167	13	from	from	ADP
ejpam-846	167	14	(	(	PUNCT
ejpam-846	167	15	12	12	NUM
ejpam-846	167	16	)	)	PUNCT
ejpam-846	167	17	,	,	PUNCT
ejpam-846	167	18	φ1(x	φ1(x	NOUN
ejpam-846	167	19	)	)	PUNCT
ejpam-846	167	20	≥	≥	NOUN
ejpam-846	167	21	inf	inf	PROPN
ejpam-846	167	22	z	z	PROPN
ejpam-846	167	23	{	{	PUNCT
ejpam-846	167	24	zk+1	zk+1	NUM
ejpam-846	167	25	∈	∈	PROPN
ejpam-846	167	26	ℜ	ℜ	PROPN
ejpam-846	167	27	:	:	PUNCT
ejpam-846	167	28	(	(	PUNCT
ejpam-846	167	29	z1	z1	NOUN
ejpam-846	167	30	,	,	PUNCT
ejpam-846	167	31	.	.	PUNCT
ejpam-846	167	32	.	.	PUNCT
ejpam-846	168	1	.	.	PUNCT
ejpam-846	169	1	,	,	PUNCT
ejpam-846	169	2	zk+1	zk+1	X
ejpam-846	169	3	)	)	PUNCT
ejpam-846	169	4	∈	∈	PROPN
ejpam-846	169	5	eϕ(x	eϕ(x	PUNCT
ejpam-846	169	6	)	)	PUNCT
ejpam-846	169	7	,	,	PUNCT
ejpam-846	169	8	zk	zk	PROPN
ejpam-846	169	9	=	=	SYM
ejpam-846	169	10	ξ̄k	ξ̄k	PROPN
ejpam-846	169	11	,	,	PUNCT
ejpam-846	169	12	k	k	NOUN
ejpam-846	169	13	=	=	SYM
ejpam-846	169	14	1	1	NUM
ejpam-846	169	15	,	,	PUNCT
ejpam-846	169	16	.	.	PUNCT
ejpam-846	169	17	.	.	PUNCT
ejpam-846	169	18	.	.	PUNCT
ejpam-846	170	1	,	,	PUNCT
ejpam-846	170	2	k	k	X
ejpam-846	170	3	}	}	PUNCT
ejpam-846	170	4	=	=	SYM
ejpam-846	170	5	inf	inf	PROPN
ejpam-846	170	6	z	z	NOUN
ejpam-846	170	7	{	{	PUNCT
ejpam-846	170	8	zk+1	zk+1	NUM
ejpam-846	170	9	∈	∈	PROPN
ejpam-846	170	10	ℜ	ℜ	PROPN
ejpam-846	170	11	:	:	PUNCT
ejpam-846	170	12	zk+1	zk+1	NUM
ejpam-846	170	13	≥	≥	NOUN
ejpam-846	170	14	ϕ(x	ϕ(x	NOUN
ejpam-846	170	15	,	,	PUNCT
ejpam-846	170	16	ξ̄	ξ̄	ADJ
ejpam-846	170	17	)	)	PUNCT
ejpam-846	170	18	}	}	PUNCT
ejpam-846	171	1	=	=	SYM
ejpam-846	171	2	ϕ(x	ϕ(x	NOUN
ejpam-846	171	3	,	,	PUNCT
ejpam-846	171	4	ξ̄	ξ̄	ADJ
ejpam-846	171	5	)	)	PUNCT
ejpam-846	171	6	.	.	PUNCT
ejpam-846	172	1	on	on	ADP
ejpam-846	172	2	the	the	DET
ejpam-846	172	3	other	other	ADJ
ejpam-846	172	4	hand	hand	NOUN
ejpam-846	172	5	,	,	PUNCT
ejpam-846	172	6	(	(	PUNCT
ejpam-846	172	7	ξ̄	ξ̄	ADJ
ejpam-846	172	8	,	,	PUNCT
ejpam-846	172	9	ϕ(x	ϕ(x	NOUN
ejpam-846	172	10	,	,	PUNCT
ejpam-846	172	11	ξ̄	ξ̄	ADJ
ejpam-846	172	12	)	)	PUNCT
ejpam-846	172	13	∈	∈	PROPN
ejpam-846	172	14	g(x	g(x	NOUN
ejpam-846	172	15	)	)	PUNCT
ejpam-846	172	16	,	,	PUNCT
ejpam-846	172	17	and	and	CCONJ
ejpam-846	172	18	since	since	SCONJ
ejpam-846	172	19	g(x	g(x	NOUN
ejpam-846	172	20	)	)	PUNCT
ejpam-846	172	21	⊆	⊆	NUM
ejpam-846	172	22	z(x	z(x	NUM
ejpam-846	172	23	)	)	PUNCT
ejpam-846	172	24	,	,	PUNCT
ejpam-846	172	25	(	(	PUNCT
ejpam-846	172	26	ξ̄1	ξ̄1	NUM
ejpam-846	172	27	,	,	PUNCT
ejpam-846	172	28	.	.	PUNCT
ejpam-846	172	29	.	.	PUNCT
ejpam-846	173	1	.	.	PUNCT
ejpam-846	174	1	,	,	PUNCT
ejpam-846	174	2	ξk	ξk	ADV
ejpam-846	174	3	,	,	PUNCT
ejpam-846	174	4	ϕ(x	ϕ(x	NOUN
ejpam-846	174	5	,	,	PUNCT
ejpam-846	174	6	ξ̄	ξ̄	ADJ
ejpam-846	174	7	)	)	PUNCT
ejpam-846	174	8	)	)	PUNCT
ejpam-846	174	9	is	be	AUX
ejpam-846	174	10	feasible	feasible	ADJ
ejpam-846	174	11	in	in	ADP
ejpam-846	174	12	(	(	PUNCT
ejpam-846	174	13	12	12	NUM
ejpam-846	174	14	)	)	PUNCT
ejpam-846	174	15	.	.	PUNCT
ejpam-846	175	1	thus	thus	ADV
ejpam-846	175	2	,	,	PUNCT
ejpam-846	175	3	φ1(x	φ1(x	NOUN
ejpam-846	175	4	)	)	PUNCT
ejpam-846	175	5	≤	≤	NOUN
ejpam-846	175	6	ϕ(x	ϕ(x	NOUN
ejpam-846	175	7	,	,	PUNCT
ejpam-846	175	8	ξ̄	ξ̄	NOUN
ejpam-846	175	9	)	)	PUNCT
ejpam-846	175	10	holds	hold	NOUN
ejpam-846	175	11	,	,	PUNCT
ejpam-846	175	12	which	which	PRON
ejpam-846	175	13	completes	complete	VERB
ejpam-846	175	14	the	the	DET
ejpam-846	175	15	proof	proof	NOUN
ejpam-846	175	16	.	.	PUNCT
ejpam-846	176	1	observe	observe	VERB
ejpam-846	176	2	that	that	SCONJ
ejpam-846	176	3	the	the	DET
ejpam-846	176	4	value	value	NOUN
ejpam-846	176	5	of	of	ADP
ejpam-846	176	6	the	the	DET
ejpam-846	176	7	first	first	ADJ
ejpam-846	176	8	-	-	PUNCT
ejpam-846	176	9	moment	moment	NOUN
ejpam-846	176	10	gmp	gmp	PROPN
ejpam-846	176	11	is	be	AUX
ejpam-846	176	12	thus	thus	ADV
ejpam-846	176	13	obtained	obtain	VERB
ejpam-846	176	14	without	without	ADP
ejpam-846	176	15	any	any	DET
ejpam-846	176	16	assumption	assumption	NOUN
ejpam-846	176	17	on	on	ADP
ejpam-846	176	18	conditions	condition	NOUN
ejpam-846	176	19	required	require	VERB
ejpam-846	176	20	for	for	ADP
ejpam-846	176	21	strong	strong	ADJ
ejpam-846	176	22	duality	duality	NOUN
ejpam-846	176	23	.	.	PUNCT
ejpam-846	177	1	note	note	VERB
ejpam-846	177	2	that	that	SCONJ
ejpam-846	177	3	ϕ(x	ϕ(x	NOUN
ejpam-846	177	4	,	,	PUNCT
ejpam-846	177	5	ξ̄	ξ̄	ADJ
ejpam-846	177	6	)	)	PUNCT
ejpam-846	177	7	is	be	AUX
ejpam-846	177	8	indeed	indeed	ADV
ejpam-846	177	9	the	the	DET
ejpam-846	177	10	well	well	ADV
ejpam-846	177	11	-	-	PUNCT
ejpam-846	177	12	known	know	VERB
ejpam-846	177	13	jensen	jensen	PROPN
ejpam-846	178	1	[	[	X
ejpam-846	178	2	10	10	NUM
ejpam-846	178	3	]	]	X
ejpam-846	178	4	lower	low	ADJ
ejpam-846	178	5	bound	bind	VERB
ejpam-846	178	6	on	on	ADP
ejpam-846	178	7	the	the	DET
ejpam-846	178	8	expectation	expectation	NOUN
ejpam-846	178	9	of	of	ADP
ejpam-846	178	10	a	a	DET
ejpam-846	178	11	convex	convex	NOUN
ejpam-846	178	12	function	function	NOUN
ejpam-846	178	13	.	.	PUNCT
ejpam-846	179	1	on	on	ADP
ejpam-846	179	2	the	the	DET
ejpam-846	179	3	other	other	ADJ
ejpam-846	179	4	hand	hand	NOUN
ejpam-846	179	5	,	,	PUNCT
ejpam-846	179	6	edirisinghe	edirisinghe	PROPN
ejpam-846	179	7	/	/	SYM
ejpam-846	179	8	eur	eur	PROPN
ejpam-846	179	9	.	.	PUNCT
ejpam-846	180	1	j.	j.	PROPN
ejpam-846	180	2	pure	pure	PROPN
ejpam-846	180	3	appl	appl	PROPN
ejpam-846	180	4	.	.	PROPN
ejpam-846	180	5	math	math	PROPN
ejpam-846	180	6	,	,	PUNCT
ejpam-846	180	7	3	3	NUM
ejpam-846	180	8	(	(	PUNCT
ejpam-846	180	9	2010	2010	NUM
ejpam-846	180	10	)	)	PUNCT
ejpam-846	180	11	,	,	PUNCT
ejpam-846	180	12	572	572	NUM
ejpam-846	180	13	-	-	SYM
ejpam-846	180	14	592	592	NUM
ejpam-846	180	15	578	578	NUM
ejpam-846	180	16	ξ̄	ξ̄	ADJ
ejpam-846	180	17	∈	∈	NOUN
ejpam-846	180	18	int(ξ	int(ξ	X
ejpam-846	180	19	)	)	PUNCT
ejpam-846	180	20	holds	hold	VERB
ejpam-846	180	21	since	since	SCONJ
ejpam-846	180	22	p	p	NOUN
ejpam-846	180	23	tr	tr	VERB
ejpam-846	180	24	is	be	AUX
ejpam-846	180	25	nondegenerate	nondegenerate	ADJ
ejpam-846	180	26	,	,	PUNCT
ejpam-846	180	27	and	and	CCONJ
ejpam-846	180	28	due	due	ADP
ejpam-846	180	29	to	to	ADP
ejpam-846	180	30	finiteness	finiteness	NOUN
ejpam-846	180	31	of	of	ADP
ejpam-846	180	32	(	(	PUNCT
ejpam-846	180	33	10	10	NUM
ejpam-846	180	34	)	)	PUNCT
ejpam-846	180	35	,	,	PUNCT
ejpam-846	180	36	proposition	proposition	NOUN
ejpam-846	180	37	3	3	NUM
ejpam-846	180	38	ensures	ensure	VERB
ejpam-846	180	39	that	that	SCONJ
ejpam-846	180	40	the	the	DET
ejpam-846	180	41	semi	semi	ADJ
ejpam-846	180	42	-	-	ADJ
ejpam-846	180	43	infinite	infinite	ADJ
ejpam-846	180	44	dual	dual	ADJ
ejpam-846	180	45	satisfies	satisfie	NOUN
ejpam-846	180	46	ϕ(x	ϕ(x	PROPN
ejpam-846	180	47	,	,	PUNCT
ejpam-846	180	48	ξ̄	ξ̄	ADJ
ejpam-846	180	49	)	)	PUNCT
ejpam-846	180	50	=	=	SYM
ejpam-846	180	51	sup	sup	NOUN
ejpam-846	180	52	π∈ℜn+1	π∈ℜn+1	PUNCT
ejpam-846	180	53	{	{	PUNCT
ejpam-846	180	54	π0	π0	NOUN
ejpam-846	180	55	+	+	CCONJ
ejpam-846	180	56	k∑	k∑	VERB
ejpam-846	180	57	k=1	k=1	X
ejpam-846	180	58	ξ̄kπk	ξ̄kπk	X
ejpam-846	180	59	:	:	PUNCT
ejpam-846	180	60	π0	π0	NOUN
ejpam-846	180	61	+	+	CCONJ
ejpam-846	180	62	k∑	k∑	VERB
ejpam-846	180	63	k=1	k=1	PROPN
ejpam-846	180	64	ξkπk	ξkπk	PROPN
ejpam-846	180	65	≤	≤	PROPN
ejpam-846	180	66	ϕ(x	ϕ(x	PROPN
ejpam-846	180	67	,	,	PUNCT
ejpam-846	180	68	ξ	ξ	NOUN
ejpam-846	180	69	)	)	PUNCT
ejpam-846	180	70	,	,	PUNCT
ejpam-846	180	71	ξ	ξ	PROPN
ejpam-846	180	72	∈	∈	PROPN
ejpam-846	180	73	ξ	ξ	X
ejpam-846	180	74	}	}	PUNCT
ejpam-846	180	75	.	.	PUNCT
ejpam-846	181	1	(	(	PUNCT
ejpam-846	181	2	15	15	X
ejpam-846	181	3	)	)	PUNCT
ejpam-846	181	4	the	the	DET
ejpam-846	181	5	solution	solution	NOUN
ejpam-846	181	6	of	of	ADP
ejpam-846	181	7	the	the	DET
ejpam-846	181	8	dual	dual	ADJ
ejpam-846	181	9	is	be	AUX
ejpam-846	181	10	then	then	ADV
ejpam-846	181	11	determined	determine	VERB
ejpam-846	181	12	by	by	ADP
ejpam-846	181	13	the	the	DET
ejpam-846	181	14	‘	'	PUNCT
ejpam-846	181	15	supporting	support	VERB
ejpam-846	181	16	hyperplane	hyperplane	NOUN
ejpam-846	181	17	’	'	PUNCT
ejpam-846	181	18	of	of	ADP
ejpam-846	181	19	the	the	DET
ejpam-846	181	20	convex	convex	NOUN
ejpam-846	181	21	function	function	NOUN
ejpam-846	181	22	ϕ(x	ϕ(x	PROPN
ejpam-846	181	23	,	,	PUNCT
ejpam-846	181	24	ξ	ξ	X
ejpam-846	181	25	)	)	PUNCT
ejpam-846	181	26	at	at	ADP
ejpam-846	181	27	ξ	ξ	X
ejpam-846	181	28	=	=	PUNCT
ejpam-846	181	29	ξ̄.	ξ̄.	X
ejpam-846	181	30	can	can	AUX
ejpam-846	181	31	the	the	DET
ejpam-846	181	32	first	first	ADJ
ejpam-846	181	33	moment	moment	NOUN
ejpam-846	181	34	lower	lower	ADV
ejpam-846	181	35	bound	bind	VERB
ejpam-846	181	36	be	be	AUX
ejpam-846	181	37	improved	improve	VERB
ejpam-846	181	38	under	under	ADP
ejpam-846	181	39	additional	additional	ADJ
ejpam-846	181	40	information	information	NOUN
ejpam-846	181	41	on	on	ADP
ejpam-846	181	42	the	the	DET
ejpam-846	181	43	random	random	ADJ
ejpam-846	181	44	vector	vector	NOUN
ejpam-846	181	45	ξ	ξ	NOUN
ejpam-846	181	46	?	?	PUNCT
ejpam-846	182	1	for	for	ADP
ejpam-846	182	2	instance	instance	NOUN
ejpam-846	182	3	,	,	PUNCT
ejpam-846	182	4	if	if	SCONJ
ejpam-846	182	5	ξ	ξ	PROPN
ejpam-846	182	6	has	have	VERB
ejpam-846	182	7	uncorrelated	uncorrelated	ADJ
ejpam-846	182	8	components	component	NOUN
ejpam-846	182	9	,	,	PUNCT
ejpam-846	182	10	would	would	AUX
ejpam-846	182	11	the	the	DET
ejpam-846	182	12	convexity	convexity	NOUN
ejpam-846	182	13	information	information	NOUN
ejpam-846	182	14	on	on	ADP
ejpam-846	182	15	ϕ	ϕ	PROPN
ejpam-846	182	16	allows	allow	VERB
ejpam-846	182	17	one	one	NUM
ejpam-846	182	18	to	to	PART
ejpam-846	182	19	develop	develop	VERB
ejpam-846	182	20	a	a	DET
ejpam-846	182	21	stronger	strong	ADJ
ejpam-846	182	22	bound	bind	VERB
ejpam-846	182	23	?	?	PUNCT
ejpam-846	183	1	to	to	PART
ejpam-846	183	2	answer	answer	VERB
ejpam-846	183	3	this	this	DET
ejpam-846	183	4	question	question	NOUN
ejpam-846	183	5	,	,	PUNCT
ejpam-846	183	6	first	first	ADV
ejpam-846	183	7	,	,	PUNCT
ejpam-846	183	8	note	note	VERB
ejpam-846	183	9	that	that	SCONJ
ejpam-846	183	10	the	the	DET
ejpam-846	183	11	components	component	NOUN
ejpam-846	183	12	of	of	ADP
ejpam-846	183	13	ξ	ξ	PROPN
ejpam-846	183	14	are	be	AUX
ejpam-846	183	15	mutually	mutually	ADV
ejpam-846	183	16	uncorrelated	uncorrelated	ADJ
ejpam-846	183	17	(	(	PUNCT
ejpam-846	183	18	under	under	ADP
ejpam-846	183	19	p	p	NOUN
ejpam-846	183	20	tr	tr	VERB
ejpam-846	183	21	)	)	PUNCT
ejpam-846	183	22	if	if	SCONJ
ejpam-846	183	23	and	and	CCONJ
ejpam-846	183	24	only	only	ADV
ejpam-846	183	25	if	if	SCONJ
ejpam-846	183	26	e	e	NOUN
ejpam-846	183	27	∏	∏	VERB
ejpam-846	183	28	j∈λ	j∈λ	NOUN
ejpam-846	183	29	ξj	ξj	NOUN
ejpam-846	183	30			NOUN
ejpam-846	183	31	=	=	SYM
ejpam-846	183	32	∏	∏	PROPN
ejpam-846	183	33	j∈λ	j∈λ	NOUN
ejpam-846	183	34	ξ̄j	ξ̄j	PROPN
ejpam-846	183	35	,	,	PUNCT
ejpam-846	183	36	∀λ	∀λ	X
ejpam-846	183	37	∈	∈	PROPN
ejpam-846	183	38	b	b	PROPN
ejpam-846	183	39	,	,	PUNCT
ejpam-846	183	40	(	(	PUNCT
ejpam-846	183	41	16	16	NUM
ejpam-846	183	42	)	)	PUNCT
ejpam-846	183	43	where	where	SCONJ
ejpam-846	183	44	b	b	NOUN
ejpam-846	183	45	is	be	AUX
ejpam-846	183	46	the	the	DET
ejpam-846	183	47	set	set	NOUN
ejpam-846	183	48	of	of	ADP
ejpam-846	183	49	all	all	DET
ejpam-846	183	50	subsets	subset	NOUN
ejpam-846	183	51	of	of	ADP
ejpam-846	183	52	{	{	PUNCT
ejpam-846	183	53	1	1	NUM
ejpam-846	183	54	,	,	PUNCT
ejpam-846	183	55	.	.	PUNCT
ejpam-846	183	56	.	.	PUNCT
ejpam-846	184	1	.	.	PUNCT
ejpam-846	185	1	,	,	PUNCT
ejpam-846	185	2	k	k	X
ejpam-846	185	3	}	}	PUNCT
ejpam-846	185	4	with	with	ADP
ejpam-846	185	5	cardinality	cardinality	NOUN
ejpam-846	185	6	2	2	NUM
ejpam-846	185	7	.	.	PUNCT
ejpam-846	186	1	then	then	ADV
ejpam-846	186	2	,	,	PUNCT
ejpam-846	186	3	the	the	DET
ejpam-846	186	4	(	(	PUNCT
ejpam-846	186	5	tight	tight	NOUN
ejpam-846	186	6	)	)	PUNCT
ejpam-846	186	7	gmp	gmp	PROPN
ejpam-846	186	8	lower	lower	ADV
ejpam-846	186	9	bound	bind	VERB
ejpam-846	186	10	under	under	ADP
ejpam-846	186	11	first	first	ADJ
ejpam-846	186	12	moments	moment	NOUN
ejpam-846	186	13	and	and	CCONJ
ejpam-846	186	14	the	the	DET
ejpam-846	186	15	uncorrelated	uncorrelated	ADJ
ejpam-846	186	16	information	information	NOUN
ejpam-846	186	17	is	be	AUX
ejpam-846	186	18	formulated	formulate	VERB
ejpam-846	186	19	as	as	ADP
ejpam-846	186	20	φ1u(x	φ1u(x	NOUN
ejpam-846	186	21	)	)	PUNCT
ejpam-846	186	22	=	=	SYM
ejpam-846	187	1	inf	inf	PROPN
ejpam-846	187	2	p∈p	p∈p	ADJ
ejpam-846	187	3			PUNCT
ejpam-846	187	4	∫	∫	PROPN
ejpam-846	187	5	ξ	ξ	X
ejpam-846	187	6	ϕ(x	ϕ(x	PROPN
ejpam-846	187	7	,	,	PUNCT
ejpam-846	187	8	ξ)p	ξ)p	ADJ
ejpam-846	187	9	(	(	PUNCT
ejpam-846	187	10	dξ	dξ	PROPN
ejpam-846	187	11	)	)	PUNCT
ejpam-846	187	12	:	:	PUNCT
ejpam-846	188	1	∫	∫	PROPN
ejpam-846	188	2	ξ	ξ	X
ejpam-846	188	3	ξp	ξp	PROPN
ejpam-846	188	4	(	(	PUNCT
ejpam-846	188	5	dξ	dξ	PROPN
ejpam-846	188	6	)	)	PUNCT
ejpam-846	189	1	=	=	SYM
ejpam-846	189	2	ξ̄	ξ̄	ADJ
ejpam-846	189	3	,	,	PUNCT
ejpam-846	189	4	∫	∫	PROPN
ejpam-846	189	5	ξ	ξ	PROPN
ejpam-846	189	6	(	(	PUNCT
ejpam-846	189	7	∏	∏	PROPN
ejpam-846	189	8	j∈λ	j∈λ	NOUN
ejpam-846	189	9	ξj)p	ξj)p	PROPN
ejpam-846	189	10	(	(	PUNCT
ejpam-846	189	11	dξ	dξ	PROPN
ejpam-846	189	12	)	)	PUNCT
ejpam-846	189	13	=	=	SYM
ejpam-846	189	14	(	(	PUNCT
ejpam-846	189	15	∏	∏	PROPN
ejpam-846	189	16	j∈λ	j∈λ	PROPN
ejpam-846	189	17	ξ̄j),∀λ	ξ̄j),∀λ	PROPN
ejpam-846	189	18	∈	∈	PROPN
ejpam-846	189	19	b	b	PROPN
ejpam-846	189	20			PROPN
ejpam-846	189	21	.	.	PUNCT
ejpam-846	190	1	(	(	PUNCT
ejpam-846	190	2	17	17	NUM
ejpam-846	190	3	)	)	PUNCT
ejpam-846	190	4	proposition	proposition	NOUN
ejpam-846	190	5	6	6	NUM
ejpam-846	190	6	.	.	PUNCT
ejpam-846	191	1	jensen	jensen	PROPN
ejpam-846	191	2	’s	’s	PART
ejpam-846	191	3	lower	lower	ADV
ejpam-846	191	4	bound	bind	VERB
ejpam-846	191	5	remains	remain	VERB
ejpam-846	191	6	tight	tight	ADJ
ejpam-846	191	7	even	even	ADV
ejpam-846	191	8	under	under	ADP
ejpam-846	191	9	uncorrelated	uncorrelated	ADJ
ejpam-846	191	10	information	information	NOUN
ejpam-846	191	11	,	,	PUNCT
ejpam-846	191	12	i.e.	i.e.	X
ejpam-846	191	13	,	,	PUNCT
ejpam-846	191	14	φ1u(x	φ1u(x	PROPN
ejpam-846	191	15	)	)	PUNCT
ejpam-846	191	16	=	=	PUNCT
ejpam-846	192	1	ϕ(x	ϕ(x	NOUN
ejpam-846	192	2	,	,	PUNCT
ejpam-846	192	3	ξ̄	ξ̄	ADJ
ejpam-846	192	4	)	)	PUNCT
ejpam-846	192	5	.	.	PUNCT
ejpam-846	193	1	proof	proof	NOUN
ejpam-846	193	2	.	.	PUNCT
ejpam-846	194	1	since	since	SCONJ
ejpam-846	194	2	the	the	DET
ejpam-846	194	3	degenerate	degenerate	ADJ
ejpam-846	194	4	distribution	distribution	NOUN
ejpam-846	194	5	with	with	ADP
ejpam-846	194	6	probability	probability	NOUN
ejpam-846	194	7	mass	mass	NOUN
ejpam-846	194	8	at	at	ADP
ejpam-846	194	9	ξ̄	ξ̄	ADJ
ejpam-846	194	10	is	be	AUX
ejpam-846	194	11	feasible	feasible	ADJ
ejpam-846	194	12	in	in	ADP
ejpam-846	194	13	(	(	PUNCT
ejpam-846	194	14	17	17	NUM
ejpam-846	194	15	)	)	PUNCT
ejpam-846	194	16	,	,	PUNCT
ejpam-846	194	17	φ1u(x	φ1u(x	PROPN
ejpam-846	194	18	)	)	PUNCT
ejpam-846	194	19	≤	≤	NOUN
ejpam-846	194	20	ϕ(x	ϕ(x	NOUN
ejpam-846	194	21	,	,	PUNCT
ejpam-846	194	22	ξ̄	ξ̄	ADJ
ejpam-846	194	23	)	)	PUNCT
ejpam-846	194	24	.	.	PUNCT
ejpam-846	195	1	on	on	ADP
ejpam-846	195	2	the	the	DET
ejpam-846	195	3	other	other	ADJ
ejpam-846	195	4	hand	hand	NOUN
ejpam-846	195	5	,	,	PUNCT
ejpam-846	195	6	(	(	PUNCT
ejpam-846	195	7	17	17	NUM
ejpam-846	195	8	)	)	PUNCT
ejpam-846	195	9	is	be	AUX
ejpam-846	195	10	obtained	obtain	VERB
ejpam-846	195	11	by	by	ADP
ejpam-846	195	12	adding	add	VERB
ejpam-846	195	13	more	more	ADJ
ejpam-846	195	14	constraints	constraint	NOUN
ejpam-846	195	15	to	to	ADP
ejpam-846	195	16	(	(	PUNCT
ejpam-846	195	17	10	10	NUM
ejpam-846	195	18	)	)	PUNCT
ejpam-846	195	19	,	,	PUNCT
ejpam-846	195	20	and	and	CCONJ
ejpam-846	195	21	thus	thus	ADV
ejpam-846	195	22	,	,	PUNCT
ejpam-846	195	23	φ1u(x	φ1u(x	PROPN
ejpam-846	195	24	)	)	PUNCT
ejpam-846	195	25	≥	≥	NOUN
ejpam-846	195	26	φ1(x	φ1(x	NOUN
ejpam-846	195	27	)	)	PUNCT
ejpam-846	195	28	=	=	PUNCT
ejpam-846	195	29	ϕ(x	ϕ(x	NOUN
ejpam-846	195	30	,	,	PUNCT
ejpam-846	195	31	ξ̄	ξ̄	ADJ
ejpam-846	195	32	)	)	PUNCT
ejpam-846	195	33	,	,	PUNCT
ejpam-846	195	34	which	which	PRON
ejpam-846	195	35	completes	complete	VERB
ejpam-846	195	36	the	the	DET
ejpam-846	195	37	proof	proof	NOUN
ejpam-846	195	38	.	.	PUNCT
ejpam-846	196	1	3	3	X
ejpam-846	196	2	.	.	NOUN
ejpam-846	196	3	second	second	ADJ
ejpam-846	196	4	moment	moment	NOUN
ejpam-846	196	5	approximation	approximation	NOUN
ejpam-846	196	6	while	while	SCONJ
ejpam-846	196	7	the	the	DET
ejpam-846	196	8	‘	'	PUNCT
ejpam-846	196	9	uncorrelated	uncorrelated	ADJ
ejpam-846	196	10	’	'	PUNCT
ejpam-846	196	11	knowledge	knowledge	NOUN
ejpam-846	196	12	does	do	AUX
ejpam-846	196	13	not	not	PART
ejpam-846	196	14	improve	improve	VERB
ejpam-846	196	15	the	the	DET
ejpam-846	196	16	first	first	ADJ
ejpam-846	196	17	moment	moment	NOUN
ejpam-846	196	18	lower	lower	ADV
ejpam-846	196	19	bound	bind	VERB
ejpam-846	196	20	,	,	PUNCT
ejpam-846	196	21	is	be	AUX
ejpam-846	196	22	it	it	PRON
ejpam-846	196	23	possible	possible	ADJ
ejpam-846	196	24	to	to	PART
ejpam-846	196	25	derive	derive	VERB
ejpam-846	196	26	an	an	DET
ejpam-846	196	27	improved	improve	VERB
ejpam-846	196	28	lower	lower	ADV
ejpam-846	196	29	bound	bind	VERB
ejpam-846	196	30	when	when	SCONJ
ejpam-846	196	31	all	all	DET
ejpam-846	196	32	variance	variance	NOUN
ejpam-846	196	33	-	-	PUNCT
ejpam-846	196	34	covariance	covariance	NOUN
ejpam-846	196	35	information	information	NOUN
ejpam-846	196	36	of	of	ADP
ejpam-846	196	37	ξ	ξ	PROPN
ejpam-846	196	38	is	be	AUX
ejpam-846	196	39	available	available	ADJ
ejpam-846	196	40	?	?	PUNCT
ejpam-846	197	1	under	under	ADP
ejpam-846	197	2	the	the	DET
ejpam-846	197	3	mean	mean	ADJ
ejpam-846	197	4	vector	vector	NOUN
ejpam-846	197	5	ξ̄	ξ̄	ADJ
ejpam-846	197	6	and	and	CCONJ
ejpam-846	197	7	the	the	DET
ejpam-846	197	8	covariance	covariance	NOUN
ejpam-846	197	9	σkl	σkl	ADJ
ejpam-846	197	10	between	between	ADP
ejpam-846	197	11	ξk	ξk	ADP
ejpam-846	197	12	and	and	CCONJ
ejpam-846	197	13	ξl	ξl	NOUN
ejpam-846	197	14	,	,	PUNCT
ejpam-846	197	15	for	for	ADP
ejpam-846	197	16	k	k	PROPN
ejpam-846	197	17	,	,	PUNCT
ejpam-846	197	18	l	l	NOUN
ejpam-846	197	19	=	=	SYM
ejpam-846	197	20	1	1	NUM
ejpam-846	197	21	,	,	PUNCT
ejpam-846	197	22	.	.	PUNCT
ejpam-846	197	23	.	.	PUNCT
ejpam-846	197	24	.	.	PUNCT
ejpam-846	198	1	,	,	PUNCT
ejpam-846	198	2	k	k	NOUN
ejpam-846	198	3	,	,	PUNCT
ejpam-846	198	4	a	a	DET
ejpam-846	198	5	tight	tight	ADV
ejpam-846	198	6	lower	lower	ADV
ejpam-846	198	7	bound	bind	VERB
ejpam-846	198	8	is	be	AUX
ejpam-846	198	9	determined	determine	VERB
ejpam-846	198	10	by	by	ADP
ejpam-846	198	11	solving	solve	VERB
ejpam-846	198	12	the	the	DET
ejpam-846	198	13	gmp	gmp	PROPN
ejpam-846	198	14	given	give	VERB
ejpam-846	198	15	by	by	ADP
ejpam-846	198	16	φ2(x	φ2(x	NUM
ejpam-846	199	1	)	)	PUNCT
ejpam-846	199	2	=	=	SYM
ejpam-846	199	3	inf	inf	PROPN
ejpam-846	199	4	p	p	NOUN
ejpam-846	199	5	{	{	PUNCT
ejpam-846	199	6	∫	∫	PROPN
ejpam-846	199	7	ξ	ξ	X
ejpam-846	199	8	ϕ(x	ϕ(x	PROPN
ejpam-846	199	9	,	,	PUNCT
ejpam-846	199	10	ξ)p	ξ)p	ADJ
ejpam-846	199	11	(	(	PUNCT
ejpam-846	199	12	dξ	dξ	PROPN
ejpam-846	199	13	)	)	PUNCT
ejpam-846	199	14	:	:	PUNCT
ejpam-846	200	1	p	p	X
ejpam-846	200	2	∈	∈	PROPN
ejpam-846	200	3	p̃	p̃	PROPN
ejpam-846	200	4	}	}	PUNCT
ejpam-846	200	5	,	,	PUNCT
ejpam-846	200	6	(	(	PUNCT
ejpam-846	200	7	18	18	NUM
ejpam-846	200	8	)	)	PUNCT
ejpam-846	200	9	where	where	SCONJ
ejpam-846	200	10	the	the	DET
ejpam-846	200	11	set	set	NOUN
ejpam-846	200	12	of	of	ADP
ejpam-846	200	13	probability	probability	NOUN
ejpam-846	200	14	measures	measure	NOUN
ejpam-846	200	15	p̃	p̃	PROPN
ejpam-846	200	16	is	be	AUX
ejpam-846	200	17	characterized	characterize	VERB
ejpam-846	200	18	by	by	ADP
ejpam-846	200	19	p̃	p̃	PROPN
ejpam-846	200	20	:	:	PUNCT
ejpam-846	200	21	=	=	X
ejpam-846	200	22	{	{	PUNCT
ejpam-846	200	23	p	p	X
ejpam-846	200	24	:	:	PUNCT
ejpam-846	200	25	∫	∫	PROPN
ejpam-846	200	26	ξ	ξ	X
ejpam-846	200	27	ξp	ξp	PROPN
ejpam-846	200	28	(	(	PUNCT
ejpam-846	200	29	dξ	dξ	PROPN
ejpam-846	200	30	)	)	PUNCT
ejpam-846	200	31	=	=	SYM
ejpam-846	201	1	ξ̄	ξ̄	ADJ
ejpam-846	201	2	,	,	PUNCT
ejpam-846	201	3	∫	∫	PROPN
ejpam-846	201	4	ξ	ξ	PROPN
ejpam-846	201	5	ξkξlp	ξkξlp	PROPN
ejpam-846	201	6	(	(	PUNCT
ejpam-846	201	7	dξ	dξ	PROPN
ejpam-846	201	8	)	)	PUNCT
ejpam-846	201	9	=	=	SYM
ejpam-846	201	10	mkl	mkl	PROPN
ejpam-846	201	11	,	,	PUNCT
ejpam-846	201	12	k	k	NOUN
ejpam-846	201	13	,	,	PUNCT
ejpam-846	201	14	l	l	NOUN
ejpam-846	201	15	=	=	SYM
ejpam-846	201	16	1	1	NUM
ejpam-846	201	17	,	,	PUNCT
ejpam-846	201	18	.	.	PUNCT
ejpam-846	201	19	.	.	PUNCT
ejpam-846	201	20	.	.	PUNCT
ejpam-846	202	1	,	,	PUNCT
ejpam-846	202	2	k	k	PROPN
ejpam-846	202	3	,	,	PUNCT
ejpam-846	202	4	k	k	PROPN
ejpam-846	202	5	≥	≥	PROPN
ejpam-846	202	6	l	l	NOUN
ejpam-846	202	7	}	}	PUNCT
ejpam-846	202	8	,	,	PUNCT
ejpam-846	202	9	(	(	PUNCT
ejpam-846	202	10	19	19	NUM
ejpam-846	202	11	)	)	PUNCT
ejpam-846	202	12	edirisinghe	edirisinghe	NOUN
ejpam-846	202	13	/	/	SYM
ejpam-846	202	14	eur	eur	PROPN
ejpam-846	202	15	.	.	PUNCT
ejpam-846	203	1	j.	j.	PROPN
ejpam-846	203	2	pure	pure	PROPN
ejpam-846	203	3	appl	appl	PROPN
ejpam-846	203	4	.	.	PROPN
ejpam-846	203	5	math	math	PROPN
ejpam-846	203	6	,	,	PUNCT
ejpam-846	203	7	3	3	NUM
ejpam-846	203	8	(	(	PUNCT
ejpam-846	203	9	2010	2010	NUM
ejpam-846	203	10	)	)	PUNCT
ejpam-846	203	11	,	,	PUNCT
ejpam-846	203	12	572	572	NUM
ejpam-846	203	13	-	-	SYM
ejpam-846	203	14	592	592	NUM
ejpam-846	203	15	579	579	NUM
ejpam-846	203	16	where	where	SCONJ
ejpam-846	203	17	mkl	mkl	PROPN
ejpam-846	203	18	=	=	SYM
ejpam-846	203	19	σkl	σkl	PROPN
ejpam-846	203	20	+	+	X
ejpam-846	203	21	ξ̄kξ̄l	ξ̄kξ̄l	NOUN
ejpam-846	203	22	.	.	PUNCT
ejpam-846	204	1	clearly	clearly	ADV
ejpam-846	204	2	,	,	PUNCT
ejpam-846	204	3	φ2(x	φ2(x	NOUN
ejpam-846	204	4	)	)	PUNCT
ejpam-846	204	5	≥	≥	NOUN
ejpam-846	204	6	ϕ(x	ϕ(x	NOUN
ejpam-846	204	7	,	,	PUNCT
ejpam-846	204	8	ξ̄	ξ̄	NOUN
ejpam-846	204	9	)	)	PUNCT
ejpam-846	204	10	with	with	ADP
ejpam-846	204	11	the	the	DET
ejpam-846	204	12	latter	latter	ADJ
ejpam-846	204	13	equality	equality	NOUN
ejpam-846	204	14	surely	surely	ADV
ejpam-846	204	15	being	be	AUX
ejpam-846	204	16	held	hold	VERB
ejpam-846	204	17	when	when	SCONJ
ejpam-846	204	18	σkl	σkl	ADJ
ejpam-846	204	19	=	=	NOUN
ejpam-846	204	20	0	0	NUM
ejpam-846	204	21	for	for	ADP
ejpam-846	204	22	k	k	PROPN
ejpam-846	204	23	̸=	̸=	PROPN
ejpam-846	204	24	l	l	NOUN
ejpam-846	204	25	,	,	PUNCT
ejpam-846	204	26	see	see	VERB
ejpam-846	204	27	proposition	proposition	NOUN
ejpam-846	204	28	6	6	NUM
ejpam-846	204	29	.	.	PUNCT
ejpam-846	205	1	the	the	DET
ejpam-846	205	2	semi	semi	ADJ
ejpam-846	205	3	-	-	ADJ
ejpam-846	205	4	infinite	infinite	ADJ
ejpam-846	205	5	dual	dual	ADJ
ejpam-846	205	6	of	of	ADP
ejpam-846	205	7	(	(	PUNCT
ejpam-846	205	8	18	18	NUM
ejpam-846	205	9	)	)	PUNCT
ejpam-846	205	10	is	be	AUX
ejpam-846	205	11	given	give	VERB
ejpam-846	205	12	by	by	ADP
ejpam-846	205	13	φ2(x	φ2(x	NUM
ejpam-846	205	14	)	)	PUNCT
ejpam-846	205	15	=	=	SYM
ejpam-846	206	1	sup	sup	NOUN
ejpam-846	206	2	π∈π	π∈π	ADV
ejpam-846	206	3	π0	π0	PROPN
ejpam-846	207	1	+	+	CCONJ
ejpam-846	208	1	π1ξ̄	π1ξ̄	PUNCT
ejpam-846	208	2	+	+	CCONJ
ejpam-846	209	1	k∑	k∑	PROPN
ejpam-846	209	2	k	k	PROPN
ejpam-846	209	3	,	,	PUNCT
ejpam-846	209	4	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	209	5	mklπkl	mklπkl	ADJ
ejpam-846	209	6			PROPN
ejpam-846	209	7	(	(	PUNCT
ejpam-846	209	8	20	20	NUM
ejpam-846	209	9	)	)	PUNCT
ejpam-846	210	1	where	where	SCONJ
ejpam-846	210	2	the	the	DET
ejpam-846	210	3	dual	dual	ADJ
ejpam-846	210	4	feasible	feasible	ADJ
ejpam-846	210	5	set	set	NOUN
ejpam-846	210	6	π	π	NOUN
ejpam-846	210	7	:	:	PUNCT
ejpam-846	210	8	=	=	SYM
ejpam-846	210	9	π	π	ADJ
ejpam-846	210	10	:	:	PUNCT
ejpam-846	210	11	π0	π0	NOUN
ejpam-846	210	12	+	+	PUNCT
ejpam-846	210	13	π1ξ	π1ξ	PUNCT
ejpam-846	210	14	+	+	CCONJ
ejpam-846	210	15	k∑	k∑	VERB
ejpam-846	210	16	k	k	NOUN
ejpam-846	210	17	,	,	PUNCT
ejpam-846	210	18	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	210	19	ξkξlπkl	ξkξlπkl	VERB
ejpam-846	210	20	≤	≤	PUNCT
ejpam-846	210	21	ϕ(x	ϕ(x	PROPN
ejpam-846	210	22	,	,	PUNCT
ejpam-846	210	23	ξ	ξ	NOUN
ejpam-846	210	24	)	)	PUNCT
ejpam-846	210	25	,	,	PUNCT
ejpam-846	210	26	ξ	ξ	PROPN
ejpam-846	210	27	∈	∈	NOUN
ejpam-846	210	28	ξ	ξ	X
ejpam-846	210	29			NOUN
ejpam-846	210	30	,	,	PUNCT
ejpam-846	210	31	(	(	PUNCT
ejpam-846	210	32	21	21	NUM
ejpam-846	210	33	)	)	PUNCT
ejpam-846	210	34	provided	provide	VERB
ejpam-846	210	35	either	either	CCONJ
ejpam-846	210	36	ξ	ξ	PROPN
ejpam-846	210	37	is	be	AUX
ejpam-846	210	38	compact	compact	ADJ
ejpam-846	210	39	or	or	CCONJ
ejpam-846	210	40	(	(	PUNCT
ejpam-846	210	41	ξ̄1	ξ̄1	NUM
ejpam-846	210	42	,	,	PUNCT
ejpam-846	210	43	.	.	PUNCT
ejpam-846	210	44	.	.	PUNCT
ejpam-846	210	45	.	.	PUNCT
ejpam-846	211	1	,	,	PUNCT
ejpam-846	211	2	ξ̄k	ξ̄k	NOUN
ejpam-846	211	3	,	,	PUNCT
ejpam-846	211	4	m11	m11	NOUN
ejpam-846	211	5	,	,	PUNCT
ejpam-846	211	6	.	.	PUNCT
ejpam-846	211	7	.	.	PUNCT
ejpam-846	211	8	.	.	PUNCT
ejpam-846	212	1	,	,	PUNCT
ejpam-846	212	2	m1k	m1k	PROPN
ejpam-846	212	3	,	,	PUNCT
ejpam-846	212	4	m22	m22	PROPN
ejpam-846	212	5	,	,	PUNCT
ejpam-846	212	6	.	.	PUNCT
ejpam-846	212	7	.	.	PUNCT
ejpam-846	212	8	.	.	PUNCT
ejpam-846	213	1	,	,	PUNCT
ejpam-846	213	2	m2k	m2k	PROPN
ejpam-846	213	3	,	,	PUNCT
ejpam-846	213	4	.	.	PUNCT
ejpam-846	213	5	.	.	PUNCT
ejpam-846	213	6	.	.	PUNCT
ejpam-846	214	1	,	,	PUNCT
ejpam-846	214	2	mk−1,k	mk−1,k	PROPN
ejpam-846	214	3	,	,	PUNCT
ejpam-846	214	4	mkk	mkk	PROPN
ejpam-846	214	5	)	)	PUNCT
ejpam-846	214	6	∈	∈	PROPN
ejpam-846	214	7	int	int	NOUN
ejpam-846	214	8	co	co	X
ejpam-846	214	9	{	{	PUNCT
ejpam-846	214	10	ξ1	ξ1	PROPN
ejpam-846	214	11	,	,	PUNCT
ejpam-846	214	12	.	.	PUNCT
ejpam-846	214	13	.	.	PUNCT
ejpam-846	215	1	.	.	PUNCT
ejpam-846	216	1	,	,	PUNCT
ejpam-846	216	2	ξk	ξk	ADP
ejpam-846	216	3	,	,	PUNCT
ejpam-846	216	4	(	(	PUNCT
ejpam-846	216	5	ξ1	ξ1	NOUN
ejpam-846	216	6	)	)	PUNCT
ejpam-846	216	7	2	2	NUM
ejpam-846	216	8	,	,	PUNCT
ejpam-846	216	9	.	.	PUNCT
ejpam-846	216	10	.	.	PUNCT
ejpam-846	216	11	.	.	PUNCT
ejpam-846	217	1	,	,	PUNCT
ejpam-846	217	2	ξ1k	ξ1k	NOUN
ejpam-846	217	3	,	,	PUNCT
ejpam-846	217	4	(	(	PUNCT
ejpam-846	217	5	ξ2	ξ2	NOUN
ejpam-846	217	6	)	)	PUNCT
ejpam-846	217	7	2	2	NUM
ejpam-846	217	8	,	,	PUNCT
ejpam-846	217	9	.	.	PUNCT
ejpam-846	217	10	.	.	PUNCT
ejpam-846	218	1	.	.	PUNCT
ejpam-846	219	1	,	,	PUNCT
ejpam-846	219	2	ξ2ξk	ξ2ξk	PROPN
ejpam-846	219	3	,	,	PUNCT
ejpam-846	219	4	.	.	PUNCT
ejpam-846	219	5	.	.	PUNCT
ejpam-846	219	6	.	.	PUNCT
ejpam-846	220	1	,	,	PUNCT
ejpam-846	220	2	ξk−1ξk	ξk−1ξk	PROPN
ejpam-846	220	3	,	,	PUNCT
ejpam-846	220	4	(	(	PUNCT
ejpam-846	220	5	ξk	ξk	ADP
ejpam-846	220	6	)	)	PUNCT
ejpam-846	220	7	2	2	NUM
ejpam-846	220	8	:	:	PUNCT
ejpam-846	221	1	ξ	ξ	X
ejpam-846	221	2	∈	∈	PROPN
ejpam-846	221	3	ξ	ξ	X
ejpam-846	221	4	}	}	PUNCT
ejpam-846	221	5	.(22	.(22	PUNCT
ejpam-846	221	6	)	)	PUNCT
ejpam-846	221	7	observe	observe	VERB
ejpam-846	221	8	that	that	SCONJ
ejpam-846	221	9	when	when	SCONJ
ejpam-846	221	10	k	k	PROPN
ejpam-846	221	11	=	=	SYM
ejpam-846	221	12	1	1	NUM
ejpam-846	221	13	and	and	CCONJ
ejpam-846	221	14	ξ	ξ	X
ejpam-846	221	15	=	=	PUNCT
ejpam-846	221	16	(	(	PUNCT
ejpam-846	221	17	−∞,+∞	−∞,+∞	NUM
ejpam-846	221	18	)	)	PUNCT
ejpam-846	221	19	,	,	PUNCT
ejpam-846	221	20	the	the	DET
ejpam-846	221	21	interior	interior	ADJ
ejpam-846	221	22	condition	condition	NOUN
ejpam-846	221	23	in	in	ADP
ejpam-846	221	24	(	(	PUNCT
ejpam-846	221	25	22	22	NUM
ejpam-846	221	26	)	)	PUNCT
ejpam-846	221	27	is	be	AUX
ejpam-846	221	28	certainly	certainly	ADV
ejpam-846	221	29	satisfied	satisfied	ADJ
ejpam-846	221	30	when	when	SCONJ
ejpam-846	221	31	e[(ξ1	e[(ξ1	NOUN
ejpam-846	221	32	)	)	PUNCT
ejpam-846	221	33	2	2	NUM
ejpam-846	221	34	]	]	PUNCT
ejpam-846	221	35	>	>	X
ejpam-846	221	36	(	(	PUNCT
ejpam-846	221	37	ξ̄)2	ξ̄)2	NOUN
ejpam-846	221	38	,	,	PUNCT
ejpam-846	221	39	i.e.	i.e.	X
ejpam-846	221	40	,	,	PUNCT
ejpam-846	221	41	p	p	PRON
ejpam-846	221	42	tr	tr	VERB
ejpam-846	221	43	is	be	AUX
ejpam-846	221	44	a	a	DET
ejpam-846	221	45	nondegenerate	nondegenerate	ADJ
ejpam-846	221	46	distribution	distribution	NOUN
ejpam-846	221	47	.	.	PUNCT
ejpam-846	222	1	however	however	ADV
ejpam-846	222	2	,	,	PUNCT
ejpam-846	222	3	we	we	PRON
ejpam-846	222	4	shall	shall	AUX
ejpam-846	222	5	assume	assume	VERB
ejpam-846	222	6	for	for	ADP
ejpam-846	222	7	(	(	PUNCT
ejpam-846	222	8	18	18	NUM
ejpam-846	222	9	)	)	PUNCT
ejpam-846	222	10	that	that	SCONJ
ejpam-846	222	11	ξ	ξ	PROPN
ejpam-846	222	12	is	be	AUX
ejpam-846	222	13	compact	compact	ADJ
ejpam-846	222	14	,	,	PUNCT
ejpam-846	222	15	as	as	SCONJ
ejpam-846	222	16	is	be	AUX
ejpam-846	222	17	followed	follow	VERB
ejpam-846	222	18	in	in	ADP
ejpam-846	222	19	the	the	DET
ejpam-846	222	20	remainder	remainder	NOUN
ejpam-846	222	21	of	of	ADP
ejpam-846	222	22	the	the	DET
ejpam-846	222	23	paper	paper	NOUN
ejpam-846	222	24	.	.	PUNCT
ejpam-846	223	1	solution	solution	NOUN
ejpam-846	223	2	of	of	ADP
ejpam-846	223	3	(	(	PUNCT
ejpam-846	223	4	18	18	NUM
ejpam-846	223	5	)	)	PUNCT
ejpam-846	223	6	or	or	CCONJ
ejpam-846	223	7	(	(	PUNCT
ejpam-846	223	8	20	20	NUM
ejpam-846	223	9	)	)	PUNCT
ejpam-846	223	10	remains	remain	VERB
ejpam-846	223	11	an	an	DET
ejpam-846	223	12	open	open	ADJ
ejpam-846	223	13	research	research	NOUN
ejpam-846	223	14	problem	problem	NOUN
ejpam-846	223	15	.	.	PUNCT
ejpam-846	224	1	the	the	DET
ejpam-846	224	2	difficulty	difficulty	NOUN
ejpam-846	224	3	lies	lie	VERB
ejpam-846	224	4	in	in	ADP
ejpam-846	224	5	that	that	PRON
ejpam-846	224	6	a	a	DET
ejpam-846	224	7	lower	lower	ADV
ejpam-846	224	8	bounding	bound	VERB
ejpam-846	224	9	quadratic	quadratic	ADJ
ejpam-846	224	10	function	function	NOUN
ejpam-846	224	11	on	on	ADP
ejpam-846	224	12	ϕ(x	ϕ(x	PROPN
ejpam-846	224	13	,	,	PUNCT
ejpam-846	224	14	.	.	PUNCT
ejpam-846	224	15	)	)	PUNCT
ejpam-846	225	1	over	over	ADP
ejpam-846	225	2	ξ	ξ	PROPN
ejpam-846	225	3	must	must	AUX
ejpam-846	225	4	be	be	AUX
ejpam-846	225	5	determined	determine	VERB
ejpam-846	225	6	toward	toward	ADP
ejpam-846	225	7	solving	solve	VERB
ejpam-846	225	8	(	(	PUNCT
ejpam-846	225	9	20	20	NUM
ejpam-846	225	10	)	)	PUNCT
ejpam-846	225	11	,	,	PUNCT
ejpam-846	225	12	which	which	PRON
ejpam-846	225	13	is	be	AUX
ejpam-846	225	14	an	an	DET
ejpam-846	225	15	onerous	onerous	ADJ
ejpam-846	225	16	task	task	NOUN
ejpam-846	225	17	for	for	ADP
ejpam-846	225	18	general	general	ADJ
ejpam-846	225	19	convex	convex	NOUN
ejpam-846	225	20	functions	function	NOUN
ejpam-846	225	21	ϕ	ϕ	NOUN
ejpam-846	225	22	and	and	CCONJ
ejpam-846	225	23	arbitrary	arbitrary	ADJ
ejpam-846	225	24	convex	convex	NOUN
ejpam-846	225	25	sets	set	VERB
ejpam-846	225	26	ξ	ξ	PROPN
ejpam-846	225	27	.	.	PUNCT
ejpam-846	226	1	under	under	ADP
ejpam-846	226	2	compact	compact	ADJ
ejpam-846	226	3	domains	domain	NOUN
ejpam-846	226	4	,	,	PUNCT
ejpam-846	226	5	let	let	VERB
ejpam-846	226	6	ξ	ξ	X
ejpam-846	226	7	be	be	AUX
ejpam-846	226	8	a	a	DET
ejpam-846	226	9	k	k	ADJ
ejpam-846	226	10	-	-	ADJ
ejpam-846	226	11	dimensional	dimensional	ADJ
ejpam-846	226	12	simplex	simplex	NOUN
ejpam-846	226	13	(	(	PUNCT
ejpam-846	226	14	if	if	SCONJ
ejpam-846	226	15	not	not	PART
ejpam-846	226	16	,	,	PUNCT
ejpam-846	226	17	the	the	DET
ejpam-846	226	18	domain	domain	NOUN
ejpam-846	226	19	can	can	AUX
ejpam-846	226	20	be	be	AUX
ejpam-846	226	21	embedded	embed	VERB
ejpam-846	226	22	in	in	ADP
ejpam-846	226	23	a	a	DET
ejpam-846	226	24	simplex	simplex	NOUN
ejpam-846	226	25	)	)	PUNCT
ejpam-846	226	26	.	.	PUNCT
ejpam-846	227	1	the	the	DET
ejpam-846	227	2	focus	focus	NOUN
ejpam-846	227	3	here	here	ADV
ejpam-846	227	4	is	be	AUX
ejpam-846	227	5	to	to	PART
ejpam-846	227	6	develop	develop	VERB
ejpam-846	227	7	bounds	bound	NOUN
ejpam-846	227	8	on	on	ADP
ejpam-846	227	9	φ2(x	φ2(x	NUM
ejpam-846	227	10	)	)	PUNCT
ejpam-846	227	11	using	use	VERB
ejpam-846	227	12	a	a	DET
ejpam-846	227	13	lower	low	ADJ
ejpam-846	227	14	bounding	bounding	NOUN
ejpam-846	227	15	polyhedral	polyhedral	ADJ
ejpam-846	227	16	function	function	NOUN
ejpam-846	227	17	on	on	ADP
ejpam-846	227	18	ϕ(x	ϕ(x	PROPN
ejpam-846	227	19	,	,	PUNCT
ejpam-846	227	20	ξ	ξ	NOUN
ejpam-846	227	21	)	)	PUNCT
ejpam-846	227	22	.	.	PUNCT
ejpam-846	228	1	toward	toward	ADP
ejpam-846	228	2	this	this	PRON
ejpam-846	228	3	,	,	PUNCT
ejpam-846	228	4	let	let	VERB
ejpam-846	228	5	the	the	DET
ejpam-846	228	6	vertices	vertex	NOUN
ejpam-846	228	7	of	of	ADP
ejpam-846	228	8	the	the	DET
ejpam-846	228	9	simplex	simplex	NOUN
ejpam-846	228	10	ξ	ξ	PROPN
ejpam-846	228	11	be	be	AUX
ejpam-846	228	12	denoted	denote	VERB
ejpam-846	228	13	by	by	ADP
ejpam-846	228	14	ui	ui	PROPN
ejpam-846	228	15	∈	∈	PROPN
ejpam-846	229	1	ℜk	ℜk	PROPN
ejpam-846	229	2	,	,	PUNCT
ejpam-846	229	3	i	i	PRON
ejpam-846	229	4	=	=	NOUN
ejpam-846	229	5	1	1	NUM
ejpam-846	229	6	,	,	PUNCT
ejpam-846	229	7	.	.	PUNCT
ejpam-846	229	8	.	.	PUNCT
ejpam-846	229	9	.	.	PUNCT
ejpam-846	230	1	,	,	PUNCT
ejpam-846	230	2	k	k	PROPN
ejpam-846	230	3	+	+	PROPN
ejpam-846	230	4	1	1	NUM
ejpam-846	230	5	,	,	PUNCT
ejpam-846	230	6	and	and	CCONJ
ejpam-846	230	7	define	define	VERB
ejpam-846	230	8	the	the	DET
ejpam-846	230	9	inverse	inverse	NOUN
ejpam-846	230	10	of	of	ADP
ejpam-846	230	11	the	the	DET
ejpam-846	230	12	vertex	vertex	NOUN
ejpam-846	230	13	matrix	matrix	NOUN
ejpam-846	230	14	by	by	ADP
ejpam-846	230	15	v	v	NOUN
ejpam-846	230	16	:	:	PUNCT
ejpam-846	230	17	=	=	SYM
ejpam-846	230	18			NOUN
ejpam-846	230	19	u11	u11	X
ejpam-846	230	20	·	·	PUNCT
ejpam-846	230	21	·	·	PUNCT
ejpam-846	230	22	·	·	PUNCT
ejpam-846	230	23	·	·	PUNCT
ejpam-846	230	24	·	·	PUNCT
ejpam-846	231	1	·	·	PUNCT
ejpam-846	231	2	uk+1	uk+1	X
ejpam-846	231	3	1	1	NUM
ejpam-846	231	4	...	...	PUNCT
ejpam-846	231	5	...	...	PUNCT
ejpam-846	231	6	...	...	PUNCT
ejpam-846	231	7	...	...	PUNCT
ejpam-846	232	1	u1k	u1k	PROPN
ejpam-846	232	2	·	·	PUNCT
ejpam-846	232	3	·	·	PUNCT
ejpam-846	232	4	·	·	PUNCT
ejpam-846	232	5	·	·	PUNCT
ejpam-846	232	6	·	·	PUNCT
ejpam-846	232	7	·	·	PUNCT
ejpam-846	232	8	uk+1	uk+1	PUNCT
ejpam-846	232	9	k	k	PROPN
ejpam-846	232	10	1	1	NUM
ejpam-846	232	11	·	·	PUNCT
ejpam-846	232	12	·	·	PUNCT
ejpam-846	232	13	·	·	PUNCT
ejpam-846	232	14	·	·	PUNCT
ejpam-846	232	15	·	·	PUNCT
ejpam-846	232	16	·	·	PUNCT
ejpam-846	232	17	1	1	NUM
ejpam-846	232	18			NUM
ejpam-846	232	19	−1	−1	NOUN
ejpam-846	232	20	(	(	PUNCT
ejpam-846	232	21	23	23	NUM
ejpam-846	232	22	)	)	PUNCT
ejpam-846	232	23	and	and	CCONJ
ejpam-846	232	24	its	its	PRON
ejpam-846	232	25	jth	jth	PROPN
ejpam-846	232	26	row	row	NOUN
ejpam-846	232	27	by	by	ADP
ejpam-846	232	28	vj	vj	PROPN
ejpam-846	232	29	≡	≡	PROPN
ejpam-846	232	30	(	(	PUNCT
ejpam-846	232	31	vj1	vj1	PROPN
ejpam-846	232	32	,	,	PUNCT
ejpam-846	232	33	.	.	PUNCT
ejpam-846	232	34	.	.	PUNCT
ejpam-846	232	35	.	.	PUNCT
ejpam-846	233	1	,	,	PUNCT
ejpam-846	233	2	v	v	X
ejpam-846	233	3	j	j	PROPN
ejpam-846	233	4	k	k	PROPN
ejpam-846	233	5	,	,	PUNCT
ejpam-846	233	6	v	v	PROPN
ejpam-846	233	7	j	j	PROPN
ejpam-846	233	8	k+1	k+1	NOUN
ejpam-846	233	9	)	)	PUNCT
ejpam-846	233	10	.	.	PUNCT
ejpam-846	234	1	it	it	PRON
ejpam-846	234	2	is	be	AUX
ejpam-846	234	3	straightforward	straightforward	ADJ
ejpam-846	234	4	to	to	PART
ejpam-846	234	5	show	show	VERB
ejpam-846	234	6	that	that	SCONJ
ejpam-846	234	7	:	:	PUNCT
ejpam-846	234	8	proposition	proposition	NOUN
ejpam-846	234	9	7	7	NUM
ejpam-846	234	10	.	.	PUNCT
ejpam-846	235	1	let	let	VERB
ejpam-846	235	2	the	the	DET
ejpam-846	235	3	linear	linear	ADJ
ejpam-846	235	4	(	(	PUNCT
ejpam-846	235	5	measurable	measurable	ADJ
ejpam-846	235	6	)	)	PUNCT
ejpam-846	235	7	function	function	NOUN
ejpam-846	235	8	λj(ξ	λj(ξ	PROPN
ejpam-846	235	9	)	)	PUNCT
ejpam-846	235	10	be	be	AUX
ejpam-846	235	11	defined	define	VERB
ejpam-846	235	12	by	by	ADP
ejpam-846	235	13	λj(ξ	λj(ξ	PROPN
ejpam-846	235	14	)	)	PUNCT
ejpam-846	236	1	:	:	PUNCT
ejpam-846	236	2	=	=	PUNCT
ejpam-846	236	3	vj1ξ1	vj1ξ1	PROPN
ejpam-846	236	4	+	+	NUM
ejpam-846	236	5	·	·	PUNCT
ejpam-846	236	6	·	·	PUNCT
ejpam-846	236	7	·	·	PUNCT
ejpam-846	236	8	+	+	NUM
ejpam-846	236	9	vjkξk	vjkξk	NOUN
ejpam-846	236	10	+	+	CCONJ
ejpam-846	236	11	vj	vj	PROPN
ejpam-846	236	12	k+1	k+1	X
ejpam-846	236	13	.	.	PROPN
ejpam-846	237	1	(	(	PUNCT
ejpam-846	237	2	24	24	NUM
ejpam-846	237	3	)	)	PUNCT
ejpam-846	237	4	then	then	ADV
ejpam-846	237	5	,	,	PUNCT
ejpam-846	237	6	ξ	ξ	PROPN
ejpam-846	237	7	∈	∈	PROPN
ejpam-846	237	8	ξ	ξ	X
ejpam-846	237	9	if	if	SCONJ
ejpam-846	237	10	and	and	CCONJ
ejpam-846	237	11	only	only	ADV
ejpam-846	237	12	if	if	SCONJ
ejpam-846	237	13	k+1∑	k+1∑	PROPN
ejpam-846	237	14	j=1	j=1	NOUN
ejpam-846	237	15	λj(ξ	λj(ξ	PUNCT
ejpam-846	237	16	)	)	PUNCT
ejpam-846	237	17	=	=	SYM
ejpam-846	237	18	1	1	NUM
ejpam-846	237	19	and	and	CCONJ
ejpam-846	237	20	λj(ξ	λj(ξ	NUM
ejpam-846	237	21	)	)	PUNCT
ejpam-846	237	22	≥	≥	NOUN
ejpam-846	237	23	0	0	NUM
ejpam-846	237	24	,	,	PUNCT
ejpam-846	237	25	j	j	PROPN
ejpam-846	237	26	=	=	SYM
ejpam-846	237	27	1	1	NUM
ejpam-846	237	28	,	,	PUNCT
ejpam-846	237	29	.	.	PUNCT
ejpam-846	237	30	.	.	PUNCT
ejpam-846	238	1	.	.	PUNCT
ejpam-846	239	1	,	,	PUNCT
ejpam-846	239	2	k	k	PROPN
ejpam-846	240	1	+	+	PROPN
ejpam-846	240	2	1	1	X
ejpam-846	240	3	.	.	PUNCT
ejpam-846	240	4	(	(	PUNCT
ejpam-846	240	5	25	25	NUM
ejpam-846	240	6	)	)	PUNCT
ejpam-846	240	7	edirisinghe	edirisinghe	PROPN
ejpam-846	240	8	/	/	SYM
ejpam-846	240	9	eur	eur	PROPN
ejpam-846	240	10	.	.	PUNCT
ejpam-846	241	1	j.	j.	PROPN
ejpam-846	241	2	pure	pure	PROPN
ejpam-846	241	3	appl	appl	PROPN
ejpam-846	241	4	.	.	PROPN
ejpam-846	241	5	math	math	PROPN
ejpam-846	241	6	,	,	PUNCT
ejpam-846	241	7	3	3	NUM
ejpam-846	241	8	(	(	PUNCT
ejpam-846	241	9	2010	2010	NUM
ejpam-846	241	10	)	)	PUNCT
ejpam-846	241	11	,	,	PUNCT
ejpam-846	241	12	572	572	NUM
ejpam-846	241	13	-	-	SYM
ejpam-846	241	14	592	592	NUM
ejpam-846	241	15	580	580	NUM
ejpam-846	241	16	consider	consider	VERB
ejpam-846	241	17	the	the	DET
ejpam-846	241	18	following	follow	VERB
ejpam-846	241	19	construction	construction	NOUN
ejpam-846	241	20	.	.	PUNCT
ejpam-846	242	1	multiply	multiply	VERB
ejpam-846	242	2	the	the	DET
ejpam-846	242	3	constraints	constraint	NOUN
ejpam-846	242	4	of	of	ADP
ejpam-846	242	5	(	(	PUNCT
ejpam-846	242	6	21	21	NUM
ejpam-846	242	7	)	)	PUNCT
ejpam-846	242	8	by	by	ADP
ejpam-846	242	9	nonnegative	nonnegative	ADJ
ejpam-846	242	10	λi(ξ	λi(ξ	NOUN
ejpam-846	242	11	)	)	PUNCT
ejpam-846	242	12	,	,	PUNCT
ejpam-846	242	13	for	for	ADP
ejpam-846	242	14	each	each	DET
ejpam-846	242	15	i	i	NOUN
ejpam-846	242	16	=	=	NOUN
ejpam-846	242	17	1	1	NUM
ejpam-846	242	18	,	,	PUNCT
ejpam-846	242	19	.	.	PUNCT
ejpam-846	242	20	.	.	PUNCT
ejpam-846	243	1	.	.	PUNCT
ejpam-846	244	1	,	,	PUNCT
ejpam-846	244	2	k	k	PROPN
ejpam-846	245	1	+	+	PROPN
ejpam-846	245	2	1	1	NUM
ejpam-846	245	3	,	,	PUNCT
ejpam-846	245	4	which	which	PRON
ejpam-846	245	5	yields	yield	VERB
ejpam-846	245	6	λi(ξ)π0+π1[λi(ξ)ξ]+	λi(ξ)π0+π1[λi(ξ)ξ]+	X
ejpam-846	245	7	k∑	k∑	PROPN
ejpam-846	245	8	k	k	NOUN
ejpam-846	245	9	,	,	PUNCT
ejpam-846	245	10	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	245	11	[	[	X
ejpam-846	245	12	λi(ξ)ξkξl]πkl	λi(ξ)ξkξl]πkl	X
ejpam-846	245	13	≤	≤	NUM
ejpam-846	245	14	λi(ξ)ϕ(x	λi(ξ)ϕ(x	PROPN
ejpam-846	245	15	,	,	PUNCT
ejpam-846	245	16	ξ	ξ	PROPN
ejpam-846	245	17	)	)	PUNCT
ejpam-846	245	18	,	,	PUNCT
ejpam-846	245	19	∀ξ	∀ξ	X
ejpam-846	245	20	∈	∈	PROPN
ejpam-846	245	21	ξ	ξ	NOUN
ejpam-846	245	22	,	,	PUNCT
ejpam-846	245	23	i	i	PRON
ejpam-846	245	24	=	=	NOUN
ejpam-846	245	25	1	1	NUM
ejpam-846	245	26	,	,	PUNCT
ejpam-846	245	27	.	.	PUNCT
ejpam-846	245	28	.	.	PUNCT
ejpam-846	246	1	.	.	PUNCT
ejpam-846	247	1	,	,	PUNCT
ejpam-846	247	2	k+1	k+1	X
ejpam-846	247	3	.	.	PROPN
ejpam-846	247	4	(	(	PUNCT
ejpam-846	247	5	26	26	NUM
ejpam-846	247	6	)	)	PUNCT
ejpam-846	247	7	upon	upon	SCONJ
ejpam-846	247	8	taking	take	VERB
ejpam-846	247	9	the	the	DET
ejpam-846	247	10	expectation	expectation	NOUN
ejpam-846	247	11	of	of	ADP
ejpam-846	247	12	(	(	PUNCT
ejpam-846	247	13	26	26	NUM
ejpam-846	247	14	)	)	PUNCT
ejpam-846	247	15	with	with	ADP
ejpam-846	247	16	respect	respect	NOUN
ejpam-846	247	17	to	to	ADP
ejpam-846	247	18	any	any	DET
ejpam-846	247	19	probability	probability	NOUN
ejpam-846	247	20	measure	measure	NOUN
ejpam-846	247	21	p	p	X
ejpam-846	247	22	∈	∈	PROPN
ejpam-846	247	23	p̃	p̃	PROPN
ejpam-846	247	24	,	,	PUNCT
ejpam-846	247	25	ep	ep	PROPN
ejpam-846	248	1	[	[	X
ejpam-846	248	2	λi(ξ)]π0	λi(ξ)]π0	X
ejpam-846	248	3	+	+	CCONJ
ejpam-846	248	4	π1ep	π1ep	PUNCT
ejpam-846	248	5	[	[	X
ejpam-846	248	6	λi(ξ)ξ	λi(ξ)ξ	X
ejpam-846	248	7	]	]	X
ejpam-846	248	8	+	+	CCONJ
ejpam-846	248	9	k∑	k∑	VERB
ejpam-846	248	10	k	k	PROPN
ejpam-846	248	11	,	,	PUNCT
ejpam-846	248	12	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	248	13	ep	ep	PROPN
ejpam-846	248	14	[	[	X
ejpam-846	248	15	λi(ξ)ξkξl]πkl	λi(ξ)ξkξl]πkl	X
ejpam-846	248	16	≤	≤	ADJ
ejpam-846	248	17	ep	ep	PROPN
ejpam-846	248	18	[	[	X
ejpam-846	248	19	λi(ξ)ϕ(x	λi(ξ)ϕ(x	PROPN
ejpam-846	248	20	,	,	PUNCT
ejpam-846	248	21	ξ	ξ	PROPN
ejpam-846	248	22	)	)	PUNCT
ejpam-846	248	23	]	]	X
ejpam-846	248	24	(	(	PUNCT
ejpam-846	248	25	27	27	NUM
ejpam-846	248	26	)	)	PUNCT
ejpam-846	248	27	holds	hold	VERB
ejpam-846	248	28	for	for	ADP
ejpam-846	248	29	i	i	PRON
ejpam-846	248	30	=	=	NOUN
ejpam-846	248	31	1	1	NUM
ejpam-846	248	32	,	,	PUNCT
ejpam-846	248	33	.	.	PUNCT
ejpam-846	248	34	.	.	PUNCT
ejpam-846	249	1	.	.	PUNCT
ejpam-846	250	1	,	,	PUNCT
ejpam-846	251	1	k	k	PROPN
ejpam-846	251	2	+	+	NOUN
ejpam-846	251	3	1	1	X
ejpam-846	251	4	.	.	PUNCT
ejpam-846	251	5	summing	sum	VERB
ejpam-846	251	6	the	the	DET
ejpam-846	251	7	latter	latter	ADJ
ejpam-846	251	8	inequalities	inequality	NOUN
ejpam-846	251	9	over	over	ADP
ejpam-846	251	10	all	all	DET
ejpam-846	251	11	i	i	PRON
ejpam-846	251	12	,	,	PUNCT
ejpam-846	251	13	thus	thus	ADV
ejpam-846	251	14	,	,	PUNCT
ejpam-846	251	15	every	every	DET
ejpam-846	251	16	feasible	feasible	ADJ
ejpam-846	251	17	solution	solution	NOUN
ejpam-846	251	18	π	π	X
ejpam-846	251	19	∈	∈	PROPN
ejpam-846	251	20	π	π	NOUN
ejpam-846	251	21	must	must	AUX
ejpam-846	251	22	satisfy	satisfy	VERB
ejpam-846	251	23	π0	π0	NOUN
ejpam-846	251	24	+	+	CCONJ
ejpam-846	251	25	π1	π1	ADJ
ejpam-846	251	26	k+1∑	k+1∑	PROPN
ejpam-846	251	27	i=1	i=1	PROPN
ejpam-846	251	28	ti	ti	PROPN
ejpam-846	251	29	+	+	CCONJ
ejpam-846	251	30	k∑	k∑	PROPN
ejpam-846	252	1	k	k	PROPN
ejpam-846	252	2	,	,	PUNCT
ejpam-846	252	3	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	252	4	(	(	PUNCT
ejpam-846	252	5	k+1∑	k+1∑	PROPN
ejpam-846	252	6	i=1	i=1	PROPN
ejpam-846	252	7	rikl	rikl	PROPN
ejpam-846	252	8	)	)	PUNCT
ejpam-846	253	1	πkl	πkl	CCONJ
ejpam-846	253	2	≤	≤	NUM
ejpam-846	254	1	k+1∑	k+1∑	PROPN
ejpam-846	255	1	i=1	i=1	PROPN
ejpam-846	256	1	ep	ep	PROPN
ejpam-846	257	1	[	[	X
ejpam-846	257	2	λi(ξ)ϕ(x	λi(ξ)ϕ(x	PROPN
ejpam-846	257	3	,	,	PUNCT
ejpam-846	257	4	ξ	ξ	PROPN
ejpam-846	257	5	)	)	PUNCT
ejpam-846	257	6	]	]	PUNCT
ejpam-846	257	7	,	,	PUNCT
ejpam-846	257	8	(	(	PUNCT
ejpam-846	257	9	28	28	NUM
ejpam-846	257	10	)	)	PUNCT
ejpam-846	257	11	since	since	SCONJ
ejpam-846	257	12	∑k+1	∑k+1	PUNCT
ejpam-846	257	13	i=1	i=1	PROPN
ejpam-846	257	14	ep	ep	PROPN
ejpam-846	258	1	[	[	X
ejpam-846	258	2	λi(ξ	λi(ξ	X
ejpam-846	258	3	)	)	PUNCT
ejpam-846	258	4	]	]	PUNCT
ejpam-846	259	1	=	=	PUNCT
ejpam-846	259	2	1	1	NUM
ejpam-846	259	3	and	and	CCONJ
ejpam-846	259	4	by	by	ADP
ejpam-846	259	5	defining	define	VERB
ejpam-846	259	6	tik	tik	NOUN
ejpam-846	259	7	:	:	PUNCT
ejpam-846	259	8	=	=	SYM
ejpam-846	259	9	ep	ep	PROPN
ejpam-846	260	1	[	[	X
ejpam-846	260	2	λi(ξ)ξk	λi(ξ)ξk	X
ejpam-846	260	3	]	]	X
ejpam-846	260	4	,	,	PUNCT
ejpam-846	260	5	k	k	PROPN
ejpam-846	260	6	=	=	SYM
ejpam-846	260	7	1	1	NUM
ejpam-846	260	8	,	,	PUNCT
ejpam-846	260	9	.	.	PUNCT
ejpam-846	260	10	.	.	PUNCT
ejpam-846	260	11	.	.	PUNCT
ejpam-846	261	1	,	,	PUNCT
ejpam-846	261	2	k	k	X
ejpam-846	261	3	(	(	PUNCT
ejpam-846	261	4	29	29	NUM
ejpam-846	261	5	)	)	PUNCT
ejpam-846	261	6	rikl	rikl	NOUN
ejpam-846	261	7	:	:	PUNCT
ejpam-846	261	8	=	=	SYM
ejpam-846	261	9	ep	ep	PROPN
ejpam-846	262	1	[	[	X
ejpam-846	262	2	λi(ξ)ξkξl	λi(ξ)ξkξl	NOUN
ejpam-846	262	3	]	]	X
ejpam-846	262	4	,	,	PUNCT
ejpam-846	262	5	k	k	X
ejpam-846	262	6	=	=	SYM
ejpam-846	262	7	1	1	NUM
ejpam-846	262	8	,	,	PUNCT
ejpam-846	262	9	.	.	PUNCT
ejpam-846	262	10	.	.	PUNCT
ejpam-846	262	11	.	.	PUNCT
ejpam-846	263	1	,	,	PUNCT
ejpam-846	263	2	k	k	NOUN
ejpam-846	263	3	,	,	PUNCT
ejpam-846	263	4	l	l	NOUN
ejpam-846	263	5	=	=	SYM
ejpam-846	263	6	k	k	NOUN
ejpam-846	263	7	,	,	PUNCT
ejpam-846	263	8	.	.	PUNCT
ejpam-846	263	9	.	.	PUNCT
ejpam-846	263	10	.	.	PUNCT
ejpam-846	264	1	,	,	PUNCT
ejpam-846	264	2	k.	k.	PROPN
ejpam-846	264	3	(	(	PUNCT
ejpam-846	264	4	30	30	X
ejpam-846	264	5	)	)	PUNCT
ejpam-846	264	6	note	note	VERB
ejpam-846	264	7	that	that	SCONJ
ejpam-846	264	8	for	for	ADP
ejpam-846	264	9	any	any	DET
ejpam-846	264	10	p	p	PROPN
ejpam-846	264	11	∈	∈	PROPN
ejpam-846	264	12	p̃	p̃	PROPN
ejpam-846	264	13	,	,	PUNCT
ejpam-846	264	14	tik	tik	PROPN
ejpam-846	264	15	and	and	CCONJ
ejpam-846	264	16	rikl	rikl	PROPN
ejpam-846	264	17	are	be	AUX
ejpam-846	264	18	(	(	PUNCT
ejpam-846	264	19	unique	unique	ADJ
ejpam-846	264	20	)	)	PUNCT
ejpam-846	264	21	constants	constant	NOUN
ejpam-846	264	22	.	.	PUNCT
ejpam-846	265	1	then	then	ADV
ejpam-846	265	2	,	,	PUNCT
ejpam-846	265	3	referring	refer	VERB
ejpam-846	265	4	to	to	ADP
ejpam-846	265	5	(	(	PUNCT
ejpam-846	265	6	25	25	NUM
ejpam-846	265	7	)	)	PUNCT
ejpam-846	265	8	,	,	PUNCT
ejpam-846	265	9	it	it	PRON
ejpam-846	265	10	follows	follow	VERB
ejpam-846	265	11	that	that	SCONJ
ejpam-846	265	12	∑	∑	PROPN
ejpam-846	265	13	i	i	PRON
ejpam-846	265	14	t	t	VERB
ejpam-846	266	1	i	i	PRON
ejpam-846	266	2	k	k	NOUN
ejpam-846	267	1	=	=	PUNCT
ejpam-846	267	2	ξ̄k	ξ̄k	PROPN
ejpam-846	267	3	and	and	CCONJ
ejpam-846	267	4	∑	∑	NOUN
ejpam-846	267	5	i	i	NOUN
ejpam-846	267	6	r	r	VERB
ejpam-846	268	1	i	i	PRON
ejpam-846	268	2	kl	kl	NOUN
ejpam-846	268	3	=	=	SYM
ejpam-846	268	4	mkl	mkl	PROPN
ejpam-846	268	5	.	.	PROPN
ejpam-846	269	1	thus	thus	ADV
ejpam-846	269	2	,	,	PUNCT
ejpam-846	269	3	every	every	DET
ejpam-846	269	4	feasible	feasible	ADJ
ejpam-846	269	5	solution	solution	NOUN
ejpam-846	269	6	π	π	X
ejpam-846	269	7	∈	∈	PROPN
ejpam-846	269	8	π	π	NOUN
ejpam-846	269	9	must	must	AUX
ejpam-846	269	10	satisfy	satisfy	VERB
ejpam-846	269	11	π0	π0	NOUN
ejpam-846	269	12	+	+	CCONJ
ejpam-846	269	13	π1ξ̄	π1ξ̄	PUNCT
ejpam-846	269	14	+	+	CCONJ
ejpam-846	269	15	k∑	k∑	PROPN
ejpam-846	270	1	k	k	PROPN
ejpam-846	270	2	,	,	PUNCT
ejpam-846	270	3	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	270	4	mklπkl	mklπkl	NOUN
ejpam-846	270	5	≤	≤	NUM
ejpam-846	270	6	k+1∑	k+1∑	PROPN
ejpam-846	270	7	i=1	i=1	PROPN
ejpam-846	271	1	ep	ep	PROPN
ejpam-846	272	1	[	[	X
ejpam-846	272	2	λi(ξ)ϕ(x	λi(ξ)ϕ(x	PROPN
ejpam-846	272	3	,	,	PUNCT
ejpam-846	272	4	ξ	ξ	PROPN
ejpam-846	272	5	)	)	PUNCT
ejpam-846	272	6	]	]	PUNCT
ejpam-846	272	7	.	.	PUNCT
ejpam-846	273	1	(	(	PUNCT
ejpam-846	273	2	31	31	NUM
ejpam-846	273	3	)	)	PUNCT
ejpam-846	273	4	therefore	therefore	ADV
ejpam-846	273	5	,	,	PUNCT
ejpam-846	273	6	adding	add	VERB
ejpam-846	273	7	(	(	PUNCT
ejpam-846	273	8	31	31	NUM
ejpam-846	273	9	)	)	PUNCT
ejpam-846	273	10	to	to	ADP
ejpam-846	273	11	(	(	PUNCT
ejpam-846	273	12	20	20	NUM
ejpam-846	273	13	)	)	PUNCT
ejpam-846	273	14	is	be	AUX
ejpam-846	273	15	not	not	PART
ejpam-846	273	16	a	a	DET
ejpam-846	273	17	restriction	restriction	NOUN
ejpam-846	273	18	;	;	PUNCT
ejpam-846	273	19	however	however	ADV
ejpam-846	273	20	,	,	PUNCT
ejpam-846	273	21	a	a	DET
ejpam-846	273	22	lower	lower	ADV
ejpam-846	273	23	bound	bind	VERB
ejpam-846	273	24	on	on	ADP
ejpam-846	273	25	the	the	DET
ejpam-846	273	26	righthand	righthand	NOUN
ejpam-846	273	27	side	side	NOUN
ejpam-846	273	28	of	of	ADP
ejpam-846	273	29	(	(	PUNCT
ejpam-846	273	30	31	31	NUM
ejpam-846	273	31	)	)	PUNCT
ejpam-846	273	32	can	can	AUX
ejpam-846	273	33	be	be	AUX
ejpam-846	273	34	used	use	VERB
ejpam-846	273	35	to	to	PART
ejpam-846	273	36	develop	develop	VERB
ejpam-846	273	37	a	a	DET
ejpam-846	273	38	restriction	restriction	NOUN
ejpam-846	273	39	on	on	ADP
ejpam-846	273	40	(	(	PUNCT
ejpam-846	273	41	21	21	NUM
ejpam-846	273	42	)	)	PUNCT
ejpam-846	273	43	.	.	PUNCT
ejpam-846	274	1	let	let	VERB
ejpam-846	274	2	ℓi(x	ℓi(x	NUM
ejpam-846	274	3	,	,	PUNCT
ejpam-846	274	4	ξ	ξ	X
ejpam-846	274	5	)	)	PUNCT
ejpam-846	274	6	,	,	PUNCT
ejpam-846	274	7	i	i	PRON
ejpam-846	274	8	=	=	NOUN
ejpam-846	274	9	1	1	NUM
ejpam-846	274	10	,	,	PUNCT
ejpam-846	274	11	.	.	PUNCT
ejpam-846	274	12	.	.	PUNCT
ejpam-846	275	1	.	.	PUNCT
ejpam-846	276	1	,	,	PUNCT
ejpam-846	276	2	k	k	PROPN
ejpam-846	276	3	+	+	NOUN
ejpam-846	276	4	1	1	NUM
ejpam-846	276	5	,	,	PUNCT
ejpam-846	276	6	be	be	AUX
ejpam-846	276	7	a	a	DET
ejpam-846	276	8	family	family	NOUN
ejpam-846	276	9	of	of	ADP
ejpam-846	276	10	lower	low	ADJ
ejpam-846	276	11	bounding	bounding	NOUN
ejpam-846	276	12	linear	linear	NOUN
ejpam-846	276	13	functions	function	NOUN
ejpam-846	276	14	on	on	ADP
ejpam-846	276	15	the	the	DET
ejpam-846	276	16	(	(	PUNCT
ejpam-846	276	17	proper	proper	ADJ
ejpam-846	276	18	)	)	PUNCT
ejpam-846	276	19	convex	convex	NOUN
ejpam-846	276	20	function	function	NOUN
ejpam-846	276	21	ϕ(x	ϕ(x	PROPN
ejpam-846	276	22	,	,	PUNCT
ejpam-846	276	23	ξ	ξ	NOUN
ejpam-846	276	24	)	)	PUNCT
ejpam-846	276	25	over	over	ADP
ejpam-846	276	26	ξ	ξ	PROPN
ejpam-846	276	27	,	,	PUNCT
ejpam-846	276	28	i.e.	i.e.	X
ejpam-846	276	29	,	,	PUNCT
ejpam-846	276	30	ℓi(x	ℓi(x	NUM
ejpam-846	276	31	,	,	PUNCT
ejpam-846	276	32	ξ	ξ	X
ejpam-846	276	33	)	)	PUNCT
ejpam-846	276	34	≤	≤	NOUN
ejpam-846	276	35	ϕ(x	ϕ(x	PROPN
ejpam-846	276	36	,	,	PUNCT
ejpam-846	276	37	ξ	ξ	NOUN
ejpam-846	276	38	)	)	PUNCT
ejpam-846	276	39	,	,	PUNCT
ejpam-846	276	40	w.p.1	w.p.1	NOUN
ejpam-846	276	41	,	,	PUNCT
ejpam-846	276	42	∀i	∀i	NOUN
ejpam-846	276	43	=	=	SYM
ejpam-846	276	44	1	1	NUM
ejpam-846	276	45	,	,	PUNCT
ejpam-846	276	46	.	.	PUNCT
ejpam-846	276	47	.	.	PUNCT
ejpam-846	277	1	.	.	PUNCT
ejpam-846	278	1	,	,	PUNCT
ejpam-846	278	2	k	k	PROPN
ejpam-846	278	3	+	+	PROPN
ejpam-846	278	4	1	1	X
ejpam-846	278	5	.	.	PUNCT
ejpam-846	278	6	(	(	PUNCT
ejpam-846	278	7	32	32	NUM
ejpam-846	278	8	)	)	PUNCT
ejpam-846	278	9	construct	construct	VERB
ejpam-846	278	10	the	the	DET
ejpam-846	278	11	polyhedral	polyhedral	ADJ
ejpam-846	278	12	lower	low	ADJ
ejpam-846	278	13	bounding	bounding	NOUN
ejpam-846	278	14	function	function	NOUN
ejpam-846	278	15	g(x	g(x	NOUN
ejpam-846	278	16	,	,	PUNCT
ejpam-846	278	17	ξ	ξ	NOUN
ejpam-846	278	18	)	)	PUNCT
ejpam-846	278	19	on	on	ADP
ejpam-846	278	20	ϕ(x	ϕ(x	PROPN
ejpam-846	278	21	,	,	PUNCT
ejpam-846	278	22	ξ	ξ	NOUN
ejpam-846	278	23	)	)	PUNCT
ejpam-846	278	24	,	,	PUNCT
ejpam-846	278	25	where	where	SCONJ
ejpam-846	278	26	for	for	ADP
ejpam-846	278	27	ξ	ξ	PROPN
ejpam-846	278	28	∈	∈	PROPN
ejpam-846	278	29	ξ	ξ	PROPN
ejpam-846	278	30	,	,	PUNCT
ejpam-846	278	31	ϕ(x	ϕ(x	PROPN
ejpam-846	278	32	,	,	PUNCT
ejpam-846	278	33	ξ	ξ	NOUN
ejpam-846	278	34	)	)	PUNCT
ejpam-846	278	35	≥	≥	NOUN
ejpam-846	278	36	g(x	g(x	NOUN
ejpam-846	278	37	,	,	PUNCT
ejpam-846	278	38	ξ	ξ	NOUN
ejpam-846	278	39	)	)	PUNCT
ejpam-846	278	40	:	:	PUNCT
ejpam-846	278	41	=	=	SYM
ejpam-846	278	42	max	max	PROPN
ejpam-846	278	43	i=1,	i=1,	PROPN
ejpam-846	278	44	...	...	PUNCT
ejpam-846	278	45	,k+1	,k+1	PUNCT
ejpam-846	278	46	ℓi(x	ℓi(x	X
ejpam-846	278	47	,	,	PUNCT
ejpam-846	278	48	ξ	ξ	NOUN
ejpam-846	278	49	)	)	PUNCT
ejpam-846	278	50	.	.	PUNCT
ejpam-846	279	1	(	(	PUNCT
ejpam-846	279	2	33	33	NUM
ejpam-846	279	3	)	)	PUNCT
ejpam-846	279	4	next	next	ADV
ejpam-846	279	5	,	,	PUNCT
ejpam-846	279	6	define	define	VERB
ejpam-846	279	7	the	the	DET
ejpam-846	279	8	points	point	NOUN
ejpam-846	279	9	ξ̃i	ξ̃i	NOUN
ejpam-846	279	10	∈	∈	NOUN
ejpam-846	280	1	ℜk	ℜk	NOUN
ejpam-846	280	2	,	,	PUNCT
ejpam-846	280	3	i	i	PRON
ejpam-846	280	4	=	=	NOUN
ejpam-846	280	5	1	1	NUM
ejpam-846	280	6	,	,	PUNCT
ejpam-846	280	7	.	.	PUNCT
ejpam-846	280	8	.	.	PUNCT
ejpam-846	280	9	.	.	PUNCT
ejpam-846	281	1	,	,	PUNCT
ejpam-846	281	2	k	k	PROPN
ejpam-846	282	1	+	+	NOUN
ejpam-846	282	2	1	1	NUM
ejpam-846	282	3	,	,	PUNCT
ejpam-846	282	4	as	as	SCONJ
ejpam-846	282	5	follows	follow	VERB
ejpam-846	282	6	:	:	PUNCT
ejpam-846	282	7	ξ̃ik	ξ̃ik	NOUN
ejpam-846	282	8	:	:	PUNCT
ejpam-846	282	9	=	=	SYM
ejpam-846	282	10	1	1	NUM
ejpam-846	282	11	ρi	ρi	NOUN
ejpam-846	282	12	[	[	PUNCT
ejpam-846	282	13	vi1mk1	vi1mk1	NOUN
ejpam-846	282	14	+	+	X
ejpam-846	282	15	·	·	PUNCT
ejpam-846	282	16	·	·	PUNCT
ejpam-846	282	17	·	·	PUNCT
ejpam-846	282	18	+	+	NUM
ejpam-846	282	19	vikmkk	vikmkk	NOUN
ejpam-846	282	20	+	+	CCONJ
ejpam-846	282	21	vik+1ξ̄k	vik+1ξ̄k	PROPN
ejpam-846	282	22	]	]	PUNCT
ejpam-846	282	23	,	,	PUNCT
ejpam-846	282	24	k	k	X
ejpam-846	282	25	=	=	SYM
ejpam-846	282	26	1	1	NUM
ejpam-846	282	27	,	,	PUNCT
ejpam-846	282	28	.	.	PUNCT
ejpam-846	282	29	.	.	PUNCT
ejpam-846	282	30	.	.	PUNCT
ejpam-846	283	1	,	,	PUNCT
ejpam-846	284	1	k	k	NOUN
ejpam-846	284	2	,	,	PUNCT
ejpam-846	284	3	(	(	PUNCT
ejpam-846	284	4	34	34	NUM
ejpam-846	284	5	)	)	PUNCT
ejpam-846	284	6	where	where	SCONJ
ejpam-846	284	7	ρi	ρi	X
ejpam-846	284	8	:	:	PUNCT
ejpam-846	284	9	=	=	NOUN
ejpam-846	284	10	vi1ξ̄1	vi1ξ̄1	X
ejpam-846	284	11	+	+	PUNCT
ejpam-846	284	12	·	·	PUNCT
ejpam-846	284	13	·	·	PUNCT
ejpam-846	284	14	·	·	PUNCT
ejpam-846	284	15	+	+	NUM
ejpam-846	284	16	vik	vik	VERB
ejpam-846	284	17	ξ̄k	ξ̄k	NOUN
ejpam-846	284	18	+	+	CCONJ
ejpam-846	284	19	vik+1	vik+1	NOUN
ejpam-846	284	20	,	,	PUNCT
ejpam-846	284	21	i	i	PRON
ejpam-846	284	22	=	=	NOUN
ejpam-846	284	23	1	1	NUM
ejpam-846	284	24	,	,	PUNCT
ejpam-846	284	25	.	.	PUNCT
ejpam-846	284	26	.	.	PUNCT
ejpam-846	284	27	.	.	PUNCT
ejpam-846	285	1	,	,	PUNCT
ejpam-846	285	2	k	k	PROPN
ejpam-846	286	1	+	+	PROPN
ejpam-846	286	2	1	1	X
ejpam-846	286	3	.	.	PUNCT
ejpam-846	286	4	(	(	PUNCT
ejpam-846	286	5	35	35	NUM
ejpam-846	286	6	)	)	PUNCT
ejpam-846	286	7	edirisinghe	edirisinghe	NOUN
ejpam-846	286	8	/	/	SYM
ejpam-846	286	9	eur	eur	PROPN
ejpam-846	286	10	.	.	PUNCT
ejpam-846	287	1	j.	j.	PROPN
ejpam-846	287	2	pure	pure	PROPN
ejpam-846	287	3	appl	appl	PROPN
ejpam-846	287	4	.	.	PROPN
ejpam-846	287	5	math	math	PROPN
ejpam-846	287	6	,	,	PUNCT
ejpam-846	287	7	3	3	NUM
ejpam-846	287	8	(	(	PUNCT
ejpam-846	287	9	2010	2010	NUM
ejpam-846	287	10	)	)	PUNCT
ejpam-846	287	11	,	,	PUNCT
ejpam-846	287	12	572	572	NUM
ejpam-846	287	13	-	-	SYM
ejpam-846	287	14	592	592	NUM
ejpam-846	287	15	581	581	NUM
ejpam-846	287	16	proposition	proposition	NOUN
ejpam-846	287	17	8	8	NUM
ejpam-846	287	18	.	.	PUNCT
ejpam-846	288	1	ξ̃i	ξ̃i	PROPN
ejpam-846	288	2	∈	∈	PROPN
ejpam-846	288	3	ξ	ξ	PROPN
ejpam-846	288	4	for	for	ADP
ejpam-846	288	5	all	all	DET
ejpam-846	288	6	i	i	PRON
ejpam-846	288	7	=	=	NOUN
ejpam-846	288	8	1	1	NUM
ejpam-846	288	9	,	,	PUNCT
ejpam-846	288	10	.	.	PUNCT
ejpam-846	288	11	.	.	PUNCT
ejpam-846	288	12	.	.	PUNCT
ejpam-846	289	1	,	,	PUNCT
ejpam-846	289	2	k	k	PROPN
ejpam-846	289	3	+	+	NOUN
ejpam-846	289	4	1	1	X
ejpam-846	289	5	.	.	X
ejpam-846	289	6	proof	proof	NOUN
ejpam-846	289	7	.	.	PUNCT
ejpam-846	290	1	for	for	ADP
ejpam-846	290	2	ξ	ξ	PROPN
ejpam-846	290	3	∈	∈	PROPN
ejpam-846	290	4	ξ	ξ	PROPN
ejpam-846	290	5	,	,	PUNCT
ejpam-846	290	6	multiplying	multiply	VERB
ejpam-846	290	7	the	the	DET
ejpam-846	290	8	expressions	expression	NOUN
ejpam-846	290	9	in	in	ADP
ejpam-846	290	10	(	(	PUNCT
ejpam-846	290	11	25	25	NUM
ejpam-846	290	12	)	)	PUNCT
ejpam-846	290	13	by	by	ADP
ejpam-846	290	14	nonnegative	nonnegative	ADJ
ejpam-846	290	15	λi(ξ	λi(ξ	NOUN
ejpam-846	290	16	)	)	PUNCT
ejpam-846	290	17	,	,	PUNCT
ejpam-846	290	18	for	for	ADP
ejpam-846	290	19	some	some	DET
ejpam-846	290	20	vertex	vertex	NOUN
ejpam-846	290	21	index	index	NOUN
ejpam-846	290	22	i	i	PRON
ejpam-846	290	23	,	,	PUNCT
ejpam-846	290	24	k+1∑	k+1∑	PROPN
ejpam-846	290	25	j=1	j=1	NOUN
ejpam-846	290	26	λj(ξ)λi(ξ	λj(ξ)λi(ξ	X
ejpam-846	290	27	)	)	PUNCT
ejpam-846	290	28	=	=	SYM
ejpam-846	291	1	λi(ξ	λi(ξ	X
ejpam-846	291	2	)	)	PUNCT
ejpam-846	291	3	and	and	CCONJ
ejpam-846	291	4	λj(ξ)λi(ξ	λj(ξ)λi(ξ	VERB
ejpam-846	291	5	)	)	PUNCT
ejpam-846	291	6	≥	≥	NOUN
ejpam-846	291	7	0	0	NUM
ejpam-846	291	8	.	.	PUNCT
ejpam-846	292	1	noting	note	VERB
ejpam-846	292	2	the	the	DET
ejpam-846	292	3	linearity	linearity	NOUN
ejpam-846	292	4	of	of	ADP
ejpam-846	292	5	λj(ξ	λj(ξ	PROPN
ejpam-846	292	6	)	)	PUNCT
ejpam-846	292	7	in	in	ADP
ejpam-846	292	8	(	(	PUNCT
ejpam-846	292	9	24	24	NUM
ejpam-846	292	10	)	)	PUNCT
ejpam-846	292	11	,	,	PUNCT
ejpam-846	293	1	k+1∑	k+1∑	PROPN
ejpam-846	293	2	j=1	j=1	PUNCT
ejpam-846	294	1	[	[	X
ejpam-846	294	2	vj1ξ1	vj1ξ1	PROPN
ejpam-846	294	3	+	+	NUM
ejpam-846	294	4	·	·	PUNCT
ejpam-846	294	5	·	·	PUNCT
ejpam-846	294	6	·	·	PUNCT
ejpam-846	294	7	+	+	NUM
ejpam-846	294	8	vjkξk	vjkξk	NOUN
ejpam-846	294	9	+	+	CCONJ
ejpam-846	294	10	vj	vj	X
ejpam-846	294	11	k+1]λi(ξ	k+1]λi(ξ	NOUN
ejpam-846	294	12	)	)	PUNCT
ejpam-846	294	13	=	=	SYM
ejpam-846	294	14	λi(ξ	λi(ξ	X
ejpam-846	294	15	)	)	PUNCT
ejpam-846	294	16	and	and	CCONJ
ejpam-846	294	17	[	[	X
ejpam-846	294	18	vj1ξ1	vj1ξ1	PROPN
ejpam-846	294	19	+	+	NUM
ejpam-846	294	20	·	·	PUNCT
ejpam-846	294	21	·	·	PUNCT
ejpam-846	294	22	·	·	PUNCT
ejpam-846	294	23	+	+	NUM
ejpam-846	294	24	vjkξk	vjkξk	NOUN
ejpam-846	294	25	+	+	CCONJ
ejpam-846	294	26	vj	vj	X
ejpam-846	294	27	k+1]λi(ξ	k+1]λi(ξ	NOUN
ejpam-846	294	28	)	)	PUNCT
ejpam-846	294	29	≥	≥	NOUN
ejpam-846	294	30	0	0	NUM
ejpam-846	294	31	.	.	PUNCT
ejpam-846	294	32	upon	upon	SCONJ
ejpam-846	294	33	taking	take	VERB
ejpam-846	294	34	the	the	DET
ejpam-846	294	35	expectation	expectation	NOUN
ejpam-846	294	36	of	of	ADP
ejpam-846	294	37	the	the	DET
ejpam-846	294	38	above	above	ADJ
ejpam-846	294	39	w.r.t	w.r.t	NOUN
ejpam-846	294	40	.	.	PUNCT
ejpam-846	295	1	any	any	DET
ejpam-846	295	2	p	p	PROPN
ejpam-846	295	3	∈	∈	PROPN
ejpam-846	295	4	p̃	p̃	PROPN
ejpam-846	295	5	,	,	PUNCT
ejpam-846	295	6	and	and	CCONJ
ejpam-846	295	7	noting	note	VERB
ejpam-846	295	8	the	the	DET
ejpam-846	295	9	definitions	definition	NOUN
ejpam-846	295	10	in	in	ADP
ejpam-846	295	11	(	(	PUNCT
ejpam-846	295	12	29	29	NUM
ejpam-846	295	13	)	)	PUNCT
ejpam-846	295	14	and	and	CCONJ
ejpam-846	295	15	(	(	PUNCT
ejpam-846	295	16	35	35	NUM
ejpam-846	295	17	)	)	PUNCT
ejpam-846	295	18	,	,	PUNCT
ejpam-846	295	19	k+1∑	k+1∑	PROPN
ejpam-846	295	20	j=1	j=1	PUNCT
ejpam-846	296	1	[	[	X
ejpam-846	296	2	vj1	vj1	X
ejpam-846	296	3	t	t	NOUN
ejpam-846	296	4	i	i	NOUN
ejpam-846	296	5	1	1	NUM
ejpam-846	296	6	+	+	CCONJ
ejpam-846	296	7	·	·	PUNCT
ejpam-846	296	8	·	·	PUNCT
ejpam-846	296	9	·	·	PUNCT
ejpam-846	296	10	+	+	NUM
ejpam-846	297	1	vjkt	vjkt	ADJ
ejpam-846	297	2	i	i	X
ejpam-846	297	3	k	k	PROPN
ejpam-846	298	1	+	+	CCONJ
ejpam-846	298	2	vj	vj	DET
ejpam-846	298	3	k+1ρi	k+1ρi	PROPN
ejpam-846	298	4	]	]	X
ejpam-846	298	5	=	=	SYM
ejpam-846	298	6	ρi	ρi	NOUN
ejpam-846	298	7	and	and	CCONJ
ejpam-846	298	8	vj1	vj1	PROPN
ejpam-846	298	9	t	t	PROPN
ejpam-846	298	10	i	i	NOUN
ejpam-846	298	11	1	1	NUM
ejpam-846	298	12	+	+	CCONJ
ejpam-846	298	13	·	·	PUNCT
ejpam-846	298	14	·	·	PUNCT
ejpam-846	298	15	·	·	PUNCT
ejpam-846	299	1	+	+	NUM
ejpam-846	300	1	vjkt	vjkt	ADJ
ejpam-846	300	2	i	i	X
ejpam-846	300	3	k	k	PROPN
ejpam-846	301	1	+	+	CCONJ
ejpam-846	301	2	vj	vj	INTJ
ejpam-846	301	3	k+1ρi	k+1ρi	PROPN
ejpam-846	301	4	≥	≥	NUM
ejpam-846	301	5	0	0	NUM
ejpam-846	301	6	.	.	PUNCT
ejpam-846	302	1	dividing	divide	VERB
ejpam-846	302	2	by	by	ADP
ejpam-846	302	3	ρi	ρi	NOUN
ejpam-846	302	4	and	and	CCONJ
ejpam-846	302	5	noting	note	VERB
ejpam-846	302	6	the	the	DET
ejpam-846	302	7	definition	definition	NOUN
ejpam-846	302	8	in	in	ADP
ejpam-846	302	9	(	(	PUNCT
ejpam-846	302	10	34	34	NUM
ejpam-846	302	11	)	)	PUNCT
ejpam-846	302	12	,	,	PUNCT
ejpam-846	302	13	k+1∑	k+1∑	PROPN
ejpam-846	302	14	j=1	j=1	PUNCT
ejpam-846	303	1	[	[	X
ejpam-846	303	2	vj1ξ̃	vj1ξ̃	ADV
ejpam-846	303	3	i	i	VERB
ejpam-846	303	4	1	1	NUM
ejpam-846	303	5	+	+	CCONJ
ejpam-846	303	6	·	·	PUNCT
ejpam-846	303	7	·	·	PUNCT
ejpam-846	303	8	·	·	PUNCT
ejpam-846	303	9	+	+	NUM
ejpam-846	303	10	vjk	vjk	NOUN
ejpam-846	303	11	ξ̃	ξ̃	PROPN
ejpam-846	304	1	i	i	NOUN
ejpam-846	304	2	k	k	PROPN
ejpam-846	305	1	+	+	CCONJ
ejpam-846	305	2	vj	vj	INTJ
ejpam-846	305	3	k+1	k+1	X
ejpam-846	305	4	]	]	X
ejpam-846	305	5	=	=	SYM
ejpam-846	305	6	1	1	NUM
ejpam-846	305	7	and	and	CCONJ
ejpam-846	305	8	vj1ξ̃	vj1ξ̃	ADV
ejpam-846	306	1	i	i	VERB
ejpam-846	306	2	1	1	NUM
ejpam-846	306	3	+	+	CCONJ
ejpam-846	306	4	·	·	PUNCT
ejpam-846	306	5	·	·	PUNCT
ejpam-846	306	6	·	·	PUNCT
ejpam-846	306	7	+	+	NUM
ejpam-846	306	8	vjk	vjk	NOUN
ejpam-846	306	9	ξ̃	ξ̃	PROPN
ejpam-846	307	1	i	i	NOUN
ejpam-846	307	2	k	k	PROPN
ejpam-846	308	1	+	+	CCONJ
ejpam-846	308	2	vj	vj	INTJ
ejpam-846	308	3	k+1	k+1	X
ejpam-846	308	4	≥	≥	NOUN
ejpam-846	308	5	0	0	NUM
ejpam-846	308	6	.	.	PUNCT
ejpam-846	309	1	since	since	SCONJ
ejpam-846	309	2	λj(ξ̃	λj(ξ̃	PROPN
ejpam-846	309	3	i	i	NOUN
ejpam-846	309	4	)	)	PUNCT
ejpam-846	309	5	=	=	PUNCT
ejpam-846	310	1	vj1ξ̃	vj1ξ̃	ADV
ejpam-846	310	2	i	i	VERB
ejpam-846	310	3	1	1	NUM
ejpam-846	310	4	+	+	CCONJ
ejpam-846	310	5	·	·	PUNCT
ejpam-846	310	6	·	·	PUNCT
ejpam-846	310	7	·	·	PUNCT
ejpam-846	310	8	+	+	NUM
ejpam-846	310	9	vjk	vjk	NOUN
ejpam-846	310	10	ξ̃	ξ̃	PROPN
ejpam-846	311	1	i	i	NOUN
ejpam-846	311	2	k	k	PROPN
ejpam-846	312	1	+	+	CCONJ
ejpam-846	312	2	vj	vj	PROPN
ejpam-846	312	3	k+1	k+1	NOUN
ejpam-846	312	4	,	,	PUNCT
ejpam-846	312	5	it	it	PRON
ejpam-846	312	6	follows	follow	VERB
ejpam-846	312	7	that	that	SCONJ
ejpam-846	312	8	k+1∑	k+1∑	PROPN
ejpam-846	312	9	j=1	j=1	PROPN
ejpam-846	312	10	λj(ξ̃	λj(ξ̃	PROPN
ejpam-846	313	1	i	i	NOUN
ejpam-846	313	2	)	)	PUNCT
ejpam-846	313	3	=	=	SYM
ejpam-846	313	4	1	1	NUM
ejpam-846	313	5	and	and	CCONJ
ejpam-846	313	6	λj(ξ̃	λj(ξ̃	PROPN
ejpam-846	313	7	i	i	PROPN
ejpam-846	313	8	)	)	PUNCT
ejpam-846	313	9	≥	≥	PROPN
ejpam-846	313	10	0	0	NUM
ejpam-846	313	11	,	,	PUNCT
ejpam-846	313	12	which	which	PRON
ejpam-846	313	13	implies	imply	VERB
ejpam-846	313	14	due	due	ADJ
ejpam-846	313	15	to	to	PART
ejpam-846	313	16	proposition	proposition	NOUN
ejpam-846	313	17	7	7	NUM
ejpam-846	314	1	that	that	SCONJ
ejpam-846	314	2	ξ̃i	ξ̃i	PROPN
ejpam-846	314	3	∈	∈	PROPN
ejpam-846	314	4	ξ	ξ	PROPN
ejpam-846	314	5	.	.	PUNCT
ejpam-846	314	6	proposition	proposition	NOUN
ejpam-846	314	7	9	9	NUM
ejpam-846	314	8	.	.	X
ejpam-846	315	1	for	for	ADP
ejpam-846	315	2	any	any	DET
ejpam-846	315	3	p	p	PROPN
ejpam-846	315	4	∈	∈	PROPN
ejpam-846	315	5	p̃	p̃	PROPN
ejpam-846	315	6	,	,	PUNCT
ejpam-846	315	7	k+1∑	k+1∑	PROPN
ejpam-846	315	8	i=1	i=1	PROPN
ejpam-846	316	1	ep	ep	PROPN
ejpam-846	317	1	[	[	X
ejpam-846	317	2	λi(ξ)ϕ(x	λi(ξ)ϕ(x	PROPN
ejpam-846	317	3	,	,	PUNCT
ejpam-846	317	4	ξ	ξ	PROPN
ejpam-846	317	5	)	)	PUNCT
ejpam-846	317	6	]	]	PUNCT
ejpam-846	317	7	≥	≥	X
ejpam-846	318	1	k+1∑	k+1∑	PROPN
ejpam-846	318	2	i=1	i=1	PROPN
ejpam-846	319	1	ep	ep	PROPN
ejpam-846	320	1	[	[	X
ejpam-846	320	2	λi(ξ)g(x	λi(ξ)g(x	X
ejpam-846	320	3	,	,	PUNCT
ejpam-846	320	4	ξ	ξ	NOUN
ejpam-846	320	5	)	)	PUNCT
ejpam-846	320	6	]	]	PUNCT
ejpam-846	320	7	≥	≥	X
ejpam-846	321	1	k+1∑	k+1∑	PROPN
ejpam-846	321	2	i=1	i=1	PROPN
ejpam-846	322	1	ρi	ρi	INTJ
ejpam-846	322	2	g(x	g(x	NOUN
ejpam-846	322	3	,	,	PUNCT
ejpam-846	322	4	ξ̃	ξ̃	PROPN
ejpam-846	322	5	i	i	NOUN
ejpam-846	322	6	)	)	PUNCT
ejpam-846	322	7	.	.	PUNCT
ejpam-846	323	1	(	(	PUNCT
ejpam-846	323	2	36	36	NUM
ejpam-846	323	3	)	)	PUNCT
ejpam-846	323	4	proof	proof	NOUN
ejpam-846	323	5	.	.	PUNCT
ejpam-846	324	1	the	the	DET
ejpam-846	324	2	first	first	ADJ
ejpam-846	324	3	inequality	inequality	NOUN
ejpam-846	324	4	follows	follow	VERB
ejpam-846	324	5	for	for	ADP
ejpam-846	324	6	any	any	DET
ejpam-846	324	7	probability	probability	NOUN
ejpam-846	324	8	measure	measure	NOUN
ejpam-846	324	9	p	p	NOUN
ejpam-846	324	10	on	on	ADP
ejpam-846	324	11	ξ	ξ	PROPN
ejpam-846	324	12	because	because	SCONJ
ejpam-846	324	13	ϕ	ϕ	PROPN
ejpam-846	324	14	≥	≥	NUM
ejpam-846	324	15	g	g	NOUN
ejpam-846	324	16	and	and	CCONJ
ejpam-846	324	17	λi	λi	X
ejpam-846	324	18	≥	≥	NUM
ejpam-846	324	19	0	0	NUM
ejpam-846	324	20	,	,	PUNCT
ejpam-846	324	21	∀i	∀i	NOUN
ejpam-846	324	22	,	,	PUNCT
ejpam-846	324	23	on	on	ADP
ejpam-846	324	24	ξ	ξ	PROPN
ejpam-846	324	25	.	.	PUNCT
ejpam-846	325	1	for	for	ADP
ejpam-846	325	2	the	the	DET
ejpam-846	325	3	second	second	ADJ
ejpam-846	325	4	inequality	inequality	NOUN
ejpam-846	325	5	,	,	PUNCT
ejpam-846	325	6	noting	note	VERB
ejpam-846	325	7	the	the	DET
ejpam-846	325	8	definition	definition	NOUN
ejpam-846	325	9	of	of	ADP
ejpam-846	325	10	g	g	NOUN
ejpam-846	325	11	in	in	ADP
ejpam-846	325	12	(	(	PUNCT
ejpam-846	325	13	33	33	NUM
ejpam-846	325	14	)	)	PUNCT
ejpam-846	325	15	,	,	PUNCT
ejpam-846	325	16	and	and	CCONJ
ejpam-846	325	17	denoting	denote	VERB
ejpam-846	325	18	the	the	DET
ejpam-846	325	19	linear	linear	ADJ
ejpam-846	325	20	function	function	NOUN
ejpam-846	325	21	ℓj(x	ℓj(x	X
ejpam-846	325	22	,	,	PUNCT
ejpam-846	325	23	ξ	ξ	X
ejpam-846	325	24	)	)	PUNCT
ejpam-846	325	25	by	by	ADP
ejpam-846	325	26	αjξ	αjξ	NOUN
ejpam-846	325	27	+	+	CCONJ
ejpam-846	325	28	θj	θj	ADV
ejpam-846	325	29	for	for	ADP
ejpam-846	325	30	some	some	DET
ejpam-846	325	31	row	row	NOUN
ejpam-846	325	32	vector	vector	NOUN
ejpam-846	325	33	αj	αj	NOUN
ejpam-846	325	34	∈	∈	PROPN
ejpam-846	325	35	ℜk	ℜk	PROPN
ejpam-846	325	36	and	and	CCONJ
ejpam-846	325	37	scalar	scalar	ADJ
ejpam-846	325	38	θj	θj	NOUN
ejpam-846	325	39	∈	∈	PROPN
ejpam-846	325	40	ℜ	ℜ	PROPN
ejpam-846	325	41	,	,	PUNCT
ejpam-846	325	42	ep	ep	PROPN
ejpam-846	326	1	[	[	X
ejpam-846	326	2	λi(ξ)g(x	λi(ξ)g(x	X
ejpam-846	326	3	,	,	PUNCT
ejpam-846	326	4	ξ	ξ	NOUN
ejpam-846	326	5	)	)	PUNCT
ejpam-846	326	6	]	]	PUNCT
ejpam-846	327	1	=	=	SYM
ejpam-846	327	2	ep	ep	PROPN
ejpam-846	327	3	[	[	PUNCT
ejpam-846	327	4	λi(ξ	λi(ξ	X
ejpam-846	327	5	)	)	PUNCT
ejpam-846	327	6	max	max	PROPN
ejpam-846	327	7	j=1,	j=1,	PROPN
ejpam-846	327	8	...	...	PUNCT
ejpam-846	327	9	,k+1	,k+1	PUNCT
ejpam-846	327	10	ℓj(x	ℓj(x	X
ejpam-846	327	11	,	,	PUNCT
ejpam-846	327	12	ξ	ξ	X
ejpam-846	327	13	)	)	PUNCT
ejpam-846	327	14	]	]	PUNCT
ejpam-846	327	15	edirisinghe	edirisinghe	PROPN
ejpam-846	327	16	/	/	SYM
ejpam-846	327	17	eur	eur	PROPN
ejpam-846	327	18	.	.	PUNCT
ejpam-846	328	1	j.	j.	PROPN
ejpam-846	328	2	pure	pure	PROPN
ejpam-846	328	3	appl	appl	PROPN
ejpam-846	328	4	.	.	PROPN
ejpam-846	328	5	math	math	PROPN
ejpam-846	328	6	,	,	PUNCT
ejpam-846	328	7	3	3	NUM
ejpam-846	328	8	(	(	PUNCT
ejpam-846	328	9	2010	2010	NUM
ejpam-846	328	10	)	)	PUNCT
ejpam-846	328	11	,	,	PUNCT
ejpam-846	328	12	572	572	NUM
ejpam-846	328	13	-	-	SYM
ejpam-846	328	14	592	592	NUM
ejpam-846	328	15	582	582	NUM
ejpam-846	328	16	=	=	SYM
ejpam-846	328	17	ep	ep	PROPN
ejpam-846	328	18	[	[	PUNCT
ejpam-846	328	19	max	max	PROPN
ejpam-846	328	20	j=1,	j=1,	PROPN
ejpam-846	328	21	...	...	PUNCT
ejpam-846	328	22	,k+1	,k+1	PUNCT
ejpam-846	328	23	λi(ξ)ℓ	λi(ξ)ℓ	PROPN
ejpam-846	328	24	j(x	j(x	PROPN
ejpam-846	328	25	,	,	PUNCT
ejpam-846	328	26	ξ	ξ	PROPN
ejpam-846	328	27	)	)	PUNCT
ejpam-846	328	28	]	]	PUNCT
ejpam-846	328	29	≥	≥	PROPN
ejpam-846	328	30	max	max	PROPN
ejpam-846	328	31	j=1,	j=1,	PROPN
ejpam-846	328	32	...	...	PUNCT
ejpam-846	328	33	,k+1	,k+1	PUNCT
ejpam-846	328	34	{	{	PUNCT
ejpam-846	328	35	ep	ep	X
ejpam-846	328	36	[	[	PUNCT
ejpam-846	328	37	λi(ξ)ℓ	λi(ξ)ℓ	PROPN
ejpam-846	328	38	j(x	j(x	PROPN
ejpam-846	328	39	,	,	PUNCT
ejpam-846	328	40	ξ	ξ	PROPN
ejpam-846	328	41	)	)	PUNCT
ejpam-846	328	42	]	]	PUNCT
ejpam-846	328	43	}	}	PUNCT
ejpam-846	328	44	=	=	SYM
ejpam-846	328	45	max	max	PROPN
ejpam-846	328	46	j=1,	j=1,	PROPN
ejpam-846	328	47	...	...	PUNCT
ejpam-846	328	48	,k+1	,k+1	PUNCT
ejpam-846	328	49	{	{	PUNCT
ejpam-846	328	50	αj	αj	X
ejpam-846	328	51	ep	ep	X
ejpam-846	329	1	[	[	X
ejpam-846	329	2	λi(ξ)ξ	λi(ξ)ξ	X
ejpam-846	329	3	]	]	X
ejpam-846	329	4	+	+	CCONJ
ejpam-846	329	5	θj	θj	DET
ejpam-846	329	6	ep	ep	PROPN
ejpam-846	330	1	[	[	X
ejpam-846	330	2	λi(ξ	λi(ξ	X
ejpam-846	330	3	)	)	PUNCT
ejpam-846	330	4	]	]	PUNCT
ejpam-846	331	1	}	}	PUNCT
ejpam-846	331	2	=	=	SYM
ejpam-846	331	3	max	max	PROPN
ejpam-846	331	4	j=1,	j=1,	PROPN
ejpam-846	331	5	...	...	PUNCT
ejpam-846	331	6	,k+1	,k+1	PUNCT
ejpam-846	331	7	{	{	PUNCT
ejpam-846	331	8	αj	αj	X
ejpam-846	331	9	ti	ti	NOUN
ejpam-846	331	10	+	+	CCONJ
ejpam-846	331	11	θj	θj	NOUN
ejpam-846	331	12	ρi	ρi	NOUN
ejpam-846	331	13	}	}	PUNCT
ejpam-846	331	14	=	=	SYM
ejpam-846	331	15	ρi	ρi	NOUN
ejpam-846	331	16	[	[	PUNCT
ejpam-846	331	17	max	max	PROPN
ejpam-846	331	18	j=1,	j=1,	PROPN
ejpam-846	331	19	...	...	PUNCT
ejpam-846	331	20	,k+1	,k+1	PUNCT
ejpam-846	331	21	{	{	PUNCT
ejpam-846	331	22	αj	αj	X
ejpam-846	331	23	(	(	PUNCT
ejpam-846	331	24	ti	ti	PROPN
ejpam-846	331	25	ρi	ρi	PROPN
ejpam-846	331	26	)	)	PUNCT
ejpam-846	332	1	+	+	CCONJ
ejpam-846	332	2	θj	θj	X
ejpam-846	332	3	}	}	PUNCT
ejpam-846	332	4	]	]	PUNCT
ejpam-846	332	5	=	=	PUNCT
ejpam-846	332	6	ρi	ρi	X
ejpam-846	332	7	[	[	PUNCT
ejpam-846	332	8	max	max	PROPN
ejpam-846	332	9	j=1,	j=1,	PROPN
ejpam-846	332	10	...	...	PUNCT
ejpam-846	332	11	,k+1	,k+1	PUNCT
ejpam-846	332	12	ℓj(x	ℓj(x	X
ejpam-846	332	13	,	,	PUNCT
ejpam-846	332	14	ξ̃i	ξ̃i	NOUN
ejpam-846	332	15	)	)	PUNCT
ejpam-846	332	16	]	]	PUNCT
ejpam-846	333	1	=	=	PUNCT
ejpam-846	333	2	ρi	ρi	PROPN
ejpam-846	333	3	g(x	g(x	PROPN
ejpam-846	333	4	,	,	PUNCT
ejpam-846	333	5	ξ̃	ξ̃	PROPN
ejpam-846	333	6	i	i	NOUN
ejpam-846	333	7	)	)	PUNCT
ejpam-846	333	8	.	.	PUNCT
ejpam-846	334	1	therefore	therefore	ADV
ejpam-846	334	2	,	,	PUNCT
ejpam-846	334	3	it	it	PRON
ejpam-846	334	4	is	be	AUX
ejpam-846	334	5	straightforward	straightforward	ADJ
ejpam-846	334	6	to	to	PART
ejpam-846	334	7	see	see	VERB
ejpam-846	334	8	that	that	PRON
ejpam-846	334	9	φ2(x	φ2(x	NOUN
ejpam-846	334	10	)	)	PUNCT
ejpam-846	334	11	≥	≥	NOUN
ejpam-846	334	12	φr	φr	ADP
ejpam-846	334	13	2	2	NUM
ejpam-846	334	14	(	(	PUNCT
ejpam-846	334	15	x	x	NOUN
ejpam-846	334	16	)	)	PUNCT
ejpam-846	334	17	:	:	PUNCT
ejpam-846	335	1	=	=	PUNCT
ejpam-846	335	2	sup	sup	NOUN
ejpam-846	335	3	π∈π	π∈π	VERB
ejpam-846	335	4	π0	π0	NOUN
ejpam-846	335	5	+	+	X
ejpam-846	335	6	π1ξ̄	π1ξ̄	PUNCT
ejpam-846	335	7	+	+	CCONJ
ejpam-846	335	8	k∑	k∑	PROPN
ejpam-846	335	9	k	k	PROPN
ejpam-846	335	10	,	,	PUNCT
ejpam-846	335	11	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	335	12	mklπkl	mklπkl	X
ejpam-846	335	13	(	(	PUNCT
ejpam-846	335	14	37	37	NUM
ejpam-846	335	15	)	)	PUNCT
ejpam-846	335	16	s.t	s.t	PROPN
ejpam-846	335	17	.	.	PROPN
ejpam-846	335	18	π0	π0	PROPN
ejpam-846	335	19	+	+	CCONJ
ejpam-846	335	20	π1ξ̄	π1ξ̄	PUNCT
ejpam-846	335	21	+	+	CCONJ
ejpam-846	335	22	k∑	k∑	PROPN
ejpam-846	335	23	k	k	PROPN
ejpam-846	335	24	,	,	PUNCT
ejpam-846	335	25	l=1,k≥l	l=1,k≥l	PROPN
ejpam-846	335	26	mklπkl	mklπkl	NOUN
ejpam-846	335	27	≤	≤	NUM
ejpam-846	335	28	k+1∑	k+1∑	PROPN
ejpam-846	335	29	i=1	i=1	PROPN
ejpam-846	336	1	ρi	ρi	PROPN
ejpam-846	336	2	g(x	g(x	NOUN
ejpam-846	336	3	,	,	PUNCT
ejpam-846	336	4	ξ̃	ξ̃	PROPN
ejpam-846	336	5	i	i	NOUN
ejpam-846	336	6	)	)	PUNCT
ejpam-846	336	7	.	.	PUNCT
ejpam-846	337	1	it	it	PRON
ejpam-846	337	2	is	be	AUX
ejpam-846	337	3	important	important	ADJ
ejpam-846	337	4	to	to	PART
ejpam-846	337	5	note	note	VERB
ejpam-846	337	6	that	that	SCONJ
ejpam-846	337	7	if	if	SCONJ
ejpam-846	337	8	an	an	DET
ejpam-846	337	9	optimal	optimal	ADJ
ejpam-846	337	10	solution	solution	NOUN
ejpam-846	337	11	π∗	π∗	PROPN
ejpam-846	337	12	∈	∈	PROPN
ejpam-846	337	13	π	π	PROPN
ejpam-846	337	14	of	of	ADP
ejpam-846	337	15	(	(	PUNCT
ejpam-846	337	16	20	20	NUM
ejpam-846	337	17	)	)	PUNCT
ejpam-846	337	18	is	be	AUX
ejpam-846	337	19	feasible	feasible	ADJ
ejpam-846	337	20	in	in	ADP
ejpam-846	337	21	the	the	DET
ejpam-846	337	22	optimization	optimization	NOUN
ejpam-846	337	23	problem	problem	NOUN
ejpam-846	337	24	(	(	PUNCT
ejpam-846	337	25	37	37	NUM
ejpam-846	337	26	)	)	PUNCT
ejpam-846	337	27	,	,	PUNCT
ejpam-846	337	28	then	then	ADV
ejpam-846	337	29	indeed	indeed	ADV
ejpam-846	337	30	φ2(x	φ2(x	VERB
ejpam-846	337	31	)	)	PUNCT
ejpam-846	337	32	=	=	PUNCT
ejpam-846	337	33	φr	φr	SCONJ
ejpam-846	337	34	2	2	NUM
ejpam-846	337	35	(	(	PUNCT
ejpam-846	337	36	x	x	NOUN
ejpam-846	337	37	)	)	PUNCT
ejpam-846	337	38	follows	follow	VERB
ejpam-846	337	39	for	for	ADP
ejpam-846	337	40	the	the	DET
ejpam-846	337	41	chosen	choose	VERB
ejpam-846	337	42	lower	low	ADJ
ejpam-846	337	43	bounding	bounding	NOUN
ejpam-846	337	44	linear	linear	NOUN
ejpam-846	337	45	functions	function	NOUN
ejpam-846	337	46	ℓj	ℓj	VERB
ejpam-846	337	47	.	.	PUNCT
ejpam-846	338	1	generally	generally	ADV
ejpam-846	338	2	,	,	PUNCT
ejpam-846	338	3	an	an	DET
ejpam-846	338	4	arbitrary	arbitrary	ADJ
ejpam-846	338	5	simplicial	simplicial	NOUN
ejpam-846	338	6	lower	low	ADJ
ejpam-846	338	7	approximating	approximate	VERB
ejpam-846	338	8	function	function	NOUN
ejpam-846	338	9	on	on	ADP
ejpam-846	338	10	ϕ	ϕ	NOUN
ejpam-846	338	11	can	can	AUX
ejpam-846	338	12	not	not	PART
ejpam-846	338	13	be	be	AUX
ejpam-846	338	14	expected	expect	VERB
ejpam-846	338	15	to	to	PART
ejpam-846	338	16	solve	solve	VERB
ejpam-846	338	17	the	the	DET
ejpam-846	338	18	moment	moment	NOUN
ejpam-846	338	19	problem	problem	NOUN
ejpam-846	338	20	in	in	ADP
ejpam-846	338	21	(	(	PUNCT
ejpam-846	338	22	18	18	NUM
ejpam-846	338	23	)	)	PUNCT
ejpam-846	338	24	,	,	PUNCT
ejpam-846	338	25	implying	imply	VERB
ejpam-846	338	26	φ2(x	φ2(x	NOUN
ejpam-846	338	27	)	)	PUNCT
ejpam-846	338	28	>	>	X
ejpam-846	338	29	φr	φr	ADP
ejpam-846	338	30	2	2	NUM
ejpam-846	338	31	(	(	PUNCT
ejpam-846	338	32	x	x	NOUN
ejpam-846	338	33	)	)	PUNCT
ejpam-846	338	34	.	.	PUNCT
ejpam-846	339	1	proposition	proposition	NOUN
ejpam-846	339	2	10	10	NUM
ejpam-846	339	3	.	.	PUNCT
ejpam-846	340	1	for	for	ADP
ejpam-846	340	2	polyhedral	polyhedral	ADJ
ejpam-846	340	3	(	(	PUNCT
ejpam-846	340	4	simplicial	simplicial	ADJ
ejpam-846	340	5	)	)	PUNCT
ejpam-846	340	6	function	function	NOUN
ejpam-846	340	7	g	g	NOUN
ejpam-846	340	8	,	,	PUNCT
ejpam-846	340	9	lower	lower	ADV
ejpam-846	340	10	approximating	approximate	VERB
ejpam-846	340	11	ϕ	ϕ	NOUN
ejpam-846	340	12	,	,	PUNCT
ejpam-846	340	13	suppose	suppose	VERB
ejpam-846	340	14	φ2(x	φ2(x	X
ejpam-846	340	15	)	)	PUNCT
ejpam-846	340	16	>	>	X
ejpam-846	340	17	φr	φr	ADP
ejpam-846	340	18	2	2	NUM
ejpam-846	340	19	(	(	PUNCT
ejpam-846	340	20	x	x	NOUN
ejpam-846	340	21	)	)	PUNCT
ejpam-846	340	22	holds	hold	VERB
ejpam-846	340	23	.	.	PUNCT
ejpam-846	341	1	then	then	ADV
ejpam-846	341	2	,	,	PUNCT
ejpam-846	341	3	φr	φr	ADP
ejpam-846	341	4	2	2	NUM
ejpam-846	341	5	(	(	PUNCT
ejpam-846	341	6	x	x	NOUN
ejpam-846	341	7	)	)	PUNCT
ejpam-846	341	8	=	=	SYM
ejpam-846	342	1	k+1∑	k+1∑	PROPN
ejpam-846	342	2	i=1	i=1	PROPN
ejpam-846	342	3	ρi	ρi	INTJ
ejpam-846	342	4	g(x	g(x	NOUN
ejpam-846	342	5	,	,	PUNCT
ejpam-846	342	6	ξ̃	ξ̃	PROPN
ejpam-846	342	7	i	i	NOUN
ejpam-846	342	8	)	)	PUNCT
ejpam-846	342	9	.	.	PUNCT
ejpam-846	343	1	(	(	PUNCT
ejpam-846	343	2	38	38	NUM
ejpam-846	343	3	)	)	PUNCT
ejpam-846	343	4	proof	proof	NOUN
ejpam-846	343	5	.	.	PUNCT
ejpam-846	344	1	considering	consider	VERB
ejpam-846	344	2	the	the	DET
ejpam-846	344	3	semi	semi	ADJ
ejpam-846	344	4	-	-	ADJ
ejpam-846	344	5	infinite	infinite	ADJ
ejpam-846	344	6	program	program	NOUN
ejpam-846	344	7	in	in	ADP
ejpam-846	344	8	(	(	PUNCT
ejpam-846	344	9	37	37	NUM
ejpam-846	344	10	)	)	PUNCT
ejpam-846	344	11	,	,	PUNCT
ejpam-846	344	12	strong	strong	ADJ
ejpam-846	344	13	duality	duality	NOUN
ejpam-846	344	14	must	must	AUX
ejpam-846	344	15	hold	hold	VERB
ejpam-846	344	16	since	since	SCONJ
ejpam-846	344	17	ξ	ξ	PROPN
ejpam-846	344	18	is	be	AUX
ejpam-846	344	19	compact	compact	ADJ
ejpam-846	344	20	and	and	CCONJ
ejpam-846	344	21	ϕ	ϕ	NOUN
ejpam-846	344	22	is	be	AUX
ejpam-846	344	23	continuous	continuous	ADJ
ejpam-846	344	24	,	,	PUNCT
ejpam-846	344	25	see	see	VERB
ejpam-846	344	26	for	for	ADP
ejpam-846	344	27	instance	instance	NOUN
ejpam-846	344	28	,	,	PUNCT
ejpam-846	344	29	anderson	anderson	PROPN
ejpam-846	344	30	and	and	CCONJ
ejpam-846	344	31	nash	nash	PROPN
ejpam-846	345	1	[	[	X
ejpam-846	345	2	1	1	NUM
ejpam-846	345	3	]	]	PUNCT
ejpam-846	345	4	.	.	PUNCT
ejpam-846	346	1	denoting	denote	VERB
ejpam-846	346	2	fg(x	fg(x	NUM
ejpam-846	346	3	)	)	PUNCT
ejpam-846	347	1	:	:	PUNCT
ejpam-846	347	2	=	=	SYM
ejpam-846	347	3	∑k+1	∑k+1	PUNCT
ejpam-846	347	4	i=1	i=1	PROPN
ejpam-846	347	5	ρi	ρi	NOUN
ejpam-846	347	6	g(x	g(x	NOUN
ejpam-846	347	7	,	,	PUNCT
ejpam-846	347	8	ξ̃	ξ̃	PROPN
ejpam-846	347	9	i	i	NOUN
ejpam-846	347	10	)	)	PUNCT
ejpam-846	347	11	,	,	PUNCT
ejpam-846	347	12	therefore	therefore	ADV
ejpam-846	347	13	,	,	PUNCT
ejpam-846	347	14	φr	φr	ADP
ejpam-846	347	15	2	2	NUM
ejpam-846	347	16	(	(	PUNCT
ejpam-846	347	17	x	x	NOUN
ejpam-846	347	18	)	)	PUNCT
ejpam-846	347	19	=	=	SYM
ejpam-846	347	20	inf	inf	PROPN
ejpam-846	347	21	σ	σ	PROPN
ejpam-846	347	22	,	,	PUNCT
ejpam-846	347	23	q	q	PROPN
ejpam-846	347	24	σ	σ	PROPN
ejpam-846	347	25	fg(x	fg(x	NUM
ejpam-846	347	26	)	)	PUNCT
ejpam-846	348	1	+	+	CCONJ
ejpam-846	349	1	∫	∫	X
ejpam-846	349	2	ξ	ξ	X
ejpam-846	349	3	ϕ(x	ϕ(x	PROPN
ejpam-846	349	4	,	,	PUNCT
ejpam-846	349	5	ξ)q(dξ	ξ)q(dξ	NUM
ejpam-846	349	6	)	)	PUNCT
ejpam-846	349	7	(	(	PUNCT
ejpam-846	349	8	39	39	NUM
ejpam-846	349	9	)	)	PUNCT
ejpam-846	349	10	s.t	s.t	PROPN
ejpam-846	349	11	.	.	PROPN
ejpam-846	349	12	σ	σ	PROPN
ejpam-846	350	1	+	+	CCONJ
ejpam-846	350	2	∫	∫	X
ejpam-846	350	3	ξ	ξ	X
ejpam-846	350	4	q(dξ	q(dξ	NOUN
ejpam-846	350	5	)	)	PUNCT
ejpam-846	350	6	=	=	SYM
ejpam-846	351	1	1	1	NUM
ejpam-846	351	2	σ	σ	NUM
ejpam-846	351	3	ξ̄	ξ̄	NOUN
ejpam-846	351	4	+	+	CCONJ
ejpam-846	351	5	∫	∫	PROPN
ejpam-846	351	6	ξ	ξ	PROPN
ejpam-846	351	7	ξq(dξ	ξq(dξ	NUM
ejpam-846	351	8	)	)	PUNCT
ejpam-846	352	1	=	=	VERB
ejpam-846	352	2	ξ̄	ξ̄	ADJ
ejpam-846	352	3	σ	σ	NUM
ejpam-846	352	4	mkl	mkl	PROPN
ejpam-846	352	5	+	+	CCONJ
ejpam-846	352	6	∫	∫	PROPN
ejpam-846	352	7	ξ	ξ	PROPN
ejpam-846	352	8	ξkξlq(dξ	ξkξlq(dξ	PROPN
ejpam-846	352	9	)	)	PUNCT
ejpam-846	352	10	=	=	SYM
ejpam-846	352	11	mkl	mkl	PROPN
ejpam-846	352	12	,	,	PUNCT
ejpam-846	352	13	k	k	NOUN
ejpam-846	352	14	,	,	PUNCT
ejpam-846	352	15	l	l	NOUN
ejpam-846	352	16	=	=	SYM
ejpam-846	352	17	1	1	NUM
ejpam-846	352	18	,	,	PUNCT
ejpam-846	352	19	.	.	PUNCT
ejpam-846	352	20	.	.	PUNCT
ejpam-846	352	21	.	.	PUNCT
ejpam-846	353	1	,	,	PUNCT
ejpam-846	353	2	k	k	PROPN
ejpam-846	353	3	,	,	PUNCT
ejpam-846	353	4	k	k	PROPN
ejpam-846	353	5	≥	≥	PROPN
ejpam-846	353	6	l	l	PROPN
ejpam-846	353	7	σ	σ	X
ejpam-846	353	8	≥	≥	NOUN
ejpam-846	353	9	0	0	NUM
ejpam-846	353	10	,	,	PUNCT
ejpam-846	353	11	q	q	X
ejpam-846	353	12	(	(	PUNCT
ejpam-846	353	13	.	.	PUNCT
ejpam-846	353	14	)	)	PUNCT
ejpam-846	353	15	≥	≥	NOUN
ejpam-846	353	16	0	0	NUM
ejpam-846	353	17	.	.	PUNCT
ejpam-846	353	18	edirisinghe	edirisinghe	PROPN
ejpam-846	353	19	/	/	SYM
ejpam-846	353	20	eur	eur	PROPN
ejpam-846	353	21	.	.	PUNCT
ejpam-846	354	1	j.	j.	PROPN
ejpam-846	354	2	pure	pure	PROPN
ejpam-846	354	3	appl	appl	PROPN
ejpam-846	354	4	.	.	PROPN
ejpam-846	354	5	math	math	PROPN
ejpam-846	354	6	,	,	PUNCT
ejpam-846	354	7	3	3	NUM
ejpam-846	354	8	(	(	PUNCT
ejpam-846	354	9	2010	2010	NUM
ejpam-846	354	10	)	)	PUNCT
ejpam-846	354	11	,	,	PUNCT
ejpam-846	354	12	572	572	NUM
ejpam-846	354	13	-	-	SYM
ejpam-846	354	14	592	592	NUM
ejpam-846	354	15	583	583	NUM
ejpam-846	354	16	since	since	ADV
ejpam-846	354	17	,	,	PUNCT
ejpam-846	354	18	σ	σ	PROPN
ejpam-846	354	19	≤	≤	NOUN
ejpam-846	354	20	1	1	NUM
ejpam-846	354	21	must	must	AUX
ejpam-846	354	22	hold	hold	VERB
ejpam-846	354	23	for	for	ADP
ejpam-846	354	24	feasibility	feasibility	NOUN
ejpam-846	354	25	of	of	ADP
ejpam-846	354	26	(	(	PUNCT
ejpam-846	354	27	39	39	NUM
ejpam-846	354	28	)	)	PUNCT
ejpam-846	354	29	,	,	PUNCT
ejpam-846	354	30	it	it	PRON
ejpam-846	354	31	follows	follow	VERB
ejpam-846	354	32	that	that	SCONJ
ejpam-846	354	33	φr	φr	ADP
ejpam-846	354	34	2	2	NUM
ejpam-846	354	35	(	(	PUNCT
ejpam-846	354	36	x	x	NOUN
ejpam-846	354	37	)	)	PUNCT
ejpam-846	354	38	=	=	SYM
ejpam-846	354	39	inf	inf	PROPN
ejpam-846	354	40	σ	σ	PROPN
ejpam-846	354	41	,	,	PUNCT
ejpam-846	354	42	p	p	PROPN
ejpam-846	354	43	σ	σ	PROPN
ejpam-846	354	44	fg(x	fg(x	NUM
ejpam-846	354	45	)	)	PUNCT
ejpam-846	355	1	+	+	CCONJ
ejpam-846	355	2	(	(	PUNCT
ejpam-846	355	3	1−	1−	NUM
ejpam-846	355	4	σ	σ	PROPN
ejpam-846	355	5	)	)	PUNCT
ejpam-846	355	6	∫	∫	PROPN
ejpam-846	355	7	ξ	ξ	X
ejpam-846	355	8	ϕ(x	ϕ(x	PROPN
ejpam-846	355	9	,	,	PUNCT
ejpam-846	355	10	ξ)p	ξ)p	ADJ
ejpam-846	355	11	(	(	PUNCT
ejpam-846	355	12	dξ	dξ	PROPN
ejpam-846	355	13	)	)	PUNCT
ejpam-846	355	14	(	(	PUNCT
ejpam-846	355	15	40	40	NUM
ejpam-846	355	16	)	)	PUNCT
ejpam-846	355	17	s.t	s.t	PROPN
ejpam-846	355	18	.	.	PROPN
ejpam-846	355	19	0	0	NUM
ejpam-846	356	1	≤	≤	NUM
ejpam-846	356	2	σ	σ	NOUN
ejpam-846	356	3	≤	≤	NUM
ejpam-846	356	4	1	1	NUM
ejpam-846	356	5	,	,	PUNCT
ejpam-846	356	6	p	p	PROPN
ejpam-846	356	7	∈	∈	PROPN
ejpam-846	356	8	p̃.	p̃.	NOUN
ejpam-846	356	9	=	=	PUNCT
ejpam-846	356	10	inf	inf	PROPN
ejpam-846	356	11	σ∈[0,1	σ∈[0,1	NOUN
ejpam-846	356	12	]	]	X
ejpam-846	356	13	σ	σ	X
ejpam-846	356	14	fg(x	fg(x	PUNCT
ejpam-846	356	15	)	)	PUNCT
ejpam-846	357	1	+	+	CCONJ
ejpam-846	357	2	(	(	PUNCT
ejpam-846	357	3	1−	1−	NUM
ejpam-846	357	4	σ)φ2(x	σ)φ2(x	NOUN
ejpam-846	357	5	)	)	PUNCT
ejpam-846	357	6	(	(	PUNCT
ejpam-846	357	7	41	41	NUM
ejpam-846	357	8	)	)	PUNCT
ejpam-846	357	9	=	=	SYM
ejpam-846	357	10	min	min	NOUN
ejpam-846	357	11	{	{	PUNCT
ejpam-846	357	12	fg(x	fg(x	NUM
ejpam-846	357	13	)	)	PUNCT
ejpam-846	357	14	,	,	PUNCT
ejpam-846	357	15	φ2(x	φ2(x	NOUN
ejpam-846	357	16	)	)	PUNCT
ejpam-846	357	17	}	}	PUNCT
ejpam-846	357	18	.	.	PUNCT
ejpam-846	358	1	since	since	SCONJ
ejpam-846	358	2	φ2(x	φ2(x	NUM
ejpam-846	358	3	)	)	PUNCT
ejpam-846	358	4	>	>	X
ejpam-846	358	5	φr	φr	ADP
ejpam-846	358	6	2	2	NUM
ejpam-846	358	7	(	(	PUNCT
ejpam-846	358	8	x	x	NOUN
ejpam-846	358	9	)	)	PUNCT
ejpam-846	358	10	=	=	SYM
ejpam-846	358	11	min	min	NOUN
ejpam-846	358	12	{	{	PUNCT
ejpam-846	358	13	fg(x	fg(x	NUM
ejpam-846	358	14	)	)	PUNCT
ejpam-846	358	15	,	,	PUNCT
ejpam-846	358	16	φ2(x	φ2(x	NOUN
ejpam-846	358	17	)	)	PUNCT
ejpam-846	358	18	}	}	PUNCT
ejpam-846	358	19	,	,	PUNCT
ejpam-846	358	20	we	we	PRON
ejpam-846	358	21	have	have	VERB
ejpam-846	358	22	φr	φr	ADP
ejpam-846	358	23	2	2	NUM
ejpam-846	358	24	(	(	PUNCT
ejpam-846	358	25	x	x	NOUN
ejpam-846	358	26	)	)	PUNCT
ejpam-846	358	27	=	=	PUNCT
ejpam-846	358	28	fg(x	fg(x	X
ejpam-846	358	29	)	)	PUNCT
ejpam-846	358	30	.	.	PUNCT
ejpam-846	359	1	so	so	ADV
ejpam-846	359	2	far	far	ADV
ejpam-846	359	3	,	,	PUNCT
ejpam-846	359	4	the	the	DET
ejpam-846	359	5	lower	low	ADJ
ejpam-846	359	6	approximating	approximate	VERB
ejpam-846	359	7	polyhedral	polyhedral	ADJ
ejpam-846	359	8	(	(	PUNCT
ejpam-846	359	9	simplicial	simplicial	ADJ
ejpam-846	359	10	)	)	PUNCT
ejpam-846	359	11	function	function	NOUN
ejpam-846	359	12	g	g	NOUN
ejpam-846	359	13	is	be	AUX
ejpam-846	359	14	chosen	choose	VERB
ejpam-846	359	15	quite	quite	ADV
ejpam-846	359	16	arbitrarily	arbitrarily	ADV
ejpam-846	359	17	,	,	PUNCT
ejpam-846	359	18	and	and	CCONJ
ejpam-846	359	19	accordingly	accordingly	ADV
ejpam-846	359	20	,	,	PUNCT
ejpam-846	359	21	the	the	DET
ejpam-846	359	22	above	above	ADV
ejpam-846	359	23	lower	lower	ADV
ejpam-846	359	24	bound	bind	VERB
ejpam-846	359	25	fg(x	fg(x	NUM
ejpam-846	359	26	)	)	PUNCT
ejpam-846	359	27	=	=	PUNCT
ejpam-846	359	28	φr	φr	SCONJ
ejpam-846	359	29	2	2	NUM
ejpam-846	359	30	(	(	PUNCT
ejpam-846	359	31	x	x	NOUN
ejpam-846	359	32	)	)	PUNCT
ejpam-846	359	33	may	may	AUX
ejpam-846	359	34	become	become	VERB
ejpam-846	359	35	arbitrarily	arbitrarily	ADV
ejpam-846	359	36	weaker	weak	ADJ
ejpam-846	359	37	compared	compare	VERB
ejpam-846	359	38	to	to	ADP
ejpam-846	359	39	φ2(x	φ2(x	NUM
ejpam-846	359	40	)	)	PUNCT
ejpam-846	359	41	.	.	PUNCT
ejpam-846	360	1	moreover	moreover	ADV
ejpam-846	360	2	,	,	PUNCT
ejpam-846	360	3	this	this	DET
ejpam-846	360	4	lower	lower	ADV
ejpam-846	360	5	bound	bind	VERB
ejpam-846	360	6	is	be	AUX
ejpam-846	360	7	computationally	computationally	ADV
ejpam-846	360	8	tedious	tedious	ADJ
ejpam-846	360	9	since	since	SCONJ
ejpam-846	360	10	g	g	PROPN
ejpam-846	360	11	can	can	AUX
ejpam-846	360	12	be	be	AUX
ejpam-846	360	13	difficult	difficult	ADJ
ejpam-846	360	14	to	to	PART
ejpam-846	360	15	compute	compute	VERB
ejpam-846	360	16	.	.	PUNCT
ejpam-846	361	1	is	be	AUX
ejpam-846	361	2	it	it	PRON
ejpam-846	361	3	possible	possible	ADJ
ejpam-846	361	4	to	to	PART
ejpam-846	361	5	lift	lift	VERB
ejpam-846	361	6	g	g	PRON
ejpam-846	361	7	such	such	ADJ
ejpam-846	361	8	that	that	SCONJ
ejpam-846	361	9	it	it	PRON
ejpam-846	361	10	is	be	AUX
ejpam-846	361	11	lower	lower	ADV
ejpam-846	361	12	-	-	PUNCT
ejpam-846	361	13	approximating	approximate	VERB
ejpam-846	361	14	to	to	ADP
ejpam-846	361	15	ϕ	ϕ	NOUN
ejpam-846	361	16	over	over	ADP
ejpam-846	361	17	ξ	ξ	PROPN
ejpam-846	362	1	and	and	CCONJ
ejpam-846	362	2	it	it	PRON
ejpam-846	362	3	is	be	AUX
ejpam-846	362	4	relatively	relatively	ADV
ejpam-846	362	5	-	-	PUNCT
ejpam-846	362	6	easy	easy	ADJ
ejpam-846	362	7	to	to	PART
ejpam-846	362	8	compute	compute	VERB
ejpam-846	362	9	?	?	PUNCT
ejpam-846	363	1	indeed	indeed	ADV
ejpam-846	363	2	,	,	PUNCT
ejpam-846	363	3	it	it	PRON
ejpam-846	363	4	is	be	AUX
ejpam-846	363	5	possible	possible	ADJ
ejpam-846	363	6	if	if	SCONJ
ejpam-846	363	7	the	the	DET
ejpam-846	363	8	linear	linear	PROPN
ejpam-846	363	9	functions	function	NOUN
ejpam-846	363	10	ℓi	ℓi	PROPN
ejpam-846	363	11	are	be	AUX
ejpam-846	363	12	chosen	choose	VERB
ejpam-846	363	13	as	as	ADP
ejpam-846	363	14	supporting	support	VERB
ejpam-846	363	15	hyperplanes	hyperplane	NOUN
ejpam-846	363	16	to	to	ADP
ejpam-846	363	17	the	the	DET
ejpam-846	363	18	convex	convex	PROPN
ejpam-846	363	19	function	function	NOUN
ejpam-846	363	20	ϕ.	ϕ.	PROPN
ejpam-846	363	21	for	for	ADP
ejpam-846	363	22	this	this	PRON
ejpam-846	363	23	,	,	PUNCT
ejpam-846	363	24	for	for	ADP
ejpam-846	363	25	each	each	DET
ejpam-846	363	26	i	i	NOUN
ejpam-846	363	27	=	=	NOUN
ejpam-846	363	28	1	1	NUM
ejpam-846	363	29	,	,	PUNCT
ejpam-846	363	30	.	.	PUNCT
ejpam-846	363	31	.	.	PUNCT
ejpam-846	364	1	.	.	PUNCT
ejpam-846	365	1	,	,	PUNCT
ejpam-846	365	2	k	k	PROPN
ejpam-846	365	3	+	+	NOUN
ejpam-846	365	4	1	1	NUM
ejpam-846	365	5	,	,	PUNCT
ejpam-846	365	6	define	define	VERB
ejpam-846	365	7	the	the	DET
ejpam-846	365	8	supporting	support	VERB
ejpam-846	365	9	hyperplanes	hyperplane	NOUN
ejpam-846	365	10	to	to	ADP
ejpam-846	365	11	ϕ	ϕ	PRON
ejpam-846	365	12	precisely	precisely	ADV
ejpam-846	365	13	at	at	ADP
ejpam-846	365	14	ξ̃i	ξ̃i	NOUN
ejpam-846	365	15	∈	∈	PROPN
ejpam-846	365	16	ξ	ξ	X
ejpam-846	365	17	by	by	ADP
ejpam-846	365	18	ℓi(x	ℓi(x	NUM
ejpam-846	365	19	,	,	PUNCT
ejpam-846	365	20	ξ	ξ	X
ejpam-846	365	21	)	)	PUNCT
ejpam-846	365	22	:	:	PUNCT
ejpam-846	365	23	=	=	PUNCT
ejpam-846	365	24	ϕ(x	ϕ(x	PROPN
ejpam-846	365	25	,	,	PUNCT
ejpam-846	365	26	ξ̃i	ξ̃i	NOUN
ejpam-846	365	27	)	)	PUNCT
ejpam-846	366	1	+	+	CCONJ
ejpam-846	366	2	∂ϕ(x	∂ϕ(x	ADV
ejpam-846	366	3	,	,	PUNCT
ejpam-846	366	4	ξ̃i)′(ξ	ξ̃i)′(ξ	PROPN
ejpam-846	366	5	−	−	PROPN
ejpam-846	366	6	ξ̃i	ξ̃i	NOUN
ejpam-846	366	7	)	)	PUNCT
ejpam-846	366	8	,	,	PUNCT
ejpam-846	366	9	where	where	SCONJ
ejpam-846	366	10	∂ϕ	∂ϕ	PROPN
ejpam-846	366	11	is	be	AUX
ejpam-846	366	12	a	a	DET
ejpam-846	366	13	subgradient	subgradient	NOUN
ejpam-846	366	14	to	to	ADP
ejpam-846	366	15	ϕ	ϕ	NOUN
ejpam-846	366	16	at	at	ADP
ejpam-846	366	17	ξ̃i	ξ̃i	NOUN
ejpam-846	366	18	.	.	PUNCT
ejpam-846	367	1	then	then	ADV
ejpam-846	367	2	,	,	PUNCT
ejpam-846	367	3	by	by	ADP
ejpam-846	367	4	convexity	convexity	NOUN
ejpam-846	367	5	of	of	ADP
ejpam-846	367	6	ϕ	ϕ	NOUN
ejpam-846	367	7	in	in	ADP
ejpam-846	367	8	ξ	ξ	PROPN
ejpam-846	367	9	,	,	PUNCT
ejpam-846	367	10	ℓi(x	ℓi(x	NUM
ejpam-846	367	11	,	,	PUNCT
ejpam-846	367	12	ξ	ξ	X
ejpam-846	367	13	)	)	PUNCT
ejpam-846	367	14	≤	≤	NOUN
ejpam-846	367	15	ϕ(x	ϕ(x	PROPN
ejpam-846	367	16	,	,	PUNCT
ejpam-846	367	17	ξ	ξ	X
ejpam-846	367	18	)	)	PUNCT
ejpam-846	367	19	on	on	ADP
ejpam-846	367	20	ξ	ξ	PROPN
ejpam-846	367	21	and	and	CCONJ
ejpam-846	367	22	ℓi(x	ℓi(x	NUM
ejpam-846	367	23	,	,	PUNCT
ejpam-846	367	24	ξ̃i	ξ̃i	ADJ
ejpam-846	367	25	)	)	PUNCT
ejpam-846	367	26	=	=	SYM
ejpam-846	367	27	ϕ(x	ϕ(x	PROPN
ejpam-846	367	28	,	,	PUNCT
ejpam-846	367	29	ξ̃i	ξ̃i	NOUN
ejpam-846	367	30	)	)	PUNCT
ejpam-846	367	31	.	.	PUNCT
ejpam-846	368	1	hence	hence	ADV
ejpam-846	368	2	,	,	PUNCT
ejpam-846	368	3	g(x	g(x	PROPN
ejpam-846	368	4	,	,	PUNCT
ejpam-846	368	5	ξ̃j	ξ̃j	NOUN
ejpam-846	368	6	)	)	PUNCT
ejpam-846	368	7	=	=	SYM
ejpam-846	368	8	max	max	PROPN
ejpam-846	368	9	i=1,	i=1,	PROPN
ejpam-846	368	10	...	...	PUNCT
ejpam-846	368	11	,k+1	,k+1	PUNCT
ejpam-846	368	12	{	{	PUNCT
ejpam-846	368	13	ϕ(x	ϕ(x	NOUN
ejpam-846	368	14	,	,	PUNCT
ejpam-846	368	15	ξ̃i	ξ̃i	NOUN
ejpam-846	368	16	)	)	PUNCT
ejpam-846	368	17	+	+	CCONJ
ejpam-846	369	1	∂ϕ(x	∂ϕ(x	ADV
ejpam-846	369	2	,	,	PUNCT
ejpam-846	369	3	ξ̃i)′(ξ̃j	ξ̃i)′(ξ̃j	PUNCT
ejpam-846	369	4	−	−	PROPN
ejpam-846	369	5	ξ̃i	ξ̃i	NOUN
ejpam-846	369	6	)	)	PUNCT
ejpam-846	369	7	}	}	PUNCT
ejpam-846	369	8	(	(	PUNCT
ejpam-846	369	9	42	42	NUM
ejpam-846	369	10	)	)	PUNCT
ejpam-846	369	11	=	=	PUNCT
ejpam-846	370	1	ϕ(x	ϕ(x	PROPN
ejpam-846	370	2	,	,	PUNCT
ejpam-846	370	3	ξ̃j	ξ̃j	NOUN
ejpam-846	370	4	)	)	PUNCT
ejpam-846	370	5	since	since	SCONJ
ejpam-846	370	6	the	the	DET
ejpam-846	370	7	right	right	ADJ
ejpam-846	370	8	hand	hand	NOUN
ejpam-846	370	9	maximum	maximum	NOUN
ejpam-846	370	10	in	in	ADP
ejpam-846	370	11	(	(	PUNCT
ejpam-846	370	12	42	42	NUM
ejpam-846	370	13	)	)	PUNCT
ejpam-846	370	14	is	be	AUX
ejpam-846	370	15	attained	attain	VERB
ejpam-846	370	16	with	with	ADP
ejpam-846	370	17	i	i	PRON
ejpam-846	370	18	=	=	PUNCT
ejpam-846	370	19	j.	j.	PROPN
ejpam-846	371	1	this	this	PRON
ejpam-846	371	2	leads	lead	VERB
ejpam-846	371	3	to	to	ADP
ejpam-846	371	4	the	the	DET
ejpam-846	371	5	following	follow	VERB
ejpam-846	371	6	main	main	ADJ
ejpam-846	371	7	result	result	NOUN
ejpam-846	371	8	:	:	PUNCT
ejpam-846	371	9	proposition	proposition	NOUN
ejpam-846	371	10	11	11	NUM
ejpam-846	371	11	.	.	PUNCT
ejpam-846	372	1	ψ(x	ψ(x	NOUN
ejpam-846	372	2	)	)	PUNCT
ejpam-846	372	3	≥	≥	NOUN
ejpam-846	373	1	φ2(x	φ2(x	NOUN
ejpam-846	373	2	)	)	PUNCT
ejpam-846	373	3	≥	≥	NOUN
ejpam-846	373	4	φr	φr	ADP
ejpam-846	373	5	2	2	NUM
ejpam-846	373	6	(	(	PUNCT
ejpam-846	373	7	x	x	NOUN
ejpam-846	373	8	)	)	PUNCT
ejpam-846	373	9	=	=	SYM
ejpam-846	374	1	k+1∑	k+1∑	PROPN
ejpam-846	374	2	i=1	i=1	PROPN
ejpam-846	375	1	ρi	ρi	PROPN
ejpam-846	375	2	ϕ(x	ϕ(x	PROPN
ejpam-846	375	3	,	,	PUNCT
ejpam-846	375	4	ξ̃	ξ̃	PROPN
ejpam-846	375	5	i	i	X
ejpam-846	375	6	)	)	PUNCT
ejpam-846	376	1	=	=	NOUN
ejpam-846	376	2	:	:	PUNCT
ejpam-846	376	3	ψl(x	ψl(x	NUM
ejpam-846	376	4	)	)	PUNCT
ejpam-846	376	5	.	.	PUNCT
ejpam-846	377	1	(	(	PUNCT
ejpam-846	377	2	43	43	NUM
ejpam-846	377	3	)	)	PUNCT
ejpam-846	377	4	proof	proof	NOUN
ejpam-846	377	5	.	.	PUNCT
ejpam-846	378	1	let	let	VERB
ejpam-846	378	2	an	an	DET
ejpam-846	378	3	optimal	optimal	ADJ
ejpam-846	378	4	probability	probability	NOUN
ejpam-846	378	5	measure	measure	NOUN
ejpam-846	378	6	solving	solve	VERB
ejpam-846	378	7	the	the	DET
ejpam-846	378	8	gmp	gmp	PROPN
ejpam-846	378	9	in	in	ADP
ejpam-846	378	10	(	(	PUNCT
ejpam-846	378	11	18	18	NUM
ejpam-846	378	12	)	)	PUNCT
ejpam-846	378	13	be	be	AUX
ejpam-846	378	14	denoted	denote	VERB
ejpam-846	378	15	by	by	ADP
ejpam-846	378	16	p	p	PROPN
ejpam-846	378	17	∗	∗	NOUN
ejpam-846	378	18	∈	∈	PROPN
ejpam-846	378	19	p̃	p̃	PROPN
ejpam-846	378	20	,	,	PUNCT
ejpam-846	378	21	i.e.	i.e.	X
ejpam-846	378	22	,	,	PUNCT
ejpam-846	378	23	φ2(x	φ2(x	NUM
ejpam-846	379	1	)	)	PUNCT
ejpam-846	379	2	=	=	SYM
ejpam-846	379	3	ep	ep	PROPN
ejpam-846	379	4	∗	∗	NOUN
ejpam-846	379	5	[	[	X
ejpam-846	379	6	ϕ(x	ϕ(x	X
ejpam-846	379	7	,	,	PUNCT
ejpam-846	379	8	ξ	ξ	NOUN
ejpam-846	379	9	)	)	PUNCT
ejpam-846	379	10	]	]	PUNCT
ejpam-846	379	11	.	.	PUNCT
ejpam-846	380	1	then	then	ADV
ejpam-846	380	2	,	,	PUNCT
ejpam-846	380	3	applying	apply	VERB
ejpam-846	380	4	theorem	theorem	NOUN
ejpam-846	380	5	4	4	NUM
ejpam-846	380	6	in	in	ADP
ejpam-846	380	7	edirisinghe	edirisinghe	NOUN
ejpam-846	380	8	[	[	X
ejpam-846	380	9	4	4	X
ejpam-846	380	10	]	]	PUNCT
ejpam-846	380	11	on	on	ADP
ejpam-846	380	12	the	the	DET
ejpam-846	380	13	convex	convex	PROPN
ejpam-846	380	14	function	function	NOUN
ejpam-846	380	15	ϕ	ϕ	NOUN
ejpam-846	380	16	under	under	ADP
ejpam-846	380	17	measure	measure	NOUN
ejpam-846	380	18	p	p	NOUN
ejpam-846	380	19	∗	∗	NOUN
ejpam-846	380	20	,	,	PUNCT
ejpam-846	380	21	φ2(x	φ2(x	NOUN
ejpam-846	380	22	)	)	PUNCT
ejpam-846	380	23	≥	≥	NOUN
ejpam-846	380	24	ψl(x	ψl(x	NUM
ejpam-846	380	25	)	)	PUNCT
ejpam-846	380	26	follows	follow	VERB
ejpam-846	380	27	.	.	PUNCT
ejpam-846	381	1	then	then	ADV
ejpam-846	381	2	,	,	PUNCT
ejpam-846	381	3	from	from	ADP
ejpam-846	381	4	the	the	DET
ejpam-846	381	5	proof	proof	NOUN
ejpam-846	381	6	of	of	ADP
ejpam-846	381	7	proposition	proposition	NOUN
ejpam-846	381	8	10	10	NUM
ejpam-846	381	9	,	,	PUNCT
ejpam-846	381	10	φr	φr	ADP
ejpam-846	381	11	2	2	NUM
ejpam-846	381	12	(	(	PUNCT
ejpam-846	381	13	x	x	NOUN
ejpam-846	381	14	)	)	PUNCT
ejpam-846	381	15	=	=	SYM
ejpam-846	381	16	min	min	NOUN
ejpam-846	381	17	{	{	PUNCT
ejpam-846	381	18	ψl(x	ψl(x	NUM
ejpam-846	381	19	)	)	PUNCT
ejpam-846	381	20	,	,	PUNCT
ejpam-846	381	21	φ2(x	φ2(x	NOUN
ejpam-846	381	22	)	)	PUNCT
ejpam-846	381	23	}	}	PUNCT
ejpam-846	381	24	=	=	SYM
ejpam-846	381	25	ψl(x	ψl(x	NUM
ejpam-846	381	26	)	)	PUNCT
ejpam-846	381	27	.	.	PUNCT
ejpam-846	382	1	therefore	therefore	ADV
ejpam-846	382	2	,	,	PUNCT
ejpam-846	382	3	the	the	DET
ejpam-846	382	4	lifted	lift	VERB
ejpam-846	382	5	simplicial	simplicial	NOUN
ejpam-846	382	6	lower	low	ADJ
ejpam-846	382	7	‘	'	PUNCT
ejpam-846	382	8	supporting	support	VERB
ejpam-846	382	9	’	'	PUNCT
ejpam-846	382	10	approximation	approximation	NOUN
ejpam-846	382	11	on	on	ADP
ejpam-846	382	12	ϕ	ϕ	NOUN
ejpam-846	382	13	at	at	ADP
ejpam-846	382	14	ξ̃i	ξ̃i	PROPN
ejpam-846	382	15	,	,	PUNCT
ejpam-846	382	16	i	i	PRON
ejpam-846	382	17	=	=	NOUN
ejpam-846	382	18	1	1	NUM
ejpam-846	382	19	,	,	PUNCT
ejpam-846	382	20	.	.	PUNCT
ejpam-846	382	21	.	.	PUNCT
ejpam-846	382	22	.	.	PUNCT
ejpam-846	383	1	,	,	PUNCT
ejpam-846	383	2	k	k	PROPN
ejpam-846	383	3	+	+	PROPN
ejpam-846	383	4	1	1	NUM
ejpam-846	383	5	,	,	PUNCT
ejpam-846	383	6	results	result	NOUN
ejpam-846	383	7	in	in	ADP
ejpam-846	383	8	solving	solve	VERB
ejpam-846	383	9	the	the	DET
ejpam-846	383	10	restricted	restricted	ADJ
ejpam-846	383	11	semi	semi	ADJ
ejpam-846	383	12	-	-	ADJ
ejpam-846	383	13	infinite	infinite	ADJ
ejpam-846	383	14	dual	dual	ADV
ejpam-846	383	15	in	in	ADP
ejpam-846	383	16	(	(	PUNCT
ejpam-846	383	17	37	37	NUM
ejpam-846	383	18	)	)	PUNCT
ejpam-846	383	19	.	.	PUNCT
ejpam-846	384	1	while	while	SCONJ
ejpam-846	384	2	the	the	DET
ejpam-846	384	3	result	result	NOUN
ejpam-846	384	4	in	in	ADP
ejpam-846	384	5	edirisinghe	edirisinghe	PROPN
ejpam-846	384	6	[	[	X
ejpam-846	384	7	4	4	NUM
ejpam-846	384	8	,	,	PUNCT
ejpam-846	384	9	theorem	theorem	VERB
ejpam-846	384	10	4	4	NUM
ejpam-846	384	11	]	]	PUNCT
ejpam-846	384	12	was	be	AUX
ejpam-846	384	13	derived	derive	VERB
ejpam-846	384	14	under	under	ADP
ejpam-846	384	15	a	a	DET
ejpam-846	384	16	quite	quite	ADV
ejpam-846	384	17	complicated	complicated	ADJ
ejpam-846	384	18	procedure	procedure	NOUN
ejpam-846	384	19	without	without	ADP
ejpam-846	384	20	any	any	DET
ejpam-846	384	21	reference	reference	NOUN
ejpam-846	384	22	to	to	ADP
ejpam-846	384	23	a	a	DET
ejpam-846	384	24	gmp	gmp	NOUN
ejpam-846	384	25	,	,	PUNCT
ejpam-846	384	26	the	the	DET
ejpam-846	384	27	preceding	precede	VERB
ejpam-846	384	28	analysis	analysis	NOUN
ejpam-846	384	29	reveals	reveal	VERB
ejpam-846	384	30	that	that	SCONJ
ejpam-846	384	31	it	it	PRON
ejpam-846	384	32	indeed	indeed	ADV
ejpam-846	384	33	is	be	AUX
ejpam-846	384	34	the	the	DET
ejpam-846	384	35	solution	solution	NOUN
ejpam-846	384	36	to	to	ADP
ejpam-846	384	37	the	the	DET
ejpam-846	384	38	restricted	restricted	ADJ
ejpam-846	384	39	dual	dual	ADJ
ejpam-846	384	40	of	of	ADP
ejpam-846	384	41	the	the	DET
ejpam-846	384	42	gmp	gmp	PROPN
ejpam-846	384	43	.	.	PUNCT
ejpam-846	385	1	that	that	PRON
ejpam-846	385	2	is	be	AUX
ejpam-846	385	3	,	,	PUNCT
ejpam-846	385	4	there	there	PRON
ejpam-846	385	5	exists	exist	VERB
ejpam-846	385	6	a	a	DET
ejpam-846	385	7	feasible	feasible	ADJ
ejpam-846	385	8	quadratic	quadratic	ADJ
ejpam-846	385	9	function	function	NOUN
ejpam-846	385	10	lower	low	ADJ
ejpam-846	385	11	edirisinghe	edirisinghe	PROPN
ejpam-846	385	12	/	/	SYM
ejpam-846	385	13	eur	eur	PROPN
ejpam-846	385	14	.	.	PUNCT
ejpam-846	386	1	j.	j.	PROPN
ejpam-846	386	2	pure	pure	PROPN
ejpam-846	386	3	appl	appl	PROPN
ejpam-846	386	4	.	.	PROPN
ejpam-846	386	5	math	math	PROPN
ejpam-846	386	6	,	,	PUNCT
ejpam-846	386	7	3	3	NUM
ejpam-846	386	8	(	(	PUNCT
ejpam-846	386	9	2010	2010	NUM
ejpam-846	386	10	)	)	PUNCT
ejpam-846	386	11	,	,	PUNCT
ejpam-846	386	12	572	572	NUM
ejpam-846	386	13	-	-	SYM
ejpam-846	386	14	592	592	NUM
ejpam-846	386	15	584	584	NUM
ejpam-846	386	16	approximating	approximate	VERB
ejpam-846	386	17	ϕ	ϕ	NOUN
ejpam-846	386	18	,	,	PUNCT
ejpam-846	386	19	see	see	VERB
ejpam-846	386	20	(	(	PUNCT
ejpam-846	386	21	21	21	NUM
ejpam-846	386	22	)	)	PUNCT
ejpam-846	386	23	,	,	PUNCT
ejpam-846	386	24	with	with	ADP
ejpam-846	386	25	an	an	DET
ejpam-846	386	26	expected	expect	VERB
ejpam-846	386	27	value	value	NOUN
ejpam-846	386	28	under	under	ADP
ejpam-846	386	29	p	p	NOUN
ejpam-846	386	30	tr	tr	VERB
ejpam-846	386	31	exactly	exactly	ADV
ejpam-846	386	32	equal	equal	ADJ
ejpam-846	386	33	to	to	ADP
ejpam-846	386	34	the	the	DET
ejpam-846	386	35	expected	expect	VERB
ejpam-846	386	36	value	value	NOUN
ejpam-846	386	37	of	of	ADP
ejpam-846	386	38	the	the	DET
ejpam-846	386	39	supporting	support	VERB
ejpam-846	386	40	simplicial	simplicial	NOUN
ejpam-846	386	41	(	(	PUNCT
ejpam-846	386	42	polyhedral	polyhedral	ADJ
ejpam-846	386	43	)	)	PUNCT
ejpam-846	386	44	function	function	NOUN
ejpam-846	386	45	on	on	ADP
ejpam-846	386	46	ϕ	ϕ	NOUN
ejpam-846	386	47	under	under	ADP
ejpam-846	386	48	the	the	DET
ejpam-846	386	49	derived	derive	VERB
ejpam-846	386	50	probability	probability	NOUN
ejpam-846	386	51	measure	measure	NOUN
ejpam-846	386	52	{	{	PUNCT
ejpam-846	386	53	(	(	PUNCT
ejpam-846	386	54	ξ̃i	ξ̃i	ADJ
ejpam-846	386	55	,	,	PUNCT
ejpam-846	386	56	ρi	ρi	PROPN
ejpam-846	386	57	)	)	PUNCT
ejpam-846	386	58	:	:	PUNCT
ejpam-846	387	1	i	i	NOUN
ejpam-846	387	2	=	=	NOUN
ejpam-846	387	3	1	1	NUM
ejpam-846	387	4	,	,	PUNCT
ejpam-846	387	5	.	.	PUNCT
ejpam-846	387	6	.	.	PUNCT
ejpam-846	387	7	.	.	PUNCT
ejpam-846	388	1	,	,	PUNCT
ejpam-846	388	2	k	k	PROPN
ejpam-846	388	3	+	+	PROPN
ejpam-846	388	4	1	1	NUM
ejpam-846	388	5	}	}	PUNCT
ejpam-846	388	6	.	.	PUNCT
ejpam-846	389	1	this	this	PRON
ejpam-846	389	2	is	be	AUX
ejpam-846	389	3	the	the	DET
ejpam-846	389	4	first	first	ADJ
ejpam-846	389	5	instance	instance	NOUN
ejpam-846	389	6	the	the	DET
ejpam-846	389	7	latter	latter	ADJ
ejpam-846	389	8	relation	relation	NOUN
ejpam-846	389	9	to	to	ADP
ejpam-846	389	10	the	the	DET
ejpam-846	389	11	underlying	underlie	VERB
ejpam-846	389	12	mean	mean	ADJ
ejpam-846	389	13	-	-	PUNCT
ejpam-846	389	14	covariance	covariance	NOUN
ejpam-846	389	15	moment	moment	NOUN
ejpam-846	389	16	problem	problem	NOUN
ejpam-846	389	17	is	be	AUX
ejpam-846	389	18	investigated	investigate	VERB
ejpam-846	389	19	.	.	PUNCT
ejpam-846	390	1	furthermore	furthermore	ADV
ejpam-846	390	2	,	,	PUNCT
ejpam-846	390	3	the	the	DET
ejpam-846	390	4	derivation	derivation	NOUN
ejpam-846	390	5	in	in	ADP
ejpam-846	390	6	this	this	DET
ejpam-846	390	7	paper	paper	NOUN
ejpam-846	390	8	underscores	underscore	VERB
ejpam-846	390	9	the	the	DET
ejpam-846	390	10	fact	fact	NOUN
ejpam-846	390	11	that	that	SCONJ
ejpam-846	390	12	a	a	DET
ejpam-846	390	13	simplicial	simplicial	ADJ
ejpam-846	390	14	polyhedral	polyhedral	ADJ
ejpam-846	390	15	lower	low	ADJ
ejpam-846	390	16	approximation	approximation	NOUN
ejpam-846	390	17	is	be	AUX
ejpam-846	390	18	likely	likely	ADJ
ejpam-846	390	19	to	to	PART
ejpam-846	390	20	fail	fail	VERB
ejpam-846	390	21	in	in	ADP
ejpam-846	390	22	solving	solve	VERB
ejpam-846	390	23	the	the	DET
ejpam-846	390	24	moment	moment	NOUN
ejpam-846	390	25	problem	problem	NOUN
ejpam-846	390	26	(	(	PUNCT
ejpam-846	390	27	18	18	NUM
ejpam-846	390	28	)	)	PUNCT
ejpam-846	390	29	as	as	ADP
ejpam-846	390	30	evident	evident	ADJ
ejpam-846	390	31	from	from	ADP
ejpam-846	390	32	the	the	DET
ejpam-846	390	33	inequality	inequality	NOUN
ejpam-846	390	34	φ2(x	φ2(x	NOUN
ejpam-846	390	35	)	)	PUNCT
ejpam-846	390	36	≥	≥	NOUN
ejpam-846	390	37	φr	φr	ADP
ejpam-846	390	38	2	2	NUM
ejpam-846	390	39	(	(	PUNCT
ejpam-846	390	40	x	x	NOUN
ejpam-846	390	41	)	)	PUNCT
ejpam-846	390	42	.	.	PUNCT
ejpam-846	391	1	hence	hence	ADV
ejpam-846	391	2	,	,	PUNCT
ejpam-846	391	3	it	it	PRON
ejpam-846	391	4	remains	remain	VERB
ejpam-846	391	5	an	an	DET
ejpam-846	391	6	open	open	ADJ
ejpam-846	391	7	question	question	NOUN
ejpam-846	391	8	at	at	ADP
ejpam-846	391	9	this	this	DET
ejpam-846	391	10	point	point	NOUN
ejpam-846	391	11	whether	whether	SCONJ
ejpam-846	391	12	φ2(x	φ2(x	VERB
ejpam-846	391	13	)	)	PUNCT
ejpam-846	391	14	=	=	PUNCT
ejpam-846	391	15	φr	φr	SCONJ
ejpam-846	391	16	2	2	NUM
ejpam-846	391	17	(	(	PUNCT
ejpam-846	391	18	x	x	NOUN
ejpam-846	391	19	)	)	PUNCT
ejpam-846	391	20	can	can	AUX
ejpam-846	391	21	be	be	AUX
ejpam-846	391	22	attained	attain	VERB
ejpam-846	391	23	with	with	ADP
ejpam-846	391	24	the	the	DET
ejpam-846	391	25	supporting	support	VERB
ejpam-846	391	26	simplicial	simplicial	ADJ
ejpam-846	391	27	function	function	NOUN
ejpam-846	391	28	constructed	construct	VERB
ejpam-846	391	29	at	at	ADP
ejpam-846	391	30	ξ̃i	ξ̃i	NOUN
ejpam-846	391	31	,	,	PUNCT
ejpam-846	391	32	i	i	PRON
ejpam-846	391	33	=	=	NOUN
ejpam-846	391	34	1	1	NUM
ejpam-846	391	35	,	,	PUNCT
ejpam-846	391	36	.	.	PUNCT
ejpam-846	391	37	.	.	PUNCT
ejpam-846	392	1	.	.	PUNCT
ejpam-846	393	1	,	,	PUNCT
ejpam-846	393	2	k	k	PROPN
ejpam-846	393	3	+	+	PROPN
ejpam-846	393	4	1	1	NUM
ejpam-846	393	5	,	,	PUNCT
ejpam-846	393	6	for	for	ADP
ejpam-846	393	7	a	a	DET
ejpam-846	393	8	general	general	ADJ
ejpam-846	393	9	convex	convex	NOUN
ejpam-846	393	10	function	function	NOUN
ejpam-846	393	11	ϕ.	ϕ.	PROPN
ejpam-846	393	12	4	4	X
ejpam-846	393	13	.	.	PUNCT
ejpam-846	393	14	financial	financial	ADJ
ejpam-846	393	15	optimization	optimization	NOUN
ejpam-846	393	16	model	model	NOUN
ejpam-846	393	17	the	the	DET
ejpam-846	393	18	usefulness	usefulness	NOUN
ejpam-846	393	19	and	and	CCONJ
ejpam-846	393	20	quality	quality	NOUN
ejpam-846	393	21	of	of	ADP
ejpam-846	393	22	the	the	DET
ejpam-846	393	23	mean	mean	ADJ
ejpam-846	393	24	and	and	CCONJ
ejpam-846	393	25	variance	variance	NOUN
ejpam-846	393	26	-	-	PUNCT
ejpam-846	393	27	covariance	covariance	NOUN
ejpam-846	393	28	approximation	approximation	NOUN
ejpam-846	393	29	of	of	ADP
ejpam-846	393	30	expectation	expectation	NOUN
ejpam-846	393	31	functionals	functional	NOUN
ejpam-846	393	32	are	be	AUX
ejpam-846	393	33	investigated	investigate	VERB
ejpam-846	393	34	in	in	ADP
ejpam-846	393	35	the	the	DET
ejpam-846	393	36	context	context	NOUN
ejpam-846	393	37	of	of	ADP
ejpam-846	393	38	a	a	DET
ejpam-846	393	39	financial	financial	ADJ
ejpam-846	393	40	optimization	optimization	NOUN
ejpam-846	393	41	model	model	NOUN
ejpam-846	393	42	.	.	PUNCT
ejpam-846	394	1	as	as	SCONJ
ejpam-846	394	2	presented	present	VERB
ejpam-846	394	3	in	in	ADP
ejpam-846	394	4	section	section	NOUN
ejpam-846	394	5	1	1	NUM
ejpam-846	394	6	,	,	PUNCT
ejpam-846	394	7	the	the	DET
ejpam-846	394	8	expectation	expectation	NOUN
ejpam-846	394	9	functional	functional	ADJ
ejpam-846	394	10	is	be	AUX
ejpam-846	394	11	the	the	DET
ejpam-846	394	12	risk	risk	NOUN
ejpam-846	394	13	component	component	NOUN
ejpam-846	394	14	ψ(x	ψ(x	NOUN
ejpam-846	394	15	)	)	PUNCT
ejpam-846	394	16	of	of	ADP
ejpam-846	394	17	the	the	DET
ejpam-846	394	18	investment	investment	NOUN
ejpam-846	394	19	portfolio	portfolio	NOUN
ejpam-846	394	20	problem	problem	NOUN
ejpam-846	394	21	(	(	PUNCT
ejpam-846	394	22	1	1	NUM
ejpam-846	394	23	)	)	PUNCT
ejpam-846	394	24	,	,	PUNCT
ejpam-846	394	25	where	where	SCONJ
ejpam-846	394	26	specific	specific	ADJ
ejpam-846	394	27	risks	risk	NOUN
ejpam-846	394	28	are	be	AUX
ejpam-846	394	29	computed	compute	VERB
ejpam-846	394	30	by	by	ADP
ejpam-846	394	31	(	(	PUNCT
ejpam-846	394	32	2	2	NUM
ejpam-846	394	33	)	)	PUNCT
ejpam-846	394	34	adapted	adapt	VERB
ejpam-846	394	35	to	to	ADP
ejpam-846	394	36	realizations	realization	NOUN
ejpam-846	394	37	ξ	ξ	PROPN
ejpam-846	394	38	.	.	PUNCT
ejpam-846	395	1	we	we	PRON
ejpam-846	395	2	will	will	AUX
ejpam-846	395	3	specialize	specialize	VERB
ejpam-846	395	4	this	this	DET
ejpam-846	395	5	model	model	NOUN
ejpam-846	395	6	in	in	ADP
ejpam-846	395	7	this	this	DET
ejpam-846	395	8	section	section	NOUN
ejpam-846	395	9	to	to	ADP
ejpam-846	395	10	the	the	DET
ejpam-846	395	11	following	follow	VERB
ejpam-846	395	12	case	case	NOUN
ejpam-846	395	13	.	.	PUNCT
ejpam-846	396	1	consider	consider	VERB
ejpam-846	396	2	k	k	PROPN
ejpam-846	396	3	risky	risky	ADJ
ejpam-846	396	4	assets	asset	NOUN
ejpam-846	396	5	for	for	ADP
ejpam-846	396	6	portfolio	portfolio	NOUN
ejpam-846	396	7	allocation	allocation	NOUN
ejpam-846	396	8	of	of	ADP
ejpam-846	396	9	a	a	DET
ejpam-846	396	10	total	total	ADJ
ejpam-846	396	11	budget	budget	NOUN
ejpam-846	396	12	b0	b0	NOUN
ejpam-846	396	13	,	,	PUNCT
ejpam-846	396	14	given	give	VERB
ejpam-846	396	15	the	the	DET
ejpam-846	396	16	current	current	ADJ
ejpam-846	396	17	(	(	PUNCT
ejpam-846	396	18	initial	initial	ADJ
ejpam-846	396	19	)	)	PUNCT
ejpam-846	396	20	$	$	SYM
ejpam-846	396	21	investment	investment	NOUN
ejpam-846	396	22	in	in	ADP
ejpam-846	396	23	each	each	DET
ejpam-846	396	24	asset	asset	NOUN
ejpam-846	396	25	by	by	ADP
ejpam-846	396	26	x0j	x0j	PROPN
ejpam-846	396	27	,	,	PUNCT
ejpam-846	396	28	j	j	PROPN
ejpam-846	396	29	=	=	SYM
ejpam-846	396	30	1	1	NUM
ejpam-846	396	31	,	,	PUNCT
ejpam-846	396	32	.	.	PUNCT
ejpam-846	396	33	.	.	PUNCT
ejpam-846	397	1	.	.	PUNCT
ejpam-846	398	1	,	,	PUNCT
ejpam-846	398	2	k.	k.	PROPN
ejpam-846	399	1	an	an	DET
ejpam-846	399	2	optimal	optimal	ADJ
ejpam-846	399	3	allocation	allocation	NOUN
ejpam-846	399	4	is	be	AUX
ejpam-846	399	5	desired	desire	VERB
ejpam-846	399	6	for	for	ADP
ejpam-846	399	7	a	a	DET
ejpam-846	399	8	future	future	ADJ
ejpam-846	399	9	period	period	NOUN
ejpam-846	399	10	(	(	PUNCT
ejpam-846	399	11	of	of	ADP
ejpam-846	399	12	length	length	NOUN
ejpam-846	399	13	τ	τ	PROPN
ejpam-846	399	14	days	day	NOUN
ejpam-846	399	15	)	)	PUNCT
ejpam-846	399	16	and	and	CCONJ
ejpam-846	399	17	it	it	PRON
ejpam-846	399	18	is	be	AUX
ejpam-846	399	19	denoted	denote	VERB
ejpam-846	399	20	by	by	ADP
ejpam-846	399	21	xj	xj	PROPN
ejpam-846	399	22	,	,	PUNCT
ejpam-846	399	23	j	j	PROPN
ejpam-846	400	1	=	=	SYM
ejpam-846	400	2	1	1	NUM
ejpam-846	400	3	,	,	PUNCT
ejpam-846	400	4	.	.	PUNCT
ejpam-846	400	5	.	.	PUNCT
ejpam-846	401	1	.	.	PUNCT
ejpam-846	402	1	,	,	PUNCT
ejpam-846	402	2	k.	k.	PROPN
ejpam-846	402	3	such	such	DET
ejpam-846	402	4	a	a	DET
ejpam-846	402	5	portfolio	portfolio	NOUN
ejpam-846	402	6	revision	revision	NOUN
ejpam-846	402	7	incurs	incur	VERB
ejpam-846	402	8	transactions	transaction	NOUN
ejpam-846	402	9	and	and	CCONJ
ejpam-846	402	10	slippage	slippage	NOUN
ejpam-846	402	11	costs	cost	NOUN
ejpam-846	402	12	and	and	CCONJ
ejpam-846	402	13	this	this	DET
ejpam-846	402	14	loss	loss	NOUN
ejpam-846	402	15	function	function	NOUN
ejpam-846	402	16	is	be	AUX
ejpam-846	402	17	denoted	denote	VERB
ejpam-846	402	18	by	by	ADP
ejpam-846	402	19	l	l	PROPN
ejpam-846	402	20	(	(	PUNCT
ejpam-846	402	21	.	.	PUNCT
ejpam-846	402	22	)	)	PUNCT
ejpam-846	402	23	.	.	PUNCT
ejpam-846	403	1	as	as	SCONJ
ejpam-846	403	2	proposed	propose	VERB
ejpam-846	403	3	in	in	ADP
ejpam-846	403	4	edirisinghe	edirisinghe	PROPN
ejpam-846	403	5	[	[	X
ejpam-846	403	6	5	5	NUM
ejpam-846	403	7	]	]	PUNCT
ejpam-846	403	8	,	,	PUNCT
ejpam-846	403	9	to	to	PART
ejpam-846	403	10	account	account	VERB
ejpam-846	403	11	for	for	ADP
ejpam-846	403	12	possibly	possibly	ADV
ejpam-846	403	13	investing	invest	VERB
ejpam-846	403	14	in	in	ADP
ejpam-846	403	15	stocks	stock	NOUN
ejpam-846	403	16	with	with	ADP
ejpam-846	403	17	relatively	relatively	ADV
ejpam-846	403	18	light	light	ADJ
ejpam-846	403	19	trading	trading	NOUN
ejpam-846	403	20	volume	volume	NOUN
ejpam-846	403	21	,	,	PUNCT
ejpam-846	403	22	a	a	DET
ejpam-846	403	23	loss	loss	NOUN
ejpam-846	403	24	function	function	NOUN
ejpam-846	403	25	that	that	PRON
ejpam-846	403	26	is	be	AUX
ejpam-846	403	27	inversely	inversely	ADV
ejpam-846	403	28	proportional	proportional	ADJ
ejpam-846	403	29	to	to	ADP
ejpam-846	403	30	the	the	DET
ejpam-846	403	31	trade	trade	NOUN
ejpam-846	403	32	size	size	NOUN
ejpam-846	403	33	,	,	PUNCT
ejpam-846	403	34	zj	zj	PROPN
ejpam-846	403	35	in	in	ADP
ejpam-846	403	36	asset	asset	PROPN
ejpam-846	403	37	j	j	PROPN
ejpam-846	403	38	,	,	PUNCT
ejpam-846	403	39	is	be	AUX
ejpam-846	403	40	desired	desire	VERB
ejpam-846	403	41	.	.	PUNCT
ejpam-846	404	1	adopting	adopt	VERB
ejpam-846	404	2	from	from	ADP
ejpam-846	404	3	the	the	DET
ejpam-846	404	4	latter	latter	ADJ
ejpam-846	404	5	reference	reference	NOUN
ejpam-846	404	6	,	,	PUNCT
ejpam-846	404	7	we	we	PRON
ejpam-846	404	8	use	use	VERB
ejpam-846	404	9	the	the	DET
ejpam-846	404	10	quadratic	quadratic	ADJ
ejpam-846	404	11	loss	loss	NOUN
ejpam-846	404	12	function	function	NOUN
ejpam-846	404	13	,	,	PUNCT
ejpam-846	404	14	for	for	SCONJ
ejpam-846	404	15	(	(	PUNCT
ejpam-846	404	16	market	market	NOUN
ejpam-846	404	17	calibrated	calibrate	VERB
ejpam-846	404	18	)	)	PUNCT
ejpam-846	404	19	constants	constant	VERB
ejpam-846	404	20	a1j	a1j	NOUN
ejpam-846	404	21	and	and	CCONJ
ejpam-846	404	22	a2j	a2j	NOUN
ejpam-846	404	23	,	,	PUNCT
ejpam-846	404	24	lj(zj	lj(zj	PROPN
ejpam-846	404	25	)	)	PUNCT
ejpam-846	404	26	=	=	PUNCT
ejpam-846	404	27	a1jzj	a1jzj	PROPN
ejpam-846	405	1	+	+	NUM
ejpam-846	405	2	a2j	a2j	PROPN
ejpam-846	405	3	(	(	PUNCT
ejpam-846	405	4	zj	zj	NOUN
ejpam-846	405	5	)	)	PUNCT
ejpam-846	405	6	2	2	NUM
ejpam-846	405	7	volj	volj	NOUN
ejpam-846	405	8	,	,	PUNCT
ejpam-846	405	9	where	where	SCONJ
ejpam-846	405	10	volj	volj	NOUN
ejpam-846	405	11	is	be	AUX
ejpam-846	405	12	the	the	DET
ejpam-846	405	13	(	(	PUNCT
ejpam-846	405	14	estimated	estimate	VERB
ejpam-846	405	15	)	)	PUNCT
ejpam-846	405	16	market	market	NOUN
ejpam-846	405	17	total	total	ADJ
ejpam-846	405	18	daily	daily	ADJ
ejpam-846	405	19	trading	trading	NOUN
ejpam-846	405	20	dollar	dollar	NOUN
ejpam-846	405	21	volume	volume	NOUN
ejpam-846	405	22	and	and	CCONJ
ejpam-846	405	23	zj	zj	PROPN
ejpam-846	405	24	is	be	AUX
ejpam-846	405	25	the	the	DET
ejpam-846	405	26	dollar	dollar	NOUN
ejpam-846	405	27	volume	volume	NOUN
ejpam-846	405	28	of	of	ADP
ejpam-846	405	29	shares	share	NOUN
ejpam-846	405	30	purchased	purchase	VERB
ejpam-846	405	31	/	/	SYM
ejpam-846	405	32	sold	sell	VERB
ejpam-846	405	33	in	in	ADP
ejpam-846	405	34	asset	asset	PROPN
ejpam-846	405	35	j	j	PROPN
ejpam-846	405	36	,	,	PUNCT
ejpam-846	405	37	i.e.	i.e.	X
ejpam-846	405	38	,	,	PUNCT
ejpam-846	405	39	zj	zj	X
ejpam-846	405	40	=	=	SYM
ejpam-846	405	41	|xj	|xj	NUM
ejpam-846	406	1	−	−	PROPN
ejpam-846	406	2	x0j	x0j	PROPN
ejpam-846	407	1	|	|	INTJ
ejpam-846	407	2	.	.	PUNCT
ejpam-846	408	1	we	we	PRON
ejpam-846	408	2	will	will	AUX
ejpam-846	408	3	allow	allow	VERB
ejpam-846	408	4	‘	'	PUNCT
ejpam-846	408	5	going	go	VERB
ejpam-846	408	6	long	long	ADV
ejpam-846	408	7	’	'	PUNCT
ejpam-846	408	8	or	or	CCONJ
ejpam-846	408	9	‘	'	PUNCT
ejpam-846	408	10	selling	sell	VERB
ejpam-846	408	11	short	short	ADJ
ejpam-846	408	12	’	'	PUNCT
ejpam-846	408	13	in	in	ADP
ejpam-846	408	14	each	each	DET
ejpam-846	408	15	asset	asset	NOUN
ejpam-846	408	16	,	,	PUNCT
ejpam-846	408	17	implying	imply	VERB
ejpam-846	408	18	xj	xj	PROPN
ejpam-846	408	19	∈	∈	PROPN
ejpam-846	408	20	ℜ	ℜ	PROPN
ejpam-846	408	21	,	,	PUNCT
ejpam-846	408	22	and	and	CCONJ
ejpam-846	408	23	thus	thus	ADV
ejpam-846	408	24	,	,	PUNCT
ejpam-846	408	25	such	such	ADJ
ejpam-846	408	26	portfolios	portfolio	NOUN
ejpam-846	408	27	are	be	AUX
ejpam-846	408	28	likely	likely	ADJ
ejpam-846	408	29	to	to	PART
ejpam-846	408	30	encounter	encounter	VERB
ejpam-846	408	31	greater	great	ADJ
ejpam-846	408	32	risk	risk	NOUN
ejpam-846	408	33	relative	relative	ADJ
ejpam-846	408	34	to	to	ADP
ejpam-846	408	35	the	the	DET
ejpam-846	408	36	overall	overall	ADJ
ejpam-846	408	37	market	market	NOUN
ejpam-846	408	38	.	.	PUNCT
ejpam-846	409	1	one	one	NUM
ejpam-846	409	2	way	way	NOUN
ejpam-846	409	3	to	to	PART
ejpam-846	409	4	circumvent	circumvent	VERB
ejpam-846	409	5	the	the	DET
ejpam-846	409	6	market	market	NOUN
ejpam-846	409	7	dependent	dependent	ADJ
ejpam-846	409	8	risk	risk	NOUN
ejpam-846	409	9	is	be	AUX
ejpam-846	409	10	to	to	PART
ejpam-846	409	11	require	require	VERB
ejpam-846	409	12	that	that	SCONJ
ejpam-846	409	13	the	the	DET
ejpam-846	409	14	portfolio	portfolio	NOUN
ejpam-846	409	15	’s	’s	PART
ejpam-846	409	16	correlation	correlation	NOUN
ejpam-846	409	17	with	with	ADP
ejpam-846	409	18	the	the	DET
ejpam-846	409	19	market	market	NOUN
ejpam-846	409	20	be	be	AUX
ejpam-846	409	21	controlled	control	VERB
ejpam-846	409	22	in	in	ADP
ejpam-846	409	23	the	the	DET
ejpam-846	409	24	sense	sense	NOUN
ejpam-846	409	25	that	that	SCONJ
ejpam-846	409	26	portfolio	portfolio	NOUN
ejpam-846	409	27	beta	beta	NOUN
ejpam-846	409	28	is	be	AUX
ejpam-846	409	29	within	within	ADP
ejpam-846	409	30	acceptable	acceptable	ADJ
ejpam-846	409	31	levels	level	NOUN
ejpam-846	409	32	,	,	PUNCT
ejpam-846	409	33	see	see	VERB
ejpam-846	409	34	edirisinghe	edirisinghe	NOUN
ejpam-846	409	35	[	[	X
ejpam-846	409	36	5	5	NUM
ejpam-846	409	37	]	]	PUNCT
ejpam-846	409	38	,	,	PUNCT
ejpam-846	409	39	referred	refer	VERB
ejpam-846	409	40	to	to	ADP
ejpam-846	409	41	as	as	ADP
ejpam-846	409	42	portfolio	portfolio	NOUN
ejpam-846	409	43	’s	’s	PART
ejpam-846	409	44	degree	degree	NOUN
ejpam-846	409	45	of	of	ADP
ejpam-846	409	46	market	market	NOUN
ejpam-846	409	47	neutrality	neutrality	NOUN
ejpam-846	409	48	(	(	PUNCT
ejpam-846	409	49	dmn	dmn	PROPN
ejpam-846	409	50	)	)	PUNCT
ejpam-846	409	51	.	.	PUNCT
ejpam-846	410	1	let	let	VERB
ejpam-846	410	2	the	the	DET
ejpam-846	410	3	“	"	PUNCT
ejpam-846	410	4	beta	beta	NOUN
ejpam-846	410	5	”	"	PUNCT
ejpam-846	410	6	of	of	ADP
ejpam-846	410	7	asset	asset	NOUN
ejpam-846	410	8	j	j	PROPN
ejpam-846	410	9	be	be	AUX
ejpam-846	410	10	given	give	VERB
ejpam-846	410	11	by	by	ADP
ejpam-846	410	12	βj	βj	PRON
ejpam-846	410	13	,	,	PUNCT
ejpam-846	410	14	which	which	PRON
ejpam-846	410	15	measures	measure	VERB
ejpam-846	410	16	the	the	DET
ejpam-846	410	17	correlated	correlate	VERB
ejpam-846	410	18	-	-	PUNCT
ejpam-846	410	19	dependence	dependence	NOUN
ejpam-846	410	20	of	of	ADP
ejpam-846	410	21	asset	asset	NOUN
ejpam-846	410	22	return	return	NOUN
ejpam-846	410	23	with	with	ADP
ejpam-846	410	24	market	market	NOUN
ejpam-846	410	25	return	return	NOUN
ejpam-846	410	26	.	.	PUNCT
ejpam-846	411	1	denoting	denote	VERB
ejpam-846	411	2	the	the	DET
ejpam-846	411	3	market	market	NOUN
ejpam-846	411	4	(	(	PUNCT
ejpam-846	411	5	τ	τ	X
ejpam-846	411	6	-day	-day	NUM
ejpam-846	411	7	)	)	PUNCT
ejpam-846	411	8	random	random	ADJ
ejpam-846	411	9	return	return	NOUN
ejpam-846	411	10	by	by	ADP
ejpam-846	411	11	ζm	ζm	ADP
ejpam-846	411	12	,	,	PUNCT
ejpam-846	411	13	and	and	CCONJ
ejpam-846	411	14	that	that	PRON
ejpam-846	411	15	of	of	ADP
ejpam-846	411	16	the	the	DET
ejpam-846	411	17	asset	asset	NOUN
ejpam-846	411	18	by	by	ADP
ejpam-846	411	19	ξj	ξj	NOUN
ejpam-846	411	20	,	,	PUNCT
ejpam-846	411	21	we	we	PRON
ejpam-846	411	22	have	have	VERB
ejpam-846	411	23	βj	βj	NOUN
ejpam-846	411	24	=	=	NOUN
ejpam-846	411	25	cov(ξj	cov(ξj	NOUN
ejpam-846	411	26	,	,	PUNCT
ejpam-846	411	27	ζm)/[σjjv	ζm)/[σjjv	PROPN
ejpam-846	411	28	ar(ζm)]0.5	ar(ζm)]0.5	NUM
ejpam-846	411	29	,	,	PUNCT
ejpam-846	411	30	where	where	SCONJ
ejpam-846	411	31	σjj	σjj	NOUN
ejpam-846	411	32	is	be	AUX
ejpam-846	411	33	the	the	DET
ejpam-846	411	34	variance	variance	NOUN
ejpam-846	411	35	of	of	ADP
ejpam-846	411	36	asset	asset	NOUN
ejpam-846	411	37	return	return	NOUN
ejpam-846	411	38	ξj	ξj	NOUN
ejpam-846	411	39	.	.	PUNCT
ejpam-846	412	1	we	we	PRON
ejpam-846	412	2	use	use	VERB
ejpam-846	412	3	standard	standard	NOUN
ejpam-846	412	4	and	and	CCONJ
ejpam-846	412	5	poors	poor	NOUN
ejpam-846	412	6	500	500	NUM
ejpam-846	412	7	index	index	NOUN
ejpam-846	412	8	as	as	ADP
ejpam-846	412	9	the	the	DET
ejpam-846	412	10	proxy	proxy	NOUN
ejpam-846	412	11	for	for	ADP
ejpam-846	412	12	the	the	DET
ejpam-846	412	13	market	market	NOUN
ejpam-846	412	14	.	.	PUNCT
ejpam-846	413	1	specifying	specify	VERB
ejpam-846	413	2	the	the	DET
ejpam-846	413	3	‘	'	PUNCT
ejpam-846	413	4	portfolio	portfolio	NOUN
ejpam-846	413	5	beta	beta	NOUN
ejpam-846	413	6	’	'	PUNCT
ejpam-846	413	7	to	to	PART
ejpam-846	413	8	be	be	AUX
ejpam-846	413	9	within	within	ADP
ejpam-846	413	10	±100ν%	±100ν%	NOUN
ejpam-846	413	11	,	,	PUNCT
ejpam-846	413	12	the	the	DET
ejpam-846	413	13	dmn	dmn	NOUN
ejpam-846	413	14	constraint	constraint	NOUN
ejpam-846	413	15	is	be	AUX
ejpam-846	413	16	given	give	VERB
ejpam-846	413	17	by	by	ADP
ejpam-846	413	18	,	,	PUNCT
ejpam-846	413	19	∑k	∑k	PROPN
ejpam-846	413	20	j=1	j=1	NOUN
ejpam-846	413	21	βjxj	βjxj	INTJ
ejpam-846	413	22	∈	∈	PROPN
ejpam-846	414	1	[	[	X
ejpam-846	414	2	−ν	−ν	NOUN
ejpam-846	414	3	b0	b0	NOUN
ejpam-846	414	4	,	,	PUNCT
ejpam-846	414	5	+	+	NOUN
ejpam-846	414	6	ν	ν	NOUN
ejpam-846	414	7	b0	b0	NOUN
ejpam-846	414	8	]	]	PUNCT
ejpam-846	414	9	,	,	PUNCT
ejpam-846	414	10	and	and	CCONJ
ejpam-846	414	11	thus	thus	ADV
ejpam-846	414	12	,	,	PUNCT
ejpam-846	414	13	when	when	SCONJ
ejpam-846	414	14	ν	ν	PROPN
ejpam-846	414	15	≈	≈	PROPN
ejpam-846	414	16	0	0	PROPN
ejpam-846	414	17	,	,	PUNCT
ejpam-846	414	18	the	the	DET
ejpam-846	414	19	optimal	optimal	ADJ
ejpam-846	414	20	portfolio	portfolio	NOUN
ejpam-846	414	21	is	be	AUX
ejpam-846	414	22	required	require	VERB
ejpam-846	414	23	to	to	PART
ejpam-846	414	24	be	be	AUX
ejpam-846	414	25	nearly	nearly	ADV
ejpam-846	414	26	beta	beta	NOUN
ejpam-846	414	27	-	-	PUNCT
ejpam-846	414	28	neutral	neutral	ADJ
ejpam-846	414	29	.	.	PUNCT
ejpam-846	415	1	the	the	DET
ejpam-846	415	2	investor	investor	NOUN
ejpam-846	415	3	desires	desire	NOUN
ejpam-846	415	4	to	to	PART
ejpam-846	415	5	maximize	maximize	VERB
ejpam-846	415	6	portfolio	portfolio	NOUN
ejpam-846	415	7	expected	expect	VERB
ejpam-846	415	8	return	return	NOUN
ejpam-846	415	9	over	over	ADP
ejpam-846	415	10	the	the	DET
ejpam-846	415	11	τ	τ	PROPN
ejpam-846	415	12	-day	-day	NOUN
ejpam-846	415	13	period	period	NOUN
ejpam-846	415	14	subject	subject	ADJ
ejpam-846	415	15	to	to	ADP
ejpam-846	415	16	satisfying	satisfy	VERB
ejpam-846	415	17	above	above	ADP
ejpam-846	415	18	concerns	concern	NOUN
ejpam-846	415	19	,	,	PUNCT
ejpam-846	415	20	as	as	ADV
ejpam-846	415	21	well	well	ADV
ejpam-846	415	22	as	as	SCONJ
ejpam-846	415	23	asset	asset	NOUN
ejpam-846	415	24	positions	position	NOUN
ejpam-846	415	25	being	be	AUX
ejpam-846	415	26	controlled	control	VERB
ejpam-846	415	27	within	within	ADP
ejpam-846	415	28	given	give	VERB
ejpam-846	415	29	edirisinghe	edirisinghe	PROPN
ejpam-846	415	30	/	/	SYM
ejpam-846	415	31	eur	eur	PROPN
ejpam-846	415	32	.	.	PUNCT
ejpam-846	416	1	j.	j.	PROPN
ejpam-846	416	2	pure	pure	PROPN
ejpam-846	416	3	appl	appl	PROPN
ejpam-846	416	4	.	.	PROPN
ejpam-846	416	5	math	math	PROPN
ejpam-846	416	6	,	,	PUNCT
ejpam-846	416	7	3	3	NUM
ejpam-846	416	8	(	(	PUNCT
ejpam-846	416	9	2010	2010	NUM
ejpam-846	416	10	)	)	PUNCT
ejpam-846	416	11	,	,	PUNCT
ejpam-846	416	12	572	572	NUM
ejpam-846	416	13	-	-	SYM
ejpam-846	416	14	592	592	NUM
ejpam-846	416	15	585	585	NUM
ejpam-846	416	16	bounds	bound	NOUN
ejpam-846	416	17	,	,	PUNCT
ejpam-846	416	18	denoted	denote	VERB
ejpam-846	416	19	by	by	ADP
ejpam-846	416	20	xmin	xmin	PROPN
ejpam-846	416	21	j	j	PROPN
ejpam-846	416	22	≤	≤	PROPN
ejpam-846	416	23	xj	xj	PROPN
ejpam-846	416	24	≤	≤	PROPN
ejpam-846	416	25	xmax	xmax	PROPN
ejpam-846	416	26	j	j	PROPN
ejpam-846	416	27	.	.	PUNCT
ejpam-846	417	1	the	the	DET
ejpam-846	417	2	number	number	NOUN
ejpam-846	417	3	of	of	ADP
ejpam-846	417	4	shares	share	NOUN
ejpam-846	417	5	purchased	purchase	VERB
ejpam-846	417	6	/	/	SYM
ejpam-846	417	7	sold	sell	VERB
ejpam-846	417	8	must	must	AUX
ejpam-846	417	9	be	be	AUX
ejpam-846	417	10	an	an	DET
ejpam-846	417	11	integer	integer	NOUN
ejpam-846	417	12	and	and	CCONJ
ejpam-846	417	13	the	the	DET
ejpam-846	417	14	share	share	NOUN
ejpam-846	417	15	price	price	NOUN
ejpam-846	417	16	of	of	ADP
ejpam-846	417	17	asset	asset	NOUN
ejpam-846	417	18	j	j	PROPN
ejpam-846	417	19	(	(	PUNCT
ejpam-846	417	20	at	at	ADP
ejpam-846	417	21	the	the	DET
ejpam-846	417	22	time	time	NOUN
ejpam-846	417	23	of	of	ADP
ejpam-846	417	24	forming	form	VERB
ejpam-846	417	25	the	the	DET
ejpam-846	417	26	portfolio	portfolio	NOUN
ejpam-846	417	27	)	)	PUNCT
ejpam-846	417	28	is	be	AUX
ejpam-846	417	29	denoted	denote	VERB
ejpam-846	417	30	by	by	ADP
ejpam-846	417	31	pj	pj	PROPN
ejpam-846	417	32	.	.	PUNCT
ejpam-846	418	1	furthermore	furthermore	ADV
ejpam-846	418	2	,	,	PUNCT
ejpam-846	418	3	an	an	DET
ejpam-846	418	4	appropriate	appropriate	ADJ
ejpam-846	418	5	risk	risk	NOUN
ejpam-846	418	6	function	function	NOUN
ejpam-846	418	7	ψ(x	ψ(x	NOUN
ejpam-846	418	8	)	)	PUNCT
ejpam-846	418	9	must	must	AUX
ejpam-846	418	10	be	be	AUX
ejpam-846	418	11	incorporated	incorporate	VERB
ejpam-846	418	12	to	to	PART
ejpam-846	418	13	ensure	ensure	VERB
ejpam-846	418	14	that	that	SCONJ
ejpam-846	418	15	the	the	DET
ejpam-846	418	16	inherent	inherent	ADJ
ejpam-846	418	17	risk	risk	NOUN
ejpam-846	418	18	in	in	ADP
ejpam-846	418	19	asset	asset	NOUN
ejpam-846	418	20	returns	return	NOUN
ejpam-846	418	21	(	(	PUNCT
ejpam-846	418	22	due	due	ADP
ejpam-846	418	23	to	to	ADP
ejpam-846	418	24	their	their	PRON
ejpam-846	418	25	correlation	correlation	NOUN
ejpam-846	418	26	with	with	ADP
ejpam-846	418	27	each	each	DET
ejpam-846	418	28	other	other	ADJ
ejpam-846	418	29	)	)	PUNCT
ejpam-846	418	30	is	be	AUX
ejpam-846	418	31	controlled	control	VERB
ejpam-846	418	32	in	in	ADP
ejpam-846	418	33	an	an	DET
ejpam-846	418	34	efficient	efficient	ADJ
ejpam-846	418	35	manner	manner	NOUN
ejpam-846	418	36	.	.	PUNCT
ejpam-846	419	1	consider	consider	VERB
ejpam-846	419	2	the	the	DET
ejpam-846	419	3	portfolio	portfolio	NOUN
ejpam-846	419	4	optimization	optimization	NOUN
ejpam-846	419	5	model	model	NOUN
ejpam-846	419	6	:	:	PUNCT
ejpam-846	419	7	z∗	z∗	NOUN
ejpam-846	419	8	:	:	PUNCT
ejpam-846	419	9	=	=	SYM
ejpam-846	419	10	max	max	NOUN
ejpam-846	419	11	x	x	PUNCT
ejpam-846	419	12	ξ̄′x−	ξ̄′x−	NOUN
ejpam-846	419	13	∑k	∑k	PROPN
ejpam-846	420	1	j=1	j=1	PROPN
ejpam-846	420	2	lj(zj)−	lj(zj)−	PROPN
ejpam-846	420	3	λ	λ	PROPN
ejpam-846	420	4	ψ(x	ψ(x	PROPN
ejpam-846	420	5	)	)	PUNCT
ejpam-846	420	6	s.t	s.t	PROPN
ejpam-846	420	7	.	.	PROPN
ejpam-846	420	8	1′x	1′x	NUM
ejpam-846	420	9	≤	≤	NUM
ejpam-846	420	10	b0	b0	NOUN
ejpam-846	420	11	−x+	−x+	NOUN
ejpam-846	420	12	x0	x0	PROPN
ejpam-846	420	13	≤	≤	PROPN
ejpam-846	420	14	z	z	NOUN
ejpam-846	420	15	≤	≤	NUM
ejpam-846	420	16	x−	x−	PROPN
ejpam-846	421	1	x0	x0	PROPN
ejpam-846	421	2	−ν	−ν	NOUN
ejpam-846	421	3	b0	b0	VERB
ejpam-846	421	4	≤	≤	NOUN
ejpam-846	421	5	β′x	β′x	ADP
ejpam-846	421	6	≤	≤	ADJ
ejpam-846	421	7	+	+	NOUN
ejpam-846	421	8	ν	ν	NOUN
ejpam-846	421	9	b0	b0	NOUN
ejpam-846	421	10	xmin	xmin	NOUN
ejpam-846	421	11	≤	≤	NUM
ejpam-846	421	12	x	x	PUNCT
ejpam-846	421	13	≤	≤	NUM
ejpam-846	421	14	xmax	xmax	NOUN
ejpam-846	421	15	,	,	PUNCT
ejpam-846	421	16	|xj	|xj	NUM
ejpam-846	421	17	pj	pj	PROPN
ejpam-846	422	1	|	|	ADV
ejpam-846	422	2	:	:	PUNCT
ejpam-846	422	3	integer	integer	NOUN
ejpam-846	422	4	,	,	PUNCT
ejpam-846	422	5	j	j	PROPN
ejpam-846	422	6	=	=	SYM
ejpam-846	422	7	1	1	NUM
ejpam-846	422	8	,	,	PUNCT
ejpam-846	422	9	.	.	PUNCT
ejpam-846	422	10	.	.	PUNCT
ejpam-846	422	11	.	.	PUNCT
ejpam-846	423	1	,	,	PUNCT
ejpam-846	423	2	k.	k.	PROPN
ejpam-846	423	3	(	(	PUNCT
ejpam-846	423	4	44	44	NUM
ejpam-846	423	5	)	)	PUNCT
ejpam-846	423	6	portfolio	portfolio	NOUN
ejpam-846	423	7	efficiency	efficiency	NOUN
ejpam-846	423	8	is	be	AUX
ejpam-846	423	9	varied	varied	ADJ
ejpam-846	423	10	using	use	VERB
ejpam-846	423	11	the	the	DET
ejpam-846	423	12	risk	risk	NOUN
ejpam-846	423	13	-	-	PUNCT
ejpam-846	423	14	aversion	aversion	NOUN
ejpam-846	423	15	parameter	parameter	NOUN
ejpam-846	423	16	λ	λ	PROPN
ejpam-846	423	17	≥	≥	PROPN
ejpam-846	423	18	0	0	NUM
ejpam-846	423	19	.	.	PUNCT
ejpam-846	424	1	choice	choice	NOUN
ejpam-846	424	2	of	of	ADP
ejpam-846	424	3	ψ(x	ψ(x	NOUN
ejpam-846	424	4	)	)	PUNCT
ejpam-846	424	5	has	have	AUX
ejpam-846	424	6	been	be	AUX
ejpam-846	424	7	a	a	DET
ejpam-846	424	8	topic	topic	NOUN
ejpam-846	424	9	of	of	ADP
ejpam-846	424	10	considerable	considerable	ADJ
ejpam-846	424	11	debate	debate	NOUN
ejpam-846	424	12	and	and	CCONJ
ejpam-846	424	13	significant	significant	ADJ
ejpam-846	424	14	progresses	progress	NOUN
ejpam-846	424	15	have	have	AUX
ejpam-846	424	16	been	be	AUX
ejpam-846	424	17	made	make	VERB
ejpam-846	424	18	in	in	ADP
ejpam-846	424	19	this	this	DET
ejpam-846	424	20	regard	regard	NOUN
ejpam-846	424	21	.	.	PUNCT
ejpam-846	425	1	edirisinghe	edirisinghe	PROPN
ejpam-846	425	2	[	[	X
ejpam-846	425	3	5	5	NUM
ejpam-846	425	4	]	]	PUNCT
ejpam-846	425	5	considers	consider	VERB
ejpam-846	425	6	ψ(x	ψ(x	NOUN
ejpam-846	425	7	)	)	PUNCT
ejpam-846	425	8	in	in	ADP
ejpam-846	425	9	the	the	DET
ejpam-846	425	10	context	context	NOUN
ejpam-846	425	11	of	of	ADP
ejpam-846	425	12	static	static	ADJ
ejpam-846	425	13	or	or	CCONJ
ejpam-846	425	14	dynamic	dynamic	ADJ
ejpam-846	425	15	risk	risk	NOUN
ejpam-846	425	16	control	control	NOUN
ejpam-846	425	17	.	.	PUNCT
ejpam-846	426	1	artzner	artzner	NOUN
ejpam-846	426	2	et	et	PROPN
ejpam-846	426	3	al	al	PROPN
ejpam-846	426	4	.	.	PUNCT
ejpam-846	427	1	[	[	X
ejpam-846	427	2	17	17	NUM
ejpam-846	427	3	]	]	PUNCT
ejpam-846	427	4	describe	describe	VERB
ejpam-846	427	5	the	the	DET
ejpam-846	427	6	principles	principle	NOUN
ejpam-846	427	7	of	of	ADP
ejpam-846	427	8	measuring	measure	VERB
ejpam-846	427	9	risk	risk	NOUN
ejpam-846	427	10	attitude	attitude	NOUN
ejpam-846	427	11	,	,	PUNCT
ejpam-846	427	12	where	where	SCONJ
ejpam-846	427	13	the	the	DET
ejpam-846	427	14	authors	author	NOUN
ejpam-846	427	15	propose	propose	VERB
ejpam-846	427	16	the	the	DET
ejpam-846	427	17	concept	concept	NOUN
ejpam-846	427	18	of	of	ADP
ejpam-846	427	19	coherent	coherent	ADJ
ejpam-846	427	20	risk	risk	NOUN
ejpam-846	427	21	measures	measure	NOUN
ejpam-846	427	22	that	that	PRON
ejpam-846	427	23	allows	allow	VERB
ejpam-846	427	24	numerical	numerical	ADJ
ejpam-846	427	25	expression	expression	NOUN
ejpam-846	427	26	of	of	ADP
ejpam-846	427	27	risk	risk	NOUN
ejpam-846	427	28	attitude	attitude	NOUN
ejpam-846	427	29	.	.	PUNCT
ejpam-846	428	1	another	another	DET
ejpam-846	428	2	interesting	interesting	ADJ
ejpam-846	428	3	method	method	NOUN
ejpam-846	428	4	of	of	ADP
ejpam-846	428	5	risk	risk	NOUN
ejpam-846	428	6	measurement	measurement	NOUN
ejpam-846	428	7	is	be	AUX
ejpam-846	428	8	to	to	PART
ejpam-846	428	9	use	use	VERB
ejpam-846	428	10	the	the	DET
ejpam-846	428	11	conditional	conditional	ADJ
ejpam-846	428	12	valueat	valueat	NOUN
ejpam-846	428	13	-	-	PUNCT
ejpam-846	428	14	risk	risk	NOUN
ejpam-846	428	15	(	(	PUNCT
ejpam-846	428	16	cvar	cvar	NOUN
ejpam-846	428	17	)	)	PUNCT
ejpam-846	428	18	,	,	PUNCT
ejpam-846	428	19	see	see	VERB
ejpam-846	428	20	rockafellar	rockafellar	ADJ
ejpam-846	428	21	and	and	CCONJ
ejpam-846	428	22	uryasev	uryasev	ADJ
ejpam-846	428	23	[	[	X
ejpam-846	428	24	18	18	NUM
ejpam-846	428	25	]	]	PUNCT
ejpam-846	428	26	and	and	CCONJ
ejpam-846	428	27	ogryczak	ogryczak	NOUN
ejpam-846	428	28	and	and	CCONJ
ejpam-846	428	29	ruszczynski	ruszczynski	ADJ
ejpam-846	428	30	[	[	X
ejpam-846	428	31	16	16	NUM
ejpam-846	428	32	]	]	PUNCT
ejpam-846	428	33	.	.	PUNCT
ejpam-846	429	1	in	in	ADP
ejpam-846	429	2	particular	particular	ADJ
ejpam-846	429	3	,	,	PUNCT
ejpam-846	429	4	risk	risk	NOUN
ejpam-846	429	5	measures	measure	NOUN
ejpam-846	429	6	based	base	VERB
ejpam-846	429	7	on	on	ADP
ejpam-846	429	8	mean	mean	NOUN
ejpam-846	429	9	and	and	CCONJ
ejpam-846	429	10	cvar	cvar	NOUN
ejpam-846	429	11	are	be	AUX
ejpam-846	429	12	coherent	coherent	ADJ
ejpam-846	429	13	.	.	PUNCT
ejpam-846	430	1	the	the	DET
ejpam-846	430	2	focus	focus	NOUN
ejpam-846	430	3	here	here	ADV
ejpam-846	430	4	is	be	AUX
ejpam-846	430	5	not	not	PART
ejpam-846	430	6	not	not	PART
ejpam-846	430	7	engage	engage	VERB
ejpam-846	430	8	in	in	ADP
ejpam-846	430	9	a	a	DET
ejpam-846	430	10	detailed	detailed	ADJ
ejpam-846	430	11	discussion	discussion	NOUN
ejpam-846	430	12	of	of	ADP
ejpam-846	430	13	the	the	DET
ejpam-846	430	14	pros	pro	NOUN
ejpam-846	430	15	and	and	CCONJ
ejpam-846	430	16	cons	con	NOUN
ejpam-846	430	17	of	of	ADP
ejpam-846	430	18	various	various	ADJ
ejpam-846	430	19	risk	risk	NOUN
ejpam-846	430	20	measures	measure	NOUN
ejpam-846	430	21	,	,	PUNCT
ejpam-846	430	22	but	but	CCONJ
ejpam-846	430	23	to	to	PART
ejpam-846	430	24	pick	pick	VERB
ejpam-846	430	25	a	a	DET
ejpam-846	430	26	risk	risk	NOUN
ejpam-846	430	27	measure	measure	NOUN
ejpam-846	430	28	that	that	PRON
ejpam-846	430	29	is	be	AUX
ejpam-846	430	30	consistent	consistent	ADJ
ejpam-846	430	31	with	with	ADP
ejpam-846	430	32	coherency	coherency	NOUN
ejpam-846	430	33	and	and	CCONJ
ejpam-846	430	34	rationality	rationality	NOUN
ejpam-846	430	35	.	.	PUNCT
ejpam-846	431	1	setting	set	VERB
ejpam-846	431	2	ψ(x	ψ(x	NOUN
ejpam-846	431	3	)	)	PUNCT
ejpam-846	431	4	=	=	SYM
ejpam-846	431	5	x′mx	x′mx	PROPN
ejpam-846	431	6	,	,	PUNCT
ejpam-846	431	7	wherem	wherem	PROPN
ejpam-846	431	8	is	be	AUX
ejpam-846	431	9	the	the	DET
ejpam-846	431	10	variance	variance	NOUN
ejpam-846	431	11	-	-	PUNCT
ejpam-846	431	12	covariance	covariance	NOUN
ejpam-846	431	13	matrix	matrix	NOUN
ejpam-846	431	14	of	of	ADP
ejpam-846	431	15	ξ	ξ	PROPN
ejpam-846	431	16	,	,	PUNCT
ejpam-846	431	17	also	also	ADV
ejpam-846	431	18	see	see	VERB
ejpam-846	431	19	section	section	NOUN
ejpam-846	431	20	1	1	NUM
ejpam-846	431	21	,	,	PUNCT
ejpam-846	431	22	i.e.	i.e.	X
ejpam-846	431	23	,	,	PUNCT
ejpam-846	431	24	markowitz	markowitz	PROPN
ejpam-846	431	25	model	model	PROPN
ejpam-846	431	26	,	,	PUNCT
ejpam-846	431	27	can	can	AUX
ejpam-846	431	28	lead	lead	VERB
ejpam-846	431	29	to	to	ADP
ejpam-846	431	30	inconsistent	inconsistent	ADJ
ejpam-846	431	31	portfolio	portfolio	NOUN
ejpam-846	431	32	choices	choice	NOUN
ejpam-846	431	33	that	that	PRON
ejpam-846	431	34	contradicts	contradict	VERB
ejpam-846	431	35	rationality	rationality	NOUN
ejpam-846	431	36	of	of	ADP
ejpam-846	431	37	an	an	DET
ejpam-846	431	38	investor	investor	NOUN
ejpam-846	431	39	.	.	PUNCT
ejpam-846	432	1	the	the	DET
ejpam-846	432	2	concept	concept	NOUN
ejpam-846	432	3	of	of	ADP
ejpam-846	432	4	‘	'	PUNCT
ejpam-846	432	5	rational	rational	ADJ
ejpam-846	432	6	’	'	PUNCT
ejpam-846	432	7	risk	risk	NOUN
ejpam-846	432	8	measures	measure	NOUN
ejpam-846	432	9	proposed	propose	VERB
ejpam-846	432	10	by	by	ADP
ejpam-846	432	11	bychkov	bychkov	NOUN
ejpam-846	432	12	and	and	CCONJ
ejpam-846	432	13	edirisinghe	edirisinghe	NOUN
ejpam-846	432	14	[	[	X
ejpam-846	432	15	3	3	X
ejpam-846	432	16	]	]	PUNCT
ejpam-846	432	17	circumvents	circumvent	VERB
ejpam-846	432	18	such	such	ADJ
ejpam-846	432	19	inconsistencies	inconsistency	NOUN
ejpam-846	432	20	by	by	ADP
ejpam-846	432	21	requiring	require	VERB
ejpam-846	432	22	the	the	DET
ejpam-846	432	23	risk	risk	NOUN
ejpam-846	432	24	functions	function	NOUN
ejpam-846	432	25	to	to	PART
ejpam-846	432	26	satisfy	satisfy	VERB
ejpam-846	432	27	properties	property	NOUN
ejpam-846	432	28	of	of	ADP
ejpam-846	432	29	coherence	coherence	NOUN
ejpam-846	432	30	and	and	CCONJ
ejpam-846	432	31	first	first	ADJ
ejpam-846	432	32	-	-	PUNCT
ejpam-846	432	33	order	order	NOUN
ejpam-846	432	34	stochastic	stochastic	ADJ
ejpam-846	432	35	dominance	dominance	NOUN
ejpam-846	432	36	(	(	PUNCT
ejpam-846	432	37	fsd	fsd	PROPN
ejpam-846	432	38	)	)	PUNCT
ejpam-846	432	39	.	.	PUNCT
ejpam-846	433	1	the	the	DET
ejpam-846	433	2	latter	latter	ADJ
ejpam-846	433	3	reference	reference	NOUN
ejpam-846	433	4	shows	show	VERB
ejpam-846	433	5	that	that	SCONJ
ejpam-846	433	6	even	even	ADV
ejpam-846	433	7	the	the	DET
ejpam-846	433	8	well	well	ADV
ejpam-846	433	9	-	-	PUNCT
ejpam-846	433	10	known	know	VERB
ejpam-846	433	11	mean	mean	NOUN
ejpam-846	433	12	/	/	SYM
ejpam-846	433	13	semi	semi	ADJ
ejpam-846	433	14	-	-	ADJ
ejpam-846	433	15	variance	variance	ADJ
ejpam-846	433	16	trade	trade	NOUN
ejpam-846	433	17	off	off	ADP
ejpam-846	433	18	,	,	PUNCT
ejpam-846	433	19	where	where	SCONJ
ejpam-846	433	20	one	one	NUM
ejpam-846	433	21	sets	set	VERB
ejpam-846	433	22	ψ(x	ψ(x	NOUN
ejpam-846	433	23	)	)	PUNCT
ejpam-846	433	24	=	=	PUNCT
ejpam-846	433	25	e[(max{ξ̄′x	e[(max{ξ̄′x	NOUN
ejpam-846	433	26	−	−	NOUN
ejpam-846	433	27	ξ′x	ξ′x	PROPN
ejpam-846	433	28	,	,	PUNCT
ejpam-846	433	29	0})2	0})2	PROPN
ejpam-846	433	30	]	]	PUNCT
ejpam-846	433	31	,	,	PUNCT
ejpam-846	433	32	is	be	AUX
ejpam-846	433	33	not	not	PART
ejpam-846	433	34	consistent	consistent	ADJ
ejpam-846	433	35	with	with	ADP
ejpam-846	433	36	fsd	fsd	PROPN
ejpam-846	433	37	.	.	PUNCT
ejpam-846	434	1	however	however	ADV
ejpam-846	434	2	,	,	PUNCT
ejpam-846	434	3	setting	set	VERB
ejpam-846	434	4	ψ(x	ψ(x	NOUN
ejpam-846	434	5	)	)	PUNCT
ejpam-846	435	1	=	=	SYM
ejpam-846	435	2	e[(max{c	e[(max{c	PROPN
ejpam-846	435	3	−	−	PROPN
ejpam-846	435	4	ξ′x	ξ′x	PROPN
ejpam-846	435	5	,	,	PUNCT
ejpam-846	435	6	0})γ	0})γ	PROPN
ejpam-846	435	7	]	]	X
ejpam-846	435	8	,	,	PUNCT
ejpam-846	435	9	for	for	ADP
ejpam-846	435	10	γ	γ	X
ejpam-846	435	11	≥	≥	PROPN
ejpam-846	435	12	1	1	NUM
ejpam-846	435	13	,	,	PUNCT
ejpam-846	435	14	yields	yield	VERB
ejpam-846	435	15	a	a	DET
ejpam-846	435	16	rational	rational	ADJ
ejpam-846	435	17	risk	risk	NOUN
ejpam-846	435	18	measure	measure	NOUN
ejpam-846	435	19	that	that	PRON
ejpam-846	435	20	is	be	AUX
ejpam-846	435	21	fsd	fsd	PROPN
ejpam-846	435	22	consistent	consistent	ADJ
ejpam-846	435	23	and	and	CCONJ
ejpam-846	435	24	convex	convex	PROPN
ejpam-846	435	25	,	,	PUNCT
ejpam-846	435	26	where	where	SCONJ
ejpam-846	435	27	c	c	PROPN
ejpam-846	435	28	is	be	AUX
ejpam-846	435	29	a	a	DET
ejpam-846	435	30	constant	constant	ADJ
ejpam-846	435	31	return	return	NOUN
ejpam-846	435	32	target	target	NOUN
ejpam-846	435	33	for	for	ADP
ejpam-846	435	34	the	the	DET
ejpam-846	435	35	portfolio	portfolio	NOUN
ejpam-846	435	36	.	.	PUNCT
ejpam-846	436	1	in	in	ADP
ejpam-846	436	2	the	the	DET
ejpam-846	436	3	sequel	sequel	NOUN
ejpam-846	436	4	,	,	PUNCT
ejpam-846	436	5	we	we	PRON
ejpam-846	436	6	employ	employ	VERB
ejpam-846	436	7	this	this	DET
ejpam-846	436	8	risk	risk	NOUN
ejpam-846	436	9	function	function	NOUN
ejpam-846	436	10	with	with	ADP
ejpam-846	436	11	γ	γ	X
ejpam-846	436	12	=	=	SYM
ejpam-846	436	13	2	2	NUM
ejpam-846	436	14	.	.	PUNCT
ejpam-846	436	15	consequently	consequently	ADV
ejpam-846	436	16	,	,	PUNCT
ejpam-846	436	17	ψ(x	ψ(x	PROPN
ejpam-846	436	18	)	)	PUNCT
ejpam-846	436	19	=	=	PUNCT
ejpam-846	436	20	e[ϕ(x	e[ϕ(x	NOUN
ejpam-846	436	21	,	,	PUNCT
ejpam-846	436	22	ξ	ξ	NOUN
ejpam-846	436	23	)	)	PUNCT
ejpam-846	436	24	]	]	PUNCT
ejpam-846	436	25	,	,	PUNCT
ejpam-846	436	26	where	where	SCONJ
ejpam-846	436	27	ϕ(x	ϕ(x	PROPN
ejpam-846	436	28	,	,	PUNCT
ejpam-846	436	29	ξ	ξ	NOUN
ejpam-846	436	30	)	)	PUNCT
ejpam-846	436	31	:	:	PUNCT
ejpam-846	437	1	=	=	SYM
ejpam-846	437	2	min	min	PROPN
ejpam-846	437	3	y	y	PROPN
ejpam-846	437	4	(	(	PUNCT
ejpam-846	437	5	y)2	y)2	NOUN
ejpam-846	437	6	s.t	s.t	PROPN
ejpam-846	437	7	.	.	PROPN
ejpam-846	437	8	y	y	PROPN
ejpam-846	437	9	≥	≥	PROPN
ejpam-846	437	10	c	c	NOUN
ejpam-846	437	11	−	−	PROPN
ejpam-846	437	12	ξ′x	ξ′x	PROPN
ejpam-846	437	13	y	y	PROPN
ejpam-846	437	14	≥	≥	NUM
ejpam-846	437	15	0	0	NUM
ejpam-846	437	16	.	.	PUNCT
ejpam-846	437	17	(	(	PUNCT
ejpam-846	437	18	45	45	NUM
ejpam-846	437	19	)	)	PUNCT
ejpam-846	437	20	4.1	4.1	NUM
ejpam-846	437	21	.	.	PUNCT
ejpam-846	438	1	data	datum	NOUN
ejpam-846	438	2	and	and	CCONJ
ejpam-846	438	3	parameters	parameter	NOUN
ejpam-846	438	4	asset	asset	NOUN
ejpam-846	438	5	(	(	PUNCT
ejpam-846	438	6	stock	stock	NOUN
ejpam-846	438	7	)	)	PUNCT
ejpam-846	438	8	returns	return	NOUN
ejpam-846	438	9	are	be	AUX
ejpam-846	438	10	quite	quite	ADV
ejpam-846	438	11	well	well	ADV
ejpam-846	438	12	-	-	PUNCT
ejpam-846	438	13	known	know	VERB
ejpam-846	438	14	to	to	PART
ejpam-846	438	15	have	have	VERB
ejpam-846	438	16	non	non	ADJ
ejpam-846	438	17	-	-	ADJ
ejpam-846	438	18	symmetric	symmetric	ADJ
ejpam-846	438	19	distributions	distribution	NOUN
ejpam-846	438	20	.	.	PUNCT
ejpam-846	439	1	more	more	ADV
ejpam-846	439	2	importantly	importantly	ADV
ejpam-846	439	3	,	,	PUNCT
ejpam-846	439	4	stock	stock	NOUN
ejpam-846	439	5	return	return	NOUN
ejpam-846	439	6	distributions	distribution	NOUN
ejpam-846	439	7	are	be	AUX
ejpam-846	439	8	shown	show	VERB
ejpam-846	439	9	to	to	PART
ejpam-846	439	10	have	have	VERB
ejpam-846	439	11	‘	'	PUNCT
ejpam-846	439	12	fatter	fat	ADJ
ejpam-846	439	13	’	'	PUNCT
ejpam-846	439	14	tails	tail	NOUN
ejpam-846	439	15	than	than	SCONJ
ejpam-846	439	16	the	the	DET
ejpam-846	439	17	normal	normal	ADJ
ejpam-846	439	18	distributions	distribution	NOUN
ejpam-846	439	19	would	would	AUX
ejpam-846	439	20	imply	imply	VERB
ejpam-846	439	21	,	,	PUNCT
ejpam-846	439	22	see	see	VERB
ejpam-846	439	23	ziemba	ziemba	PROPN
ejpam-846	440	1	[	[	X
ejpam-846	440	2	21	21	NUM
ejpam-846	440	3	]	]	PUNCT
ejpam-846	440	4	.	.	PUNCT
ejpam-846	441	1	consequently	consequently	ADV
ejpam-846	441	2	,	,	PUNCT
ejpam-846	441	3	normal	normal	ADJ
ejpam-846	441	4	distribution	distribution	NOUN
ejpam-846	441	5	assumption	assumption	NOUN
ejpam-846	441	6	(	(	PUNCT
ejpam-846	441	7	or	or	CCONJ
ejpam-846	441	8	many	many	ADJ
ejpam-846	441	9	other	other	ADJ
ejpam-846	441	10	theoretical	theoretical	ADJ
ejpam-846	441	11	distributions	distribution	NOUN
ejpam-846	441	12	)	)	PUNCT
ejpam-846	441	13	on	on	ADP
ejpam-846	441	14	ξ	ξ	PROPN
ejpam-846	441	15	often	often	ADV
ejpam-846	441	16	leads	lead	VERB
ejpam-846	441	17	to	to	ADP
ejpam-846	441	18	portfolios	portfolio	NOUN
ejpam-846	441	19	that	that	PRON
ejpam-846	441	20	perform	perform	VERB
ejpam-846	441	21	poorly	poorly	ADV
ejpam-846	441	22	edirisinghe	edirisinghe	ADJ
ejpam-846	441	23	/	/	SYM
ejpam-846	441	24	eur	eur	PROPN
ejpam-846	441	25	.	.	PUNCT
ejpam-846	442	1	j.	j.	PROPN
ejpam-846	442	2	pure	pure	PROPN
ejpam-846	442	3	appl	appl	PROPN
ejpam-846	442	4	.	.	PROPN
ejpam-846	442	5	math	math	PROPN
ejpam-846	442	6	,	,	PUNCT
ejpam-846	442	7	3	3	NUM
ejpam-846	442	8	(	(	PUNCT
ejpam-846	442	9	2010	2010	NUM
ejpam-846	442	10	)	)	PUNCT
ejpam-846	442	11	,	,	PUNCT
ejpam-846	442	12	572	572	NUM
ejpam-846	442	13	-	-	SYM
ejpam-846	442	14	592	592	NUM
ejpam-846	442	15	586	586	NUM
ejpam-846	442	16	in	in	ADP
ejpam-846	442	17	practice	practice	NOUN
ejpam-846	442	18	.	.	PUNCT
ejpam-846	443	1	the	the	DET
ejpam-846	443	2	main	main	ADJ
ejpam-846	443	3	reason	reason	NOUN
ejpam-846	443	4	is	be	AUX
ejpam-846	443	5	that	that	SCONJ
ejpam-846	443	6	rare	rare	ADJ
ejpam-846	443	7	events	event	NOUN
ejpam-846	443	8	do	do	AUX
ejpam-846	443	9	occur	occur	VERB
ejpam-846	443	10	much	much	ADV
ejpam-846	443	11	more	more	ADV
ejpam-846	443	12	frequently	frequently	ADV
ejpam-846	443	13	than	than	ADP
ejpam-846	443	14	most	most	ADJ
ejpam-846	443	15	theoretical	theoretical	ADJ
ejpam-846	443	16	distributions	distribution	NOUN
ejpam-846	443	17	correspond	correspond	VERB
ejpam-846	443	18	to	to	ADP
ejpam-846	443	19	.	.	PUNCT
ejpam-846	444	1	in	in	ADP
ejpam-846	444	2	this	this	DET
ejpam-846	444	3	paper	paper	NOUN
ejpam-846	444	4	,	,	PUNCT
ejpam-846	444	5	we	we	PRON
ejpam-846	444	6	employ	employ	VERB
ejpam-846	444	7	a	a	DET
ejpam-846	444	8	historical	historical	ADJ
ejpam-846	444	9	daily	daily	ADJ
ejpam-846	444	10	return	return	NOUN
ejpam-846	444	11	sample	sample	NOUN
ejpam-846	444	12	of	of	ADP
ejpam-846	444	13	t	t	NOUN
ejpam-846	444	14	days	day	NOUN
ejpam-846	444	15	for	for	ADP
ejpam-846	444	16	the	the	DET
ejpam-846	444	17	k	k	PROPN
ejpam-846	444	18	assets	asset	NOUN
ejpam-846	444	19	(	(	PUNCT
ejpam-846	444	20	t	t	NOUN
ejpam-846	444	21	>	>	PUNCT
ejpam-846	444	22	>	>	X
ejpam-846	444	23	k	k	PROPN
ejpam-846	444	24	)	)	PUNCT
ejpam-846	444	25	,	,	PUNCT
ejpam-846	444	26	and	and	CCONJ
ejpam-846	444	27	only	only	ADV
ejpam-846	444	28	the	the	DET
ejpam-846	444	29	first	first	ADJ
ejpam-846	444	30	and	and	CCONJ
ejpam-846	444	31	second	second	ADJ
ejpam-846	444	32	-	-	PUNCT
ejpam-846	444	33	order	order	NOUN
ejpam-846	444	34	cross	cross	NOUN
ejpam-846	444	35	moments	moment	NOUN
ejpam-846	444	36	are	be	AUX
ejpam-846	444	37	estimated	estimate	VERB
ejpam-846	444	38	from	from	ADP
ejpam-846	444	39	the	the	DET
ejpam-846	444	40	sample	sample	NOUN
ejpam-846	444	41	.	.	PUNCT
ejpam-846	445	1	without	without	ADP
ejpam-846	445	2	making	make	VERB
ejpam-846	445	3	further	further	ADJ
ejpam-846	445	4	distributional	distributional	ADJ
ejpam-846	445	5	assumptions	assumption	NOUN
ejpam-846	445	6	,	,	PUNCT
ejpam-846	445	7	these	these	DET
ejpam-846	445	8	moment	moment	NOUN
ejpam-846	445	9	estimates	estimate	NOUN
ejpam-846	445	10	are	be	AUX
ejpam-846	445	11	employed	employ	VERB
ejpam-846	445	12	in	in	ADP
ejpam-846	445	13	the	the	DET
ejpam-846	445	14	context	context	NOUN
ejpam-846	445	15	of	of	ADP
ejpam-846	445	16	the	the	DET
ejpam-846	445	17	second	second	ADJ
ejpam-846	445	18	moment	moment	NOUN
ejpam-846	445	19	lower	lower	ADV
ejpam-846	445	20	bound	bind	VERB
ejpam-846	445	21	discussed	discuss	VERB
ejpam-846	445	22	in	in	ADP
ejpam-846	445	23	section	section	NOUN
ejpam-846	445	24	3	3	NUM
ejpam-846	445	25	to	to	PART
ejpam-846	445	26	approximate	approximate	VERB
ejpam-846	445	27	the	the	DET
ejpam-846	445	28	risk	risk	NOUN
ejpam-846	445	29	function	function	NOUN
ejpam-846	445	30	ψ(x	ψ(x	PROPN
ejpam-846	445	31	)	)	PUNCT
ejpam-846	445	32	.	.	PUNCT
ejpam-846	446	1	this	this	DET
ejpam-846	446	2	approximation	approximation	NOUN
ejpam-846	446	3	then	then	ADV
ejpam-846	446	4	constructs	construct	VERB
ejpam-846	446	5	precisely	precisely	ADV
ejpam-846	446	6	k	k	PROPN
ejpam-846	446	7	+	+	CCONJ
ejpam-846	446	8	1	1	NUM
ejpam-846	446	9	stock	stock	NOUN
ejpam-846	446	10	return	return	NOUN
ejpam-846	446	11	vectors	vector	NOUN
ejpam-846	446	12	that	that	PRON
ejpam-846	446	13	are	be	AUX
ejpam-846	446	14	located	locate	VERB
ejpam-846	446	15	relative	relative	ADJ
ejpam-846	446	16	to	to	ADP
ejpam-846	446	17	both	both	PRON
ejpam-846	446	18	the	the	DET
ejpam-846	446	19	mean	mean	ADJ
ejpam-846	446	20	and	and	CCONJ
ejpam-846	446	21	variance	variance	NOUN
ejpam-846	446	22	-	-	PUNCT
ejpam-846	446	23	covariance	covariance	NOUN
ejpam-846	446	24	information	information	NOUN
ejpam-846	446	25	,	,	PUNCT
ejpam-846	446	26	as	as	ADV
ejpam-846	446	27	well	well	ADV
ejpam-846	446	28	as	as	ADP
ejpam-846	446	29	based	base	VERB
ejpam-846	446	30	on	on	ADP
ejpam-846	446	31	the	the	DET
ejpam-846	446	32	extremeness	extremeness	NOUN
ejpam-846	446	33	of	of	ADP
ejpam-846	446	34	returns	return	NOUN
ejpam-846	446	35	observed	observe	VERB
ejpam-846	446	36	during	during	ADP
ejpam-846	446	37	the	the	DET
ejpam-846	446	38	historical	historical	ADJ
ejpam-846	446	39	t	t	NOUN
ejpam-846	446	40	periods	period	NOUN
ejpam-846	446	41	.	.	PUNCT
ejpam-846	447	1	let	let	VERB
ejpam-846	447	2	the	the	DET
ejpam-846	447	3	return	return	NOUN
ejpam-846	447	4	sample	sample	NOUN
ejpam-846	447	5	be	be	AUX
ejpam-846	447	6	denoted	denote	VERB
ejpam-846	447	7	by	by	ADP
ejpam-846	447	8	ξ1	ξ1	NOUN
ejpam-846	447	9	,	,	PUNCT
ejpam-846	447	10	.	.	PUNCT
ejpam-846	447	11	.	.	PUNCT
ejpam-846	448	1	.	.	PUNCT
ejpam-846	449	1	,	,	PUNCT
ejpam-846	449	2	ξt	ξt	X
ejpam-846	449	3	∈	∈	PROPN
ejpam-846	449	4	ℜk	ℜk	NOUN
ejpam-846	449	5	.	.	PUNCT
ejpam-846	450	1	a	a	DET
ejpam-846	450	2	simplicial	simplicial	ADJ
ejpam-846	450	3	support	support	NOUN
ejpam-846	450	4	ξ	ξ	PROPN
ejpam-846	450	5	is	be	AUX
ejpam-846	450	6	needed	need	VERB
ejpam-846	450	7	such	such	ADJ
ejpam-846	450	8	that	that	SCONJ
ejpam-846	450	9	co{ξ1	co{ξ1	NOUN
ejpam-846	450	10	,	,	PUNCT
ejpam-846	450	11	.	.	PUNCT
ejpam-846	450	12	.	.	PUNCT
ejpam-846	451	1	.	.	PUNCT
ejpam-846	452	1	,	,	PUNCT
ejpam-846	452	2	ξt	ξt	X
ejpam-846	452	3	}	}	PUNCT
ejpam-846	452	4	⊆	⊆	NUM
ejpam-846	452	5	ξ	ξ	NUM
ejpam-846	452	6	,	,	PUNCT
ejpam-846	452	7	see	see	VERB
ejpam-846	452	8	figure	figure	NOUN
ejpam-846	452	9	1	1	NUM
ejpam-846	452	10	.	.	PUNCT
ejpam-846	453	1	the	the	DET
ejpam-846	453	2	problem	problem	NOUN
ejpam-846	453	3	of	of	ADP
ejpam-846	453	4	determining	determine	VERB
ejpam-846	453	5	a	a	DET
ejpam-846	453	6	compact	compact	ADJ
ejpam-846	453	7	multidimensional	multidimensional	ADJ
ejpam-846	453	8	simplex	simplex	NOUN
ejpam-846	453	9	covering	cover	VERB
ejpam-846	453	10	multivariate	multivariate	NOUN
ejpam-846	453	11	points	point	NOUN
ejpam-846	453	12	is	be	AUX
ejpam-846	453	13	addressed	address	VERB
ejpam-846	453	14	in	in	ADP
ejpam-846	453	15	edirisinghe	edirisinghe	NOUN
ejpam-846	453	16	[	[	X
ejpam-846	453	17	6	6	NUM
ejpam-846	453	18	]	]	PUNCT
ejpam-846	453	19	;	;	PUNCT
ejpam-846	453	20	also	also	ADV
ejpam-846	453	21	see	see	VERB
ejpam-846	453	22	edirisinghe	edirisinghe	ADJ
ejpam-846	453	23	and	and	CCONJ
ejpam-846	453	24	you	you	PRON
ejpam-846	454	1	[	[	X
ejpam-846	454	2	7	7	NUM
ejpam-846	454	3	]	]	PUNCT
ejpam-846	454	4	.	.	PUNCT
ejpam-846	455	1	for	for	ADP
ejpam-846	455	2	ξ	ξ	PROPN
ejpam-846	455	3	as	as	SCONJ
ejpam-846	455	4	determined	determined	ADJ
ejpam-846	455	5	above	above	ADV
ejpam-846	455	6	,	,	PUNCT
ejpam-846	455	7	denoting	denote	VERB
ejpam-846	455	8	the	the	DET
ejpam-846	455	9	inverse	inverse	NOUN
ejpam-846	455	10	of	of	ADP
ejpam-846	455	11	vertex	vertex	NOUN
ejpam-846	455	12	matrix	matrix	NOUN
ejpam-846	455	13	by	by	ADP
ejpam-846	455	14	v	v	NUM
ejpam-846	455	15	,	,	PUNCT
ejpam-846	455	16	the	the	DET
ejpam-846	455	17	second	second	ADJ
ejpam-846	455	18	moment	moment	NOUN
ejpam-846	455	19	approximated	approximate	VERB
ejpam-846	455	20	scenario	scenario	NOUN
ejpam-846	455	21	sample	sample	NOUN
ejpam-846	455	22	,	,	PUNCT
ejpam-846	455	23	given	give	VERB
ejpam-846	455	24	by	by	ADP
ejpam-846	455	25	ξ̃i	ξ̃i	NOUN
ejpam-846	455	26	,	,	PUNCT
ejpam-846	455	27	i	i	PRON
ejpam-846	455	28	=	=	NOUN
ejpam-846	455	29	1	1	NUM
ejpam-846	455	30	,	,	PUNCT
ejpam-846	455	31	.	.	PUNCT
ejpam-846	455	32	.	.	PUNCT
ejpam-846	456	1	.	.	PUNCT
ejpam-846	457	1	,	,	PUNCT
ejpam-846	457	2	k	k	PROPN
ejpam-846	457	3	+	+	NOUN
ejpam-846	457	4	1	1	NUM
ejpam-846	457	5	,	,	PUNCT
ejpam-846	457	6	is	be	AUX
ejpam-846	457	7	computed	compute	VERB
ejpam-846	457	8	according	accord	VERB
ejpam-846	457	9	to	to	ADP
ejpam-846	457	10	equations	equation	NOUN
ejpam-846	457	11	(	(	PUNCT
ejpam-846	457	12	34)-(35	34)-(35	PROPN
ejpam-846	457	13	)	)	PUNCT
ejpam-846	457	14	,	,	PUNCT
ejpam-846	457	15	where	where	SCONJ
ejpam-846	457	16	ξ̄k	ξ̄k	NOUN
ejpam-846	457	17	=	=	SYM
ejpam-846	457	18	1	1	NUM
ejpam-846	457	19	t	t	X
ejpam-846	457	20	∑t	∑t	PROPN
ejpam-846	457	21	t=1	t=1	PROPN
ejpam-846	457	22	ξ	ξ	PROPN
ejpam-846	457	23	t	t	PROPN
ejpam-846	457	24	k	k	X
ejpam-846	457	25	andmkl	andmkl	PROPN
ejpam-846	457	26	=	=	PUNCT
ejpam-846	457	27	1	1	NUM
ejpam-846	457	28	t	t	X
ejpam-846	457	29	∑t	∑t	PROPN
ejpam-846	457	30	t=1	t=1	PROPN
ejpam-846	457	31	ξ	ξ	PROPN
ejpam-846	457	32	t	t	PROPN
ejpam-846	457	33	kξ	kξ	NOUN
ejpam-846	457	34	t	t	PROPN
ejpam-846	457	35	l	l	NOUN
ejpam-846	457	36	,	,	PUNCT
ejpam-846	457	37	∀k	∀k	PROPN
ejpam-846	457	38	,	,	PUNCT
ejpam-846	457	39	l.	l.	NOUN
ejpam-846	457	40	for	for	ADP
ejpam-846	457	41	the	the	DET
ejpam-846	457	42	illustration	illustration	NOUN
ejpam-846	457	43	here	here	ADV
ejpam-846	457	44	,	,	PUNCT
ejpam-846	457	45	we	we	PRON
ejpam-846	457	46	use	use	VERB
ejpam-846	457	47	the	the	DET
ejpam-846	457	48	10	10	NUM
ejpam-846	457	49	-	-	PUNCT
ejpam-846	457	50	year	year	NOUN
ejpam-846	457	51	historical	historical	ADJ
ejpam-846	457	52	period	period	NOUN
ejpam-846	457	53	from	from	ADP
ejpam-846	457	54	january	january	PROPN
ejpam-846	457	55	2000	2000	NUM
ejpam-846	457	56	to	to	ADP
ejpam-846	457	57	historical	historical	ADJ
ejpam-846	457	58	return	return	NOUN
ejpam-846	457	59	samplesimplicial	samplesimplicial	ADJ
ejpam-846	457	60	2	2	NUM
ejpam-846	457	61	u	u	NOUN
ejpam-846	457	62	of	of	ADP
ejpam-846	457	63	t	t	NOUN
ejpam-846	457	64	periodscoverage	periodscoverage	NOUN
ejpam-846	457	65	,	,	PUNCT
ejpam-846	457	66	moment	moment	NOUN
ejpam-846	457	67	approximated1	approximated1	NOUN
ejpam-846	457	68	u	u	NOUN
ejpam-846	457	69	3	3	NUM
ejpam-846	457	70	u	u	NOUN
ejpam-846	457	71	scenarios	scenario	NOUN
ejpam-846	457	72	u	u	PRON
ejpam-846	457	73	figure	figure	VERB
ejpam-846	457	74	1	1	NUM
ejpam-846	457	75	:	:	PUNCT
ejpam-846	457	76	second	second	ADJ
ejpam-846	457	77	moment	moment	NOUN
ejpam-846	457	78	approximated	approximate	VERB
ejpam-846	457	79	historical	historical	ADJ
ejpam-846	457	80	return	return	NOUN
ejpam-846	457	81	sample	sample	NOUN
ejpam-846	457	82	in	in	ADP
ejpam-846	457	83	ℜ2	ℜ2	NOUN
ejpam-846	457	84	.	.	PUNCT
ejpam-846	458	1	december	december	PROPN
ejpam-846	458	2	2009	2009	NUM
ejpam-846	458	3	,	,	PUNCT
ejpam-846	458	4	and	and	CCONJ
ejpam-846	458	5	the	the	DET
ejpam-846	458	6	underlying	underlie	VERB
ejpam-846	458	7	assets	asset	NOUN
ejpam-846	458	8	are	be	AUX
ejpam-846	458	9	s&p	s&p	PROPN
ejpam-846	458	10	100	100	NUM
ejpam-846	458	11	stocks	stock	NOUN
ejpam-846	458	12	,	,	PUNCT
ejpam-846	458	13	see	see	VERB
ejpam-846	458	14	table	table	NOUN
ejpam-846	458	15	1	1	NUM
ejpam-846	458	16	.	.	X
ejpam-846	459	1	six	six	NUM
ejpam-846	459	2	stocks	stock	NOUN
ejpam-846	459	3	have	have	AUX
ejpam-846	459	4	been	be	AUX
ejpam-846	459	5	removed	remove	VERB
ejpam-846	459	6	from	from	ADP
ejpam-846	459	7	the	the	DET
ejpam-846	459	8	s&p	s&p	PROPN
ejpam-846	459	9	100	100	NUM
ejpam-846	459	10	list	list	NOUN
ejpam-846	459	11	as	as	SCONJ
ejpam-846	459	12	those	those	PRON
ejpam-846	459	13	do	do	AUX
ejpam-846	459	14	not	not	PART
ejpam-846	459	15	have	have	VERB
ejpam-846	459	16	listings	listing	NOUN
ejpam-846	459	17	for	for	ADP
ejpam-846	459	18	the	the	DET
ejpam-846	459	19	entire	entire	ADJ
ejpam-846	459	20	10year	10year	NUM
ejpam-846	459	21	duration	duration	NOUN
ejpam-846	459	22	,	,	PUNCT
ejpam-846	459	23	and	and	CCONJ
ejpam-846	460	1	thus	thus	ADV
ejpam-846	460	2	,	,	PUNCT
ejpam-846	460	3	k	k	PROPN
ejpam-846	460	4	=	=	SYM
ejpam-846	460	5	95	95	NUM
ejpam-846	460	6	.	.	PUNCT
ejpam-846	461	1	we	we	PRON
ejpam-846	461	2	use	use	VERB
ejpam-846	461	3	the	the	DET
ejpam-846	461	4	spdr	spdr	PROPN
ejpam-846	461	5	trust	trust	PROPN
ejpam-846	461	6	,	,	PUNCT
ejpam-846	461	7	which	which	PRON
ejpam-846	461	8	is	be	AUX
ejpam-846	461	9	an	an	DET
ejpam-846	461	10	exchange	exchange	NOUN
ejpam-846	461	11	-	-	PUNCT
ejpam-846	461	12	traded	trade	VERB
ejpam-846	461	13	fund	fund	NOUN
ejpam-846	461	14	that	that	PRON
ejpam-846	461	15	holds	hold	VERB
ejpam-846	461	16	all	all	PRON
ejpam-846	461	17	of	of	ADP
ejpam-846	461	18	the	the	DET
ejpam-846	461	19	s&p	s&p	PROPN
ejpam-846	461	20	500	500	NUM
ejpam-846	461	21	index	index	NOUN
ejpam-846	461	22	stocks	stock	NOUN
ejpam-846	461	23	,	,	PUNCT
ejpam-846	461	24	as	as	ADP
ejpam-846	461	25	the	the	DET
ejpam-846	461	26	market	market	NOUN
ejpam-846	461	27	barometer	barometer	NOUN
ejpam-846	461	28	for	for	ADP
ejpam-846	461	29	stock	stock	NOUN
ejpam-846	461	30	-	-	PUNCT
ejpam-846	461	31	beta	beta	NOUN
ejpam-846	461	32	calculations	calculation	NOUN
ejpam-846	461	33	.	.	PUNCT
ejpam-846	462	1	spdr	spdr	NOUN
ejpam-846	462	2	trades	trade	NOUN
ejpam-846	462	3	under	under	ADP
ejpam-846	462	4	the	the	DET
ejpam-846	462	5	ticker	ticker	NOUN
ejpam-846	462	6	symbol	symbol	NOUN
ejpam-846	462	7	spy	spy	NOUN
ejpam-846	462	8	and	and	CCONJ
ejpam-846	462	9	it	it	PRON
ejpam-846	462	10	is	be	AUX
ejpam-846	462	11	listed	list	VERB
ejpam-846	462	12	as	as	ADP
ejpam-846	462	13	the	the	DET
ejpam-846	462	14	last	last	ADJ
ejpam-846	462	15	ticker	ticker	NOUN
ejpam-846	462	16	in	in	ADP
ejpam-846	462	17	table	table	NOUN
ejpam-846	462	18	1	1	NUM
ejpam-846	462	19	.	.	PUNCT
ejpam-846	463	1	since	since	SCONJ
ejpam-846	463	2	k	k	PROPN
ejpam-846	463	3	=	=	SYM
ejpam-846	463	4	95	95	NUM
ejpam-846	463	5	,	,	PUNCT
ejpam-846	463	6	the	the	DET
ejpam-846	463	7	second	second	ADJ
ejpam-846	463	8	moment	moment	NOUN
ejpam-846	463	9	approximation	approximation	NOUN
ejpam-846	463	10	yields	yield	VERB
ejpam-846	463	11	96	96	NUM
ejpam-846	463	12	return	return	NOUN
ejpam-846	463	13	scenarios	scenario	NOUN
ejpam-846	463	14	,	,	PUNCT
ejpam-846	463	15	while	while	SCONJ
ejpam-846	463	16	the	the	DET
ejpam-846	463	17	historical	historical	ADJ
ejpam-846	463	18	sample	sample	NOUN
ejpam-846	463	19	has	have	VERB
ejpam-846	463	20	over	over	ADP
ejpam-846	463	21	2,500	2,500	NUM
ejpam-846	463	22	return	return	NOUN
ejpam-846	463	23	vectors	vector	NOUN
ejpam-846	463	24	.	.	PUNCT
ejpam-846	464	1	the	the	DET
ejpam-846	464	2	objective	objective	NOUN
ejpam-846	464	3	of	of	ADP
ejpam-846	464	4	the	the	DET
ejpam-846	464	5	financial	financial	ADJ
ejpam-846	464	6	decision	decision	NOUN
ejpam-846	464	7	problem	problem	NOUN
ejpam-846	464	8	is	be	AUX
ejpam-846	464	9	to	to	PART
ejpam-846	464	10	choose	choose	VERB
ejpam-846	464	11	assets	asset	NOUN
ejpam-846	464	12	to	to	PART
ejpam-846	464	13	invest	invest	VERB
ejpam-846	464	14	(	(	PUNCT
ejpam-846	464	15	long	long	ADJ
ejpam-846	464	16	or	or	CCONJ
ejpam-846	464	17	short	short	ADJ
ejpam-846	464	18	)	)	PUNCT
ejpam-846	464	19	at	at	ADP
ejpam-846	464	20	the	the	DET
ejpam-846	464	21	beginning	beginning	NOUN
ejpam-846	464	22	of	of	ADP
ejpam-846	464	23	the	the	DET
ejpam-846	464	24	year	year	NOUN
ejpam-846	464	25	2010	2010	NUM
ejpam-846	464	26	for	for	ADP
ejpam-846	464	27	a	a	DET
ejpam-846	464	28	duration	duration	NOUN
ejpam-846	464	29	of	of	ADP
ejpam-846	464	30	a	a	DET
ejpam-846	464	31	half	half	ADJ
ejpam-846	464	32	-	-	PUNCT
ejpam-846	464	33	year	year	NOUN
ejpam-846	464	34	,	,	PUNCT
ejpam-846	464	35	i.e.	i.e.	X
ejpam-846	464	36	,	,	PUNCT
ejpam-846	464	37	until	until	ADP
ejpam-846	464	38	june	june	PROPN
ejpam-846	464	39	30	30	NUM
ejpam-846	464	40	.	.	PUNCT
ejpam-846	465	1	however	however	ADV
ejpam-846	465	2	,	,	PUNCT
ejpam-846	465	3	the	the	DET
ejpam-846	465	4	portfolio	portfolio	NOUN
ejpam-846	465	5	formed	form	VERB
ejpam-846	465	6	at	at	ADP
ejpam-846	465	7	the	the	DET
ejpam-846	465	8	beginning	beginning	NOUN
ejpam-846	465	9	of	of	ADP
ejpam-846	465	10	2010	2010	NUM
ejpam-846	465	11	will	will	AUX
ejpam-846	465	12	be	be	AUX
ejpam-846	465	13	rebalanced	rebalance	VERB
ejpam-846	465	14	at	at	ADP
ejpam-846	465	15	the	the	DET
ejpam-846	465	16	end	end	NOUN
ejpam-846	465	17	of	of	ADP
ejpam-846	465	18	every	every	DET
ejpam-846	465	19	month	month	NOUN
ejpam-846	465	20	as	as	SCONJ
ejpam-846	465	21	market	market	NOUN
ejpam-846	465	22	dynamics	dynamic	NOUN
ejpam-846	465	23	evolve	evolve	VERB
ejpam-846	465	24	.	.	PUNCT
ejpam-846	466	1	therefore	therefore	ADV
ejpam-846	466	2	,	,	PUNCT
ejpam-846	466	3	when	when	SCONJ
ejpam-846	466	4	the	the	DET
ejpam-846	466	5	portfolio	portfolio	NOUN
ejpam-846	466	6	is	be	AUX
ejpam-846	466	7	rebalanced	rebalance	VERB
ejpam-846	466	8	at	at	ADP
ejpam-846	466	9	the	the	DET
ejpam-846	466	10	beginning	beginning	NOUN
ejpam-846	466	11	of	of	ADP
ejpam-846	466	12	february	february	PROPN
ejpam-846	466	13	2010	2010	NUM
ejpam-846	466	14	,	,	PUNCT
ejpam-846	466	15	an	an	DET
ejpam-846	466	16	additional	additional	ADJ
ejpam-846	466	17	data	datum	NOUN
ejpam-846	466	18	set	set	VERB
ejpam-846	466	19	for	for	ADP
ejpam-846	466	20	january	january	PROPN
ejpam-846	466	21	2010	2010	NUM
ejpam-846	466	22	will	will	AUX
ejpam-846	466	23	be	be	AUX
ejpam-846	466	24	available	available	ADJ
ejpam-846	466	25	and	and	CCONJ
ejpam-846	466	26	it	it	PRON
ejpam-846	466	27	is	be	AUX
ejpam-846	466	28	used	use	VERB
ejpam-846	466	29	to	to	PART
ejpam-846	466	30	append	append	VERB
ejpam-846	466	31	the	the	DET
ejpam-846	466	32	historical	historical	ADJ
ejpam-846	466	33	data	datum	NOUN
ejpam-846	466	34	set	set	VERB
ejpam-846	466	35	of	of	ADP
ejpam-846	466	36	2000	2000	NUM
ejpam-846	466	37	-	-	SYM
ejpam-846	466	38	2009	2009	NUM
ejpam-846	466	39	when	when	SCONJ
ejpam-846	466	40	constructing	construct	VERB
ejpam-846	466	41	the	the	DET
ejpam-846	466	42	approximated	approximated	ADJ
ejpam-846	466	43	scenario	scenario	NOUN
ejpam-846	466	44	set	set	VERB
ejpam-846	466	45	for	for	ADP
ejpam-846	466	46	the	the	DET
ejpam-846	466	47	period	period	NOUN
ejpam-846	466	48	of	of	ADP
ejpam-846	466	49	february	february	PROPN
ejpam-846	466	50	2010	2010	NUM
ejpam-846	466	51	.	.	PUNCT
ejpam-846	467	1	under	under	ADP
ejpam-846	467	2	the	the	DET
ejpam-846	467	3	monthly	monthly	ADJ
ejpam-846	467	4	rebalancing	rebalancing	NOUN
ejpam-846	467	5	edirisinghe	edirisinghe	NOUN
ejpam-846	467	6	/	/	SYM
ejpam-846	467	7	eur	eur	PROPN
ejpam-846	467	8	.	.	PUNCT
ejpam-846	468	1	j.	j.	PROPN
ejpam-846	468	2	pure	pure	PROPN
ejpam-846	468	3	appl	appl	PROPN
ejpam-846	468	4	.	.	PROPN
ejpam-846	468	5	math	math	PROPN
ejpam-846	468	6	,	,	PUNCT
ejpam-846	468	7	3	3	NUM
ejpam-846	468	8	(	(	PUNCT
ejpam-846	468	9	2010	2010	NUM
ejpam-846	468	10	)	)	PUNCT
ejpam-846	468	11	,	,	PUNCT
ejpam-846	468	12	572	572	NUM
ejpam-846	468	13	-	-	SYM
ejpam-846	468	14	592	592	NUM
ejpam-846	468	15	587	587	NUM
ejpam-846	468	16	aa	aa	PROPN
ejpam-846	468	17	aapl	aapl	PROPN
ejpam-846	468	18	abt	abt	PROPN
ejpam-846	468	19	aep	aep	PROPN
ejpam-846	469	1	all	all	PRON
ejpam-846	469	2	amgn	amgn	PROPN
ejpam-846	469	3	amzn	amzn	PROPN
ejpam-846	469	4	avp	avp	PROPN
ejpam-846	469	5	axp	axp	PROPN
ejpam-846	469	6	ba	ba	PROPN
ejpam-846	469	7	bac	bac	PROPN
ejpam-846	469	8	bax	bax	PROPN
ejpam-846	469	9	bhi	bhi	PROPN
ejpam-846	469	10	bk	bk	PROPN
ejpam-846	469	11	bmy	bmy	PROPN
ejpam-846	469	12	brk	brk	PROPN
ejpam-846	469	13	-	-	PUNCT
ejpam-846	469	14	b	b	PROPN
ejpam-846	469	15	c	c	PROPN
ejpam-846	469	16	cat	cat	PROPN
ejpam-846	469	17	cl	cl	PROPN
ejpam-846	469	18	cmcsa	cmcsa	VERB
ejpam-846	469	19	cof	cof	PROPN
ejpam-846	469	20	cop	cop	PROPN
ejpam-846	469	21	cost	cost	PROPN
ejpam-846	469	22	cpb	cpb	PROPN
ejpam-846	469	23	csco	csco	PROPN
ejpam-846	469	24	cvs	cvs	PROPN
ejpam-846	469	25	cvx	cvx	PROPN
ejpam-846	469	26	dd	dd	PROPN
ejpam-846	469	27	dell	dell	PROPN
ejpam-846	469	28	dis	dis	PROPN
ejpam-846	469	29	dow	dow	PROPN
ejpam-846	469	30	dvn	dvn	PROPN
ejpam-846	469	31	emc	emc	PROPN
ejpam-846	469	32	etr	etr	PROPN
ejpam-846	469	33	exc	exc	PROPN
ejpam-846	469	34	f	f	PROPN
ejpam-846	469	35	fcx	fcx	PROPN
ejpam-846	469	36	fdx	fdx	PROPN
ejpam-846	469	37	gd	gd	PROPN
ejpam-846	469	38	ge	ge	PROPN
ejpam-846	469	39	gild	gild	PROPN
ejpam-846	470	1	gs	gs	PROPN
ejpam-846	470	2	hal	hal	PROPN
ejpam-846	470	3	hd	hd	PROPN
ejpam-846	470	4	hnz	hnz	PROPN
ejpam-846	470	5	hon	hon	PROPN
ejpam-846	470	6	hpq	hpq	PROPN
ejpam-846	470	7	ibm	ibm	PROPN
ejpam-846	470	8	intc	intc	NOUN
ejpam-846	470	9	jnj	jnj	PROPN
ejpam-846	470	10	jpm	jpm	PROPN
ejpam-846	470	11	kft	kft	PROPN
ejpam-846	470	12	ko	ko	PROPN
ejpam-846	470	13	lmt	lmt	PROPN
ejpam-846	470	14	low	low	PROPN
ejpam-846	470	15	mcd	mcd	PROPN
ejpam-846	470	16	mdt	mdt	PROPN
ejpam-846	470	17	met	meet	VERB
ejpam-846	470	18	mmm	mmm	INTJ
ejpam-846	470	19	mo	mo	PROPN
ejpam-846	470	20	mon	mon	PROPN
ejpam-846	470	21	mrk	mrk	PROPN
ejpam-846	470	22	ms	ms	PROPN
ejpam-846	470	23	msft	msft	PROPN
ejpam-846	470	24	nke	nke	PROPN
ejpam-846	470	25	nov	nov	PROPN
ejpam-846	470	26	nsc	nsc	PROPN
ejpam-846	470	27	nwsa	nwsa	PROPN
ejpam-846	470	28	orcl	orcl	PROPN
ejpam-846	470	29	oxy	oxy	PROPN
ejpam-846	470	30	pep	pep	NOUN
ejpam-846	471	1	pfe	pfe	PROPN
ejpam-846	471	2	pg	pg	PROPN
ejpam-846	471	3	qcom	qcom	PROPN
ejpam-846	471	4	rf	rf	PROPN
ejpam-846	471	5	rtn	rtn	PROPN
ejpam-846	471	6	s	s	PROPN
ejpam-846	472	1	slb	slb	PROPN
ejpam-846	472	2	sle	sle	PROPN
ejpam-846	472	3	so	so	SCONJ
ejpam-846	472	4	t	t	PROPN
ejpam-846	472	5	tgt	tgt	PROPN
ejpam-846	473	1	twx	twx	PROPN
ejpam-846	473	2	txn	txn	VERB
ejpam-846	473	3	unh	unh	PROPN
ejpam-846	473	4	ups	up	NOUN
ejpam-846	473	5	utx	utx	PROPN
ejpam-846	473	6	vz	vz	PROPN
ejpam-846	473	7	wag	wag	PROPN
ejpam-846	473	8	wfc	wfc	PROPN
ejpam-846	473	9	wmb	wmb	PROPN
ejpam-846	473	10	wmt	wmt	PROPN
ejpam-846	473	11	wy	wy	PROPN
ejpam-846	473	12	xom	xom	PROPN
ejpam-846	473	13	xrx	xrx	PROPN
ejpam-846	473	14	spy	spy	NOUN
ejpam-846	473	15	table	table	NOUN
ejpam-846	473	16	1	1	NUM
ejpam-846	473	17	:	:	PUNCT
ejpam-846	473	18	list	list	NOUN
ejpam-846	473	19	of	of	ADP
ejpam-846	473	20	stock	stock	PROPN
ejpam-846	473	21	ticker	ticker	PROPN
ejpam-846	473	22	symbols	symbols	PROPN
ejpam-846	473	23	strategy	strategy	NOUN
ejpam-846	473	24	,	,	PUNCT
ejpam-846	473	25	such	such	DET
ejpam-846	473	26	an	an	DET
ejpam-846	473	27	approximation	approximation	NOUN
ejpam-846	473	28	is	be	AUX
ejpam-846	473	29	needed	need	VERB
ejpam-846	473	30	at	at	ADP
ejpam-846	473	31	the	the	DET
ejpam-846	473	32	beginning	beginning	NOUN
ejpam-846	473	33	of	of	ADP
ejpam-846	473	34	each	each	DET
ejpam-846	473	35	month	month	NOUN
ejpam-846	473	36	in	in	ADP
ejpam-846	473	37	the	the	DET
ejpam-846	473	38	horizon	horizon	NOUN
ejpam-846	473	39	,	,	PUNCT
ejpam-846	473	40	conditional	conditional	ADJ
ejpam-846	473	41	upon	upon	SCONJ
ejpam-846	473	42	the	the	DET
ejpam-846	473	43	data	datum	NOUN
ejpam-846	473	44	available	available	ADJ
ejpam-846	473	45	prior	prior	ADV
ejpam-846	473	46	to	to	ADP
ejpam-846	473	47	that	that	DET
ejpam-846	473	48	point	point	NOUN
ejpam-846	473	49	in	in	ADP
ejpam-846	473	50	time	time	NOUN
ejpam-846	473	51	.	.	PUNCT
ejpam-846	474	1	this	this	DET
ejpam-846	474	2	approach	approach	NOUN
ejpam-846	474	3	results	result	VERB
ejpam-846	474	4	in	in	ADP
ejpam-846	474	5	a	a	DET
ejpam-846	474	6	dynamically	dynamically	ADV
ejpam-846	474	7	evolving	evolve	VERB
ejpam-846	474	8	portfolio	portfolio	NOUN
ejpam-846	474	9	,	,	PUNCT
ejpam-846	474	10	and	and	CCONJ
ejpam-846	474	11	the	the	DET
ejpam-846	474	12	resulting	result	VERB
ejpam-846	474	13	portfolios	portfolio	NOUN
ejpam-846	474	14	are	be	AUX
ejpam-846	474	15	(	(	PUNCT
ejpam-846	474	16	out	out	ADV
ejpam-846	474	17	-	-	PUNCT
ejpam-846	474	18	of	of	ADP
ejpam-846	474	19	-	-	PUNCT
ejpam-846	474	20	sample	sample	NOUN
ejpam-846	474	21	)	)	PUNCT
ejpam-846	474	22	simulated	simulate	VERB
ejpam-846	474	23	using	use	VERB
ejpam-846	474	24	the	the	DET
ejpam-846	474	25	(	(	PUNCT
ejpam-846	474	26	actual	actual	ADJ
ejpam-846	474	27	)	)	PUNCT
ejpam-846	474	28	realized	realize	VERB
ejpam-846	474	29	stock	stock	NOUN
ejpam-846	474	30	price	price	NOUN
ejpam-846	474	31	series	series	NOUN
ejpam-846	474	32	during	during	ADP
ejpam-846	474	33	the	the	DET
ejpam-846	474	34	concerned	concerned	ADJ
ejpam-846	474	35	monthly	monthly	ADJ
ejpam-846	474	36	period	period	NOUN
ejpam-846	474	37	.	.	PUNCT
ejpam-846	475	1	then	then	ADV
ejpam-846	475	2	,	,	PUNCT
ejpam-846	475	3	the	the	DET
ejpam-846	475	4	portfolio	portfolio	NOUN
ejpam-846	475	5	performance	performance	NOUN
ejpam-846	475	6	is	be	AUX
ejpam-846	475	7	compared	compare	VERB
ejpam-846	475	8	against	against	ADP
ejpam-846	475	9	the	the	DET
ejpam-846	475	10	market	market	NOUN
ejpam-846	475	11	tracker	tracker	NOUN
ejpam-846	475	12	,	,	PUNCT
ejpam-846	475	13	spy	spy	NOUN
ejpam-846	475	14	,	,	PUNCT
ejpam-846	475	15	for	for	ADP
ejpam-846	475	16	january	january	PROPN
ejpam-846	475	17	-	-	SYM
ejpam-846	475	18	june	june	PROPN
ejpam-846	475	19	,	,	PUNCT
ejpam-846	475	20	2010	2010	NUM
ejpam-846	475	21	.	.	PUNCT
ejpam-846	476	1	for	for	ADP
ejpam-846	476	2	the	the	DET
ejpam-846	476	3	specific	specific	ADJ
ejpam-846	476	4	experiment	experiment	NOUN
ejpam-846	476	5	here	here	ADV
ejpam-846	476	6	,	,	PUNCT
ejpam-846	476	7	we	we	PRON
ejpam-846	476	8	set	set	VERB
ejpam-846	476	9	b0	b0	NOUN
ejpam-846	476	10	=	=	SYM
ejpam-846	476	11	$	$	SYM
ejpam-846	476	12	1	1	NUM
ejpam-846	476	13	million	million	NUM
ejpam-846	476	14	at	at	ADP
ejpam-846	476	15	the	the	DET
ejpam-846	476	16	end	end	NOUN
ejpam-846	476	17	of	of	ADP
ejpam-846	476	18	2009	2009	NUM
ejpam-846	476	19	,	,	PUNCT
ejpam-846	476	20	xmin	xmin	PROPN
ejpam-846	476	21	j	j	PROPN
ejpam-846	476	22	=	=	SYM
ejpam-846	476	23	−10%b0	−10%b0	PROPN
ejpam-846	476	24	,	,	PUNCT
ejpam-846	476	25	xmax	xmax	PROPN
ejpam-846	476	26	j	j	PROPN
ejpam-846	477	1	=	=	SYM
ejpam-846	477	2	10%b0	10%b0	NUM
ejpam-846	477	3	,	,	PUNCT
ejpam-846	477	4	and	and	CCONJ
ejpam-846	477	5	ν	ν	X
ejpam-846	477	6	=	=	SYM
ejpam-846	477	7	5	5	NUM
ejpam-846	477	8	%	%	NOUN
ejpam-846	477	9	.	.	PUNCT
ejpam-846	478	1	therefore	therefore	ADV
ejpam-846	478	2	,	,	PUNCT
ejpam-846	478	3	no	no	DET
ejpam-846	478	4	stock	stock	NOUN
ejpam-846	478	5	receives	receive	VERB
ejpam-846	478	6	more	more	ADJ
ejpam-846	478	7	than	than	ADP
ejpam-846	478	8	10	10	NUM
ejpam-846	478	9	%	%	NOUN
ejpam-846	478	10	of	of	ADP
ejpam-846	478	11	wealth	wealth	NOUN
ejpam-846	478	12	for	for	ADP
ejpam-846	478	13	long	long	ADV
ejpam-846	478	14	/	/	SYM
ejpam-846	478	15	short	short	ADJ
ejpam-846	478	16	investment	investment	NOUN
ejpam-846	478	17	,	,	PUNCT
ejpam-846	478	18	and	and	CCONJ
ejpam-846	478	19	the	the	DET
ejpam-846	478	20	portfolio	portfolio	NOUN
ejpam-846	478	21	’s	’s	PART
ejpam-846	478	22	market	market	NOUN
ejpam-846	478	23	dependency	dependency	NOUN
ejpam-846	478	24	is	be	AUX
ejpam-846	478	25	controlled	control	VERB
ejpam-846	478	26	within	within	ADP
ejpam-846	478	27	5	5	NUM
ejpam-846	478	28	%	%	NOUN
ejpam-846	478	29	.	.	PUNCT
ejpam-846	479	1	all	all	DET
ejpam-846	479	2	initial	initial	ADJ
ejpam-846	479	3	positions	position	NOUN
ejpam-846	479	4	,	,	PUNCT
ejpam-846	479	5	at	at	ADP
ejpam-846	479	6	the	the	DET
ejpam-846	479	7	beginning	beginning	NOUN
ejpam-846	479	8	of	of	ADP
ejpam-846	479	9	2010	2010	NUM
ejpam-846	479	10	is	be	AUX
ejpam-846	479	11	set	set	VERB
ejpam-846	479	12	to	to	ADP
ejpam-846	479	13	zero	zero	NUM
ejpam-846	479	14	.	.	PUNCT
ejpam-846	480	1	as	as	SCONJ
ejpam-846	480	2	the	the	DET
ejpam-846	480	3	portfolio	portfolio	NOUN
ejpam-846	480	4	is	be	AUX
ejpam-846	480	5	monthly	monthly	ADV
ejpam-846	480	6	-	-	PUNCT
ejpam-846	480	7	rebalanced	rebalance	VERB
ejpam-846	480	8	,	,	PUNCT
ejpam-846	480	9	b0	b0	NOUN
ejpam-846	480	10	is	be	AUX
ejpam-846	480	11	automatically	automatically	ADV
ejpam-846	480	12	adjusted	adjust	VERB
ejpam-846	480	13	to	to	ADP
ejpam-846	480	14	the	the	DET
ejpam-846	480	15	cash	cash	NOUN
ejpam-846	480	16	position	position	NOUN
ejpam-846	480	17	carried	carry	VERB
ejpam-846	480	18	forward	forward	ADV
ejpam-846	480	19	in	in	ADP
ejpam-846	480	20	the	the	DET
ejpam-846	480	21	portfolio	portfolio	NOUN
ejpam-846	480	22	and	and	CCONJ
ejpam-846	480	23	x0	x0	PROPN
ejpam-846	480	24	is	be	AUX
ejpam-846	480	25	set	set	VERB
ejpam-846	480	26	to	to	ADP
ejpam-846	480	27	the	the	DET
ejpam-846	480	28	beginning	begin	VERB
ejpam-846	480	29	stock	stock	NOUN
ejpam-846	480	30	positions	position	NOUN
ejpam-846	480	31	at	at	ADP
ejpam-846	480	32	the	the	DET
ejpam-846	480	33	rebalancing	rebalancing	NOUN
ejpam-846	480	34	time	time	NOUN
ejpam-846	480	35	.	.	PUNCT
ejpam-846	481	1	for	for	ADP
ejpam-846	481	2	the	the	DET
ejpam-846	481	3	transactions	transaction	NOUN
ejpam-846	481	4	and	and	CCONJ
ejpam-846	481	5	slippage	slippage	NOUN
ejpam-846	481	6	cost	cost	NOUN
ejpam-846	481	7	model	model	NOUN
ejpam-846	481	8	,	,	PUNCT
ejpam-846	481	9	a1j	a1j	X
ejpam-846	481	10	=	=	SYM
ejpam-846	481	11	0.02	0.02	NUM
ejpam-846	481	12	and	and	CCONJ
ejpam-846	481	13	a2j	a2j	NOUN
ejpam-846	481	14	=	=	PRON
ejpam-846	481	15	1.0	1.0	NUM
ejpam-846	481	16	are	be	AUX
ejpam-846	481	17	set	set	VERB
ejpam-846	481	18	for	for	ADP
ejpam-846	481	19	all	all	DET
ejpam-846	481	20	stocks	stock	NOUN
ejpam-846	481	21	.	.	PUNCT
ejpam-846	482	1	while	while	SCONJ
ejpam-846	482	2	these	these	DET
ejpam-846	482	3	parameters	parameter	NOUN
ejpam-846	482	4	depend	depend	VERB
ejpam-846	482	5	on	on	ADP
ejpam-846	482	6	the	the	DET
ejpam-846	482	7	asset	asset	NOUN
ejpam-846	482	8	and	and	CCONJ
ejpam-846	482	9	they	they	PRON
ejpam-846	482	10	need	need	VERB
ejpam-846	482	11	to	to	PART
ejpam-846	482	12	be	be	AUX
ejpam-846	482	13	calibrated	calibrate	VERB
ejpam-846	482	14	to	to	ADP
ejpam-846	482	15	the	the	DET
ejpam-846	482	16	market	market	NOUN
ejpam-846	482	17	dynamics	dynamic	NOUN
ejpam-846	482	18	,	,	PUNCT
ejpam-846	482	19	for	for	ADP
ejpam-846	482	20	simplicity	simplicity	NOUN
ejpam-846	482	21	here	here	ADV
ejpam-846	482	22	,	,	PUNCT
ejpam-846	482	23	stationary	stationary	ADJ
ejpam-846	482	24	constants	constant	NOUN
ejpam-846	482	25	are	be	AUX
ejpam-846	482	26	assumed	assume	VERB
ejpam-846	482	27	.	.	PUNCT
ejpam-846	483	1	expected	expect	VERB
ejpam-846	483	2	trading	trading	NOUN
ejpam-846	483	3	volume	volume	NOUN
ejpam-846	483	4	for	for	ADP
ejpam-846	483	5	each	each	DET
ejpam-846	483	6	asset	asset	NOUN
ejpam-846	483	7	for	for	ADP
ejpam-846	483	8	computing	compute	VERB
ejpam-846	483	9	the	the	DET
ejpam-846	483	10	slippage	slippage	NOUN
ejpam-846	483	11	costs	cost	NOUN
ejpam-846	483	12	is	be	AUX
ejpam-846	483	13	determined	determine	VERB
ejpam-846	483	14	for	for	ADP
ejpam-846	483	15	the	the	DET
ejpam-846	483	16	trading	trading	NOUN
ejpam-846	483	17	day	day	NOUN
ejpam-846	483	18	by	by	ADP
ejpam-846	483	19	the	the	DET
ejpam-846	483	20	average	average	ADJ
ejpam-846	483	21	volume	volume	NOUN
ejpam-846	483	22	of	of	ADP
ejpam-846	483	23	the	the	DET
ejpam-846	483	24	preceding	precede	VERB
ejpam-846	483	25	(	(	PUNCT
ejpam-846	483	26	historical	historical	ADJ
ejpam-846	483	27	)	)	PUNCT
ejpam-846	483	28	month	month	NOUN
ejpam-846	483	29	.	.	PUNCT
ejpam-846	484	1	the	the	DET
ejpam-846	484	2	portfolio	portfolio	NOUN
ejpam-846	484	3	monthly	monthly	ADJ
ejpam-846	484	4	target	target	NOUN
ejpam-846	484	5	return	return	NOUN
ejpam-846	484	6	is	be	AUX
ejpam-846	484	7	set	set	VERB
ejpam-846	484	8	at	at	ADP
ejpam-846	484	9	an	an	DET
ejpam-846	484	10	aggressive	aggressive	ADJ
ejpam-846	484	11	c	c	NOUN
ejpam-846	484	12	=	=	SYM
ejpam-846	484	13	3	3	NUM
ejpam-846	484	14	%	%	NOUN
ejpam-846	484	15	during	during	ADP
ejpam-846	484	16	jan	jan	PROPN
ejpam-846	484	17	-	-	PUNCT
ejpam-846	484	18	jun	jun	PROPN
ejpam-846	484	19	,	,	PUNCT
ejpam-846	484	20	2010	2010	NUM
ejpam-846	484	21	.	.	PUNCT
ejpam-846	485	1	thus	thus	ADV
ejpam-846	485	2	,	,	PUNCT
ejpam-846	485	3	it	it	PRON
ejpam-846	485	4	corresponds	correspond	VERB
ejpam-846	485	5	to	to	ADP
ejpam-846	485	6	a	a	DET
ejpam-846	485	7	compounded	compound	VERB
ejpam-846	485	8	half	half	ADJ
ejpam-846	485	9	-	-	PUNCT
ejpam-846	485	10	year	year	NOUN
ejpam-846	485	11	return	return	NOUN
ejpam-846	485	12	target	target	NOUN
ejpam-846	485	13	of	of	ADP
ejpam-846	485	14	19.41	19.41	NUM
ejpam-846	485	15	%	%	NOUN
ejpam-846	485	16	.	.	PUNCT
ejpam-846	486	1	the	the	DET
ejpam-846	486	2	riskfree	riskfree	NOUN
ejpam-846	486	3	rate	rate	NOUN
ejpam-846	486	4	is	be	AUX
ejpam-846	486	5	assumed	assume	VERB
ejpam-846	486	6	to	to	PART
ejpam-846	486	7	be	be	AUX
ejpam-846	486	8	zero	zero	NUM
ejpam-846	486	9	.	.	PUNCT
ejpam-846	487	1	5	5	X
ejpam-846	487	2	.	.	X
ejpam-846	487	3	portfolio	portfolio	NOUN
ejpam-846	487	4	performance	performance	NOUN
ejpam-846	487	5	the	the	DET
ejpam-846	487	6	portfolio	portfolio	NOUN
ejpam-846	487	7	model	model	NOUN
ejpam-846	487	8	with	with	ADP
ejpam-846	487	9	approximating	approximate	VERB
ejpam-846	487	10	scenarios	scenario	NOUN
ejpam-846	487	11	is	be	AUX
ejpam-846	487	12	evaluated	evaluate	VERB
ejpam-846	487	13	by	by	ADP
ejpam-846	487	14	computing	compute	VERB
ejpam-846	487	15	performance	performance	NOUN
ejpam-846	487	16	metrics	metric	NOUN
ejpam-846	487	17	for	for	ADP
ejpam-846	487	18	the	the	DET
ejpam-846	487	19	(	(	PUNCT
ejpam-846	487	20	out	out	ADP
ejpam-846	487	21	-	-	PUNCT
ejpam-846	487	22	of	of	ADP
ejpam-846	487	23	-	-	PUNCT
ejpam-846	487	24	sample	sample	NOUN
ejpam-846	487	25	simulated	simulate	VERB
ejpam-846	487	26	)	)	PUNCT
ejpam-846	487	27	wealth	wealth	NOUN
ejpam-846	487	28	series	series	NOUN
ejpam-846	487	29	of	of	ADP
ejpam-846	487	30	the	the	DET
ejpam-846	487	31	managed	manage	VERB
ejpam-846	487	32	portfolio	portfolio	NOUN
ejpam-846	487	33	.	.	PUNCT
ejpam-846	488	1	we	we	PRON
ejpam-846	488	2	consider	consider	VERB
ejpam-846	488	3	annualized	annualize	VERB
ejpam-846	488	4	rate	rate	NOUN
ejpam-846	488	5	of	of	ADP
ejpam-846	488	6	return	return	NOUN
ejpam-846	488	7	(	(	PUNCT
ejpam-846	488	8	aror	aror	NOUN
ejpam-846	488	9	)	)	PUNCT
ejpam-846	488	10	,	,	PUNCT
ejpam-846	488	11	which	which	PRON
ejpam-846	488	12	is	be	AUX
ejpam-846	488	13	the	the	DET
ejpam-846	488	14	portfolio	portfolio	NOUN
ejpam-846	488	15	daily	daily	ADJ
ejpam-846	488	16	average	average	ADJ
ejpam-846	488	17	rate	rate	NOUN
ejpam-846	488	18	of	of	ADP
ejpam-846	488	19	return	return	NOUN
ejpam-846	488	20	,	,	PUNCT
ejpam-846	488	21	net	net	NOUN
ejpam-846	488	22	of	of	ADP
ejpam-846	488	23	trading	trading	NOUN
ejpam-846	488	24	costs	cost	NOUN
ejpam-846	488	25	,	,	PUNCT
ejpam-846	488	26	annualized	annualize	VERB
ejpam-846	488	27	over	over	ADP
ejpam-846	488	28	250	250	NUM
ejpam-846	488	29	days	day	NOUN
ejpam-846	488	30	of	of	ADP
ejpam-846	488	31	trading	trading	NOUN
ejpam-846	488	32	,	,	PUNCT
ejpam-846	488	33	as	as	ADV
ejpam-846	488	34	well	well	ADV
ejpam-846	488	35	as	as	ADP
ejpam-846	488	36	the	the	DET
ejpam-846	488	37	annualized	annualize	VERB
ejpam-846	488	38	standard	standard	ADJ
ejpam-846	488	39	deviation	deviation	NOUN
ejpam-846	488	40	(	(	PUNCT
ejpam-846	488	41	astd	astd	PROPN
ejpam-846	488	42	)	)	PUNCT
ejpam-846	488	43	,	,	PUNCT
ejpam-846	488	44	which	which	PRON
ejpam-846	488	45	is	be	AUX
ejpam-846	488	46	the	the	DET
ejpam-846	488	47	standard	standard	ADJ
ejpam-846	488	48	deviation	deviation	NOUN
ejpam-846	488	49	of	of	ADP
ejpam-846	488	50	the	the	DET
ejpam-846	488	51	daily	daily	ADJ
ejpam-846	488	52	portfolio	portfolio	NOUN
ejpam-846	488	53	net	net	ADJ
ejpam-846	488	54	rate	rate	NOUN
ejpam-846	488	55	of	of	ADP
ejpam-846	488	56	return	return	NOUN
ejpam-846	488	57	series	series	NOUN
ejpam-846	488	58	,	,	PUNCT
ejpam-846	488	59	annualized	annualize	VERB
ejpam-846	488	60	over	over	ADP
ejpam-846	488	61	250	250	NUM
ejpam-846	488	62	days	day	NOUN
ejpam-846	488	63	of	of	ADP
ejpam-846	488	64	trading	trading	NOUN
ejpam-846	488	65	.	.	PUNCT
ejpam-846	489	1	in	in	ADP
ejpam-846	489	2	addition	addition	NOUN
ejpam-846	489	3	,	,	PUNCT
ejpam-846	489	4	we	we	PRON
ejpam-846	489	5	consider	consider	VERB
ejpam-846	489	6	an	an	DET
ejpam-846	489	7	important	important	ADJ
ejpam-846	489	8	metric	metric	ADJ
ejpam-846	489	9	portfolio	portfolio	NOUN
ejpam-846	489	10	performance	performance	NOUN
ejpam-846	489	11	,	,	PUNCT
ejpam-846	489	12	typically	typically	ADV
ejpam-846	489	13	used	use	VERB
ejpam-846	489	14	by	by	ADP
ejpam-846	489	15	fund	fund	NOUN
ejpam-846	489	16	mangers	manger	NOUN
ejpam-846	489	17	,	,	PUNCT
ejpam-846	489	18	termed	term	VERB
ejpam-846	489	19	the	the	DET
ejpam-846	489	20	maximum	maximum	NOUN
ejpam-846	489	21	draw	draw	VERB
ejpam-846	489	22	down	down	ADP
ejpam-846	489	23	(	(	PUNCT
ejpam-846	489	24	maxdd	maxdd	PROPN
ejpam-846	489	25	)	)	PUNCT
ejpam-846	489	26	.	.	PUNCT
ejpam-846	490	1	investors	investor	NOUN
ejpam-846	490	2	do	do	AUX
ejpam-846	490	3	not	not	PART
ejpam-846	490	4	wish	wish	VERB
ejpam-846	490	5	to	to	PART
ejpam-846	490	6	see	see	VERB
ejpam-846	490	7	the	the	DET
ejpam-846	490	8	value	value	NOUN
ejpam-846	490	9	of	of	ADP
ejpam-846	490	10	the	the	DET
ejpam-846	490	11	portfolio	portfolio	NOUN
ejpam-846	490	12	decline	decline	VERB
ejpam-846	490	13	considerably	considerably	ADV
ejpam-846	490	14	over	over	ADP
ejpam-846	490	15	time	time	NOUN
ejpam-846	490	16	.	.	PUNCT
ejpam-846	491	1	such	such	ADJ
ejpam-846	491	2	drastic	drastic	ADJ
ejpam-846	491	3	declines	decline	NOUN
ejpam-846	491	4	in	in	ADP
ejpam-846	491	5	portfolio	portfolio	NOUN
ejpam-846	491	6	value	value	NOUN
ejpam-846	491	7	may	may	AUX
ejpam-846	491	8	lead	lead	VERB
ejpam-846	491	9	to	to	ADP
ejpam-846	491	10	perceptions	perception	NOUN
ejpam-846	491	11	that	that	SCONJ
ejpam-846	491	12	the	the	DET
ejpam-846	491	13	fund	fund	NOUN
ejpam-846	491	14	is	be	AUX
ejpam-846	491	15	too	too	ADV
ejpam-846	491	16	risky	risky	ADJ
ejpam-846	491	17	;	;	PUNCT
ejpam-846	491	18	it	it	PRON
ejpam-846	491	19	may	may	AUX
ejpam-846	491	20	even	even	ADV
ejpam-846	491	21	lead	lead	VERB
ejpam-846	491	22	to	to	ADP
ejpam-846	491	23	losing	lose	VERB
ejpam-846	491	24	important	important	ADJ
ejpam-846	491	25	client	client	NOUN
ejpam-846	491	26	accounts	account	NOUN
ejpam-846	491	27	from	from	ADP
ejpam-846	491	28	the	the	DET
ejpam-846	491	29	fund	fund	NOUN
ejpam-846	491	30	.	.	PUNCT
ejpam-846	492	1	portfolio	portfolio	NOUN
ejpam-846	492	2	draw	draw	VERB
ejpam-846	492	3	down	down	ADP
ejpam-846	492	4	is	be	AUX
ejpam-846	492	5	defined	define	VERB
ejpam-846	492	6	as	as	ADP
ejpam-846	492	7	the	the	DET
ejpam-846	492	8	relative	relative	ADJ
ejpam-846	492	9	equity	equity	NOUN
ejpam-846	492	10	loss	loss	NOUN
ejpam-846	492	11	from	from	ADP
ejpam-846	492	12	the	the	DET
ejpam-846	492	13	highest	high	ADJ
ejpam-846	492	14	peak	peak	NOUN
ejpam-846	492	15	to	to	ADP
ejpam-846	492	16	the	the	DET
ejpam-846	492	17	lowest	low	ADJ
ejpam-846	492	18	valley	valley	NOUN
ejpam-846	492	19	of	of	ADP
ejpam-846	492	20	a	a	DET
ejpam-846	492	21	portfolio	portfolio	NOUN
ejpam-846	492	22	value	value	NOUN
ejpam-846	492	23	decline	decline	NOUN
ejpam-846	492	24	edirisinghe	edirisinghe	PROPN
ejpam-846	492	25	/	/	SYM
ejpam-846	492	26	eur	eur	PROPN
ejpam-846	492	27	.	.	PUNCT
ejpam-846	493	1	j.	j.	PROPN
ejpam-846	493	2	pure	pure	PROPN
ejpam-846	493	3	appl	appl	PROPN
ejpam-846	493	4	.	.	PROPN
ejpam-846	493	5	math	math	PROPN
ejpam-846	493	6	,	,	PUNCT
ejpam-846	493	7	3	3	NUM
ejpam-846	493	8	(	(	PUNCT
ejpam-846	493	9	2010	2010	NUM
ejpam-846	493	10	)	)	PUNCT
ejpam-846	493	11	,	,	PUNCT
ejpam-846	493	12	572	572	NUM
ejpam-846	493	13	-	-	SYM
ejpam-846	493	14	592	592	NUM
ejpam-846	493	15	588	588	NUM
ejpam-846	493	16	within	within	ADP
ejpam-846	493	17	a	a	DET
ejpam-846	493	18	given	give	VERB
ejpam-846	493	19	window	window	NOUN
ejpam-846	493	20	of	of	ADP
ejpam-846	493	21	observation	observation	NOUN
ejpam-846	493	22	.	.	PUNCT
ejpam-846	494	1	we	we	PRON
ejpam-846	494	2	set	set	VERB
ejpam-846	494	3	this	this	DET
ejpam-846	494	4	time	time	NOUN
ejpam-846	494	5	window	window	NOUN
ejpam-846	494	6	to	to	ADP
ejpam-846	494	7	jan	jan	PROPN
ejpam-846	494	8	01	01	NUM
ejpam-846	494	9	-	-	PUNCT
ejpam-846	494	10	jun	jun	PROPN
ejpam-846	494	11	30	30	NUM
ejpam-846	494	12	,	,	PUNCT
ejpam-846	494	13	2010	2010	NUM
ejpam-846	494	14	for	for	ADP
ejpam-846	494	15	the	the	DET
ejpam-846	494	16	monthly	monthly	ADJ
ejpam-846	494	17	rebalanced	rebalance	VERB
ejpam-846	494	18	portfolio	portfolio	NOUN
ejpam-846	494	19	.	.	PUNCT
ejpam-846	495	1	for	for	ADP
ejpam-846	495	2	the	the	DET
ejpam-846	495	3	s&p	s&p	PROPN
ejpam-846	495	4	500	500	NUM
ejpam-846	495	5	index	index	NOUN
ejpam-846	495	6	(	(	PUNCT
ejpam-846	495	7	spy	spy	NOUN
ejpam-846	495	8	)	)	PUNCT
ejpam-846	495	9	,	,	PUNCT
ejpam-846	495	10	for	for	ADP
ejpam-846	495	11	the	the	DET
ejpam-846	495	12	period	period	NOUN
ejpam-846	495	13	of	of	ADP
ejpam-846	495	14	interest	interest	NOUN
ejpam-846	495	15	,	,	PUNCT
ejpam-846	495	16	aror=−13.49	aror=−13.49	NUM
ejpam-846	495	17	%	%	NOUN
ejpam-846	495	18	,	,	PUNCT
ejpam-846	495	19	astd=20.46	astd=20.46	PROPN
ejpam-846	495	20	%	%	NOUN
ejpam-846	495	21	,	,	PUNCT
ejpam-846	495	22	and	and	CCONJ
ejpam-846	495	23	maxdd=14.86	maxdd=14.86	NUM
ejpam-846	495	24	%	%	NOUN
ejpam-846	495	25	,	,	PUNCT
ejpam-846	495	26	expressed	express	VERB
ejpam-846	495	27	as	as	ADP
ejpam-846	495	28	‘	'	PUNCT
ejpam-846	495	29	percent	percent	NOUN
ejpam-846	495	30	of	of	ADP
ejpam-846	495	31	the	the	DET
ejpam-846	495	32	initial	initial	ADJ
ejpam-846	495	33	budget	budget	NOUN
ejpam-846	495	34	’	'	PUNCT
ejpam-846	495	35	.	.	PUNCT
ejpam-846	496	1	we	we	PRON
ejpam-846	496	2	consider	consider	VERB
ejpam-846	496	3	two	two	NUM
ejpam-846	496	4	models	model	NOUN
ejpam-846	496	5	for	for	ADP
ejpam-846	496	6	comparison	comparison	NOUN
ejpam-846	496	7	,	,	PUNCT
ejpam-846	496	8	both	both	PRON
ejpam-846	496	9	of	of	ADP
ejpam-846	496	10	which	which	PRON
ejpam-846	496	11	use	use	VERB
ejpam-846	496	12	the	the	DET
ejpam-846	496	13	historical	historical	ADJ
ejpam-846	496	14	returns	return	NOUN
ejpam-846	496	15	from	from	ADP
ejpam-846	496	16	2000	2000	NUM
ejpam-846	496	17	-	-	SYM
ejpam-846	496	18	2009	2009	NUM
ejpam-846	496	19	for	for	ADP
ejpam-846	496	20	computing	computing	NOUN
ejpam-846	496	21	mean	mean	NOUN
ejpam-846	496	22	and	and	CCONJ
ejpam-846	496	23	var	var	NOUN
ejpam-846	496	24	/	/	SYM
ejpam-846	496	25	cov	cov	NOUN
ejpam-846	496	26	information	information	NOUN
ejpam-846	496	27	of	of	ADP
ejpam-846	496	28	the	the	DET
ejpam-846	496	29	95	95	NUM
ejpam-846	496	30	stocks	stock	NOUN
ejpam-846	496	31	in	in	ADP
ejpam-846	496	32	table	table	NOUN
ejpam-846	496	33	1	1	NUM
ejpam-846	496	34	:	:	SYM
ejpam-846	496	35	•	•	NOUN
ejpam-846	496	36	target	target	NOUN
ejpam-846	496	37	deviation	deviation	NOUN
ejpam-846	496	38	(	(	PUNCT
ejpam-846	496	39	td	td	NOUN
ejpam-846	496	40	)	)	PUNCT
ejpam-846	496	41	model	model	NOUN
ejpam-846	496	42	:	:	PUNCT
ejpam-846	496	43	under	under	ADP
ejpam-846	496	44	the	the	DET
ejpam-846	496	45	hypothesis	hypothesis	NOUN
ejpam-846	496	46	that	that	PRON
ejpam-846	496	47	future	future	ADJ
ejpam-846	496	48	stock	stock	NOUN
ejpam-846	496	49	returns	return	NOUN
ejpam-846	496	50	are	be	AUX
ejpam-846	496	51	possibly	possibly	ADV
ejpam-846	496	52	asymmetric	asymmetric	ADJ
ejpam-846	496	53	and	and	CCONJ
ejpam-846	496	54	non	non	ADJ
ejpam-846	496	55	-	-	ADJ
ejpam-846	496	56	normal	normal	ADJ
ejpam-846	496	57	,	,	PUNCT
ejpam-846	496	58	compute	compute	VERB
ejpam-846	496	59	the	the	DET
ejpam-846	496	60	second	second	ADJ
ejpam-846	496	61	moment	moment	NOUN
ejpam-846	496	62	-	-	PUNCT
ejpam-846	496	63	approximated	approximate	VERB
ejpam-846	496	64	scenarios	scenario	NOUN
ejpam-846	496	65	for	for	ADP
ejpam-846	496	66	the	the	DET
ejpam-846	496	67	risk	risk	NOUN
ejpam-846	496	68	function	function	NOUN
ejpam-846	496	69	in	in	ADP
ejpam-846	496	70	(	(	PUNCT
ejpam-846	496	71	45	45	NUM
ejpam-846	496	72	)	)	PUNCT
ejpam-846	496	73	.	.	PUNCT
ejpam-846	497	1	•	•	NUM
ejpam-846	497	2	mean	mean	ADJ
ejpam-846	497	3	-	-	PUNCT
ejpam-846	497	4	variance	variance	NOUN
ejpam-846	497	5	(	(	PUNCT
ejpam-846	497	6	mv	mv	NOUN
ejpam-846	497	7	)	)	PUNCT
ejpam-846	497	8	model	model	NOUN
ejpam-846	497	9	:	:	PUNCT
ejpam-846	497	10	under	under	ADP
ejpam-846	497	11	the	the	DET
ejpam-846	497	12	assumption	assumption	NOUN
ejpam-846	497	13	that	that	SCONJ
ejpam-846	497	14	stock	stock	NOUN
ejpam-846	497	15	returns	return	NOUN
ejpam-846	497	16	are	be	AUX
ejpam-846	497	17	normally	normally	ADV
ejpam-846	497	18	distributed	distribute	VERB
ejpam-846	497	19	,	,	PUNCT
ejpam-846	497	20	apply	apply	VERB
ejpam-846	497	21	markowitz	markowitz	PROPN
ejpam-846	497	22	’s	’s	PART
ejpam-846	497	23	mean	mean	ADJ
ejpam-846	497	24	-	-	PUNCT
ejpam-846	497	25	variance	variance	NOUN
ejpam-846	497	26	trade	trade	NOUN
ejpam-846	497	27	off	off	ADP
ejpam-846	497	28	by	by	ADP
ejpam-846	497	29	setting	set	VERB
ejpam-846	497	30	the	the	DET
ejpam-846	497	31	risk	risk	NOUN
ejpam-846	497	32	function	function	NOUN
ejpam-846	497	33	ϕ(x	ϕ(x	X
ejpam-846	497	34	)	)	PUNCT
ejpam-846	497	35	=	=	PUNCT
ejpam-846	497	36	x′mx	x′mx	PROPN
ejpam-846	497	37	.	.	PUNCT
ejpam-846	498	1	the	the	DET
ejpam-846	498	2	model	model	NOUN
ejpam-846	498	3	-	-	PUNCT
ejpam-846	498	4	based	base	VERB
ejpam-846	498	5	(	(	PUNCT
ejpam-846	498	6	in	in	ADP
ejpam-846	498	7	-	-	PUNCT
ejpam-846	498	8	sample	sample	NOUN
ejpam-846	498	9	)	)	PUNCT
ejpam-846	498	10	aror	aror	NOUN
ejpam-846	498	11	vs	vs	ADP
ejpam-846	498	12	astd	astd	PROPN
ejpam-846	498	13	portfolio	portfolio	PROPN
ejpam-846	498	14	trade	trade	NOUN
ejpam-846	498	15	-	-	PUNCT
ejpam-846	498	16	off	off	NOUN
ejpam-846	498	17	under	under	ADP
ejpam-846	498	18	monthly	monthly	ADJ
ejpam-846	498	19	rebalancing	rebalancing	NOUN
ejpam-846	498	20	of	of	ADP
ejpam-846	498	21	the	the	DET
ejpam-846	498	22	model	model	NOUN
ejpam-846	498	23	in	in	ADP
ejpam-846	498	24	(	(	PUNCT
ejpam-846	498	25	44	44	NUM
ejpam-846	498	26	)	)	PUNCT
ejpam-846	498	27	is	be	AUX
ejpam-846	498	28	plotted	plot	VERB
ejpam-846	498	29	for	for	ADP
ejpam-846	498	30	td	td	NOUN
ejpam-846	498	31	and	and	CCONJ
ejpam-846	498	32	mv	mv	PROPN
ejpam-846	498	33	models	model	NOUN
ejpam-846	498	34	,	,	PUNCT
ejpam-846	498	35	see	see	VERB
ejpam-846	498	36	figure	figure	NOUN
ejpam-846	498	37	2	2	NUM
ejpam-846	498	38	.	.	PUNCT
ejpam-846	498	39	as	as	SCONJ
ejpam-846	498	40	expected	expect	VERB
ejpam-846	498	41	,	,	PUNCT
ejpam-846	498	42	mv	mv	PROPN
ejpam-846	498	43	model	model	NOUN
ejpam-846	498	44	displays	display	VERB
ejpam-846	498	45	a	a	DET
ejpam-846	498	46	better	well	ADJ
ejpam-846	498	47	in	in	ADP
ejpam-846	498	48	-	-	PUNCT
ejpam-846	498	49	sample	sample	NOUN
ejpam-846	498	50	performance	performance	NOUN
ejpam-846	498	51	relative	relative	ADJ
ejpam-846	498	52	to	to	ADP
ejpam-846	498	53	td	td	NOUN
ejpam-846	498	54	model	model	NOUN
ejpam-846	498	55	since	since	SCONJ
ejpam-846	498	56	the	the	DET
ejpam-846	498	57	mv	mv	PROPN
ejpam-846	498	58	model	model	NOUN
ejpam-846	498	59	is	be	AUX
ejpam-846	498	60	optimized	optimize	VERB
ejpam-846	498	61	for	for	ADP
ejpam-846	498	62	mean	mean	ADJ
ejpam-846	498	63	/	/	SYM
ejpam-846	498	64	variance	variance	NOUN
ejpam-846	498	65	trade	trade	NOUN
ejpam-846	498	66	off	off	ADP
ejpam-846	498	67	.	.	PUNCT
ejpam-846	499	1	the	the	DET
ejpam-846	499	2	relative	relative	ADJ
ejpam-846	499	3	performance	performance	NOUN
ejpam-846	499	4	of	of	ADP
ejpam-846	499	5	td	td	NOUN
ejpam-846	499	6	model	model	NOUN
ejpam-846	499	7	is	be	AUX
ejpam-846	499	8	weaker	weak	ADJ
ejpam-846	499	9	at	at	ADP
ejpam-846	499	10	low	low	ADJ
ejpam-846	499	11	portfolio	portfolio	NOUN
ejpam-846	499	12	astd	astd	PROPN
ejpam-846	499	13	,	,	PUNCT
ejpam-846	499	14	while	while	SCONJ
ejpam-846	499	15	at	at	ADP
ejpam-846	499	16	increased	increase	VERB
ejpam-846	499	17	risk	risk	NOUN
ejpam-846	499	18	levels	level	NOUN
ejpam-846	499	19	,	,	PUNCT
ejpam-846	499	20	td	td	NOUN
ejpam-846	499	21	performs	perform	VERB
ejpam-846	499	22	as	as	ADV
ejpam-846	499	23	well	well	ADV
ejpam-846	499	24	as	as	ADP
ejpam-846	499	25	the	the	DET
ejpam-846	499	26	mv	mv	PROPN
ejpam-846	499	27	.	.	PROPN
ejpam-846	499	28	portfolio	portfolio	NOUN
ejpam-846	499	29	strategies	strategy	NOUN
ejpam-846	499	30	of	of	ADP
ejpam-846	499	31	the	the	DET
ejpam-846	499	32	two	two	NUM
ejpam-846	499	33	models	model	NOUN
ejpam-846	499	34	are	be	AUX
ejpam-846	499	35	quite	quite	ADV
ejpam-846	499	36	different	different	ADJ
ejpam-846	499	37	as	as	SCONJ
ejpam-846	499	38	depicted	depict	VERB
ejpam-846	499	39	in	in	ADP
ejpam-846	499	40	figure	figure	NOUN
ejpam-846	499	41	3	3	NUM
ejpam-846	499	42	.	.	PUNCT
ejpam-846	500	1	at	at	ADP
ejpam-846	500	2	low	low	ADJ
ejpam-846	500	3	values	value	NOUN
ejpam-846	500	4	of	of	ADP
ejpam-846	500	5	λ	λ	NOUN
ejpam-846	500	6	,	,	PUNCT
ejpam-846	500	7	i.e.	i.e.	X
ejpam-846	500	8	,	,	PUNCT
ejpam-846	500	9	less	less	ADJ
ejpam-846	500	10	risk	risk	NOUN
ejpam-846	500	11	-	-	PUNCT
ejpam-846	500	12	averse	averse	ADJ
ejpam-846	500	13	,	,	PUNCT
ejpam-846	500	14	both	both	DET
ejpam-846	500	15	models	model	NOUN
ejpam-846	500	16	indicate	indicate	VERB
ejpam-846	500	17	lower	low	ADJ
ejpam-846	500	18	levels	level	NOUN
ejpam-846	500	19	of	of	ADP
ejpam-846	500	20	diversification	diversification	NOUN
ejpam-846	500	21	with	with	ADP
ejpam-846	500	22	increased	increase	VERB
ejpam-846	500	23	short	short	ADJ
ejpam-846	500	24	positions	position	NOUN
ejpam-846	500	25	in	in	ADP
ejpam-846	500	26	the	the	DET
ejpam-846	500	27	portfolios	portfolio	NOUN
ejpam-846	500	28	.	.	PUNCT
ejpam-846	501	1	but	but	CCONJ
ejpam-846	501	2	,	,	PUNCT
ejpam-846	501	3	as	as	SCONJ
ejpam-846	501	4	the	the	DET
ejpam-846	501	5	investor	investor	NOUN
ejpam-846	501	6	becomes	become	VERB
ejpam-846	501	7	more	more	ADJ
ejpam-846	501	8	risk	risk	NOUN
ejpam-846	501	9	-	-	PUNCT
ejpam-846	501	10	averse	averse	ADJ
ejpam-846	501	11	,	,	PUNCT
ejpam-846	501	12	td	td	NOUN
ejpam-846	501	13	model	model	NOUN
ejpam-846	501	14	increases	increase	VERB
ejpam-846	501	15	long	long	ADJ
ejpam-846	501	16	positions	position	NOUN
ejpam-846	501	17	at	at	ADP
ejpam-846	501	18	the	the	DET
ejpam-846	501	19	expense	expense	NOUN
ejpam-846	501	20	of	of	ADP
ejpam-846	501	21	short	short	ADJ
ejpam-846	501	22	positions	position	NOUN
ejpam-846	501	23	,	,	PUNCT
ejpam-846	501	24	but	but	CCONJ
ejpam-846	501	25	with	with	ADP
ejpam-846	501	26	no	no	DET
ejpam-846	501	27	significant	significant	ADJ
ejpam-846	501	28	change	change	NOUN
ejpam-846	501	29	in	in	ADP
ejpam-846	501	30	diversification	diversification	NOUN
ejpam-846	501	31	.	.	PUNCT
ejpam-846	502	1	in	in	ADP
ejpam-846	502	2	contrast	contrast	NOUN
ejpam-846	502	3	,	,	PUNCT
ejpam-846	502	4	the	the	DET
ejpam-846	502	5	mv	mv	PROPN
ejpam-846	502	6	model	model	NOUN
ejpam-846	502	7	dictates	dictate	VERB
ejpam-846	502	8	increased	increase	VERB
ejpam-846	502	9	diversification	diversification	NOUN
ejpam-846	502	10	,	,	PUNCT
ejpam-846	502	11	both	both	CCONJ
ejpam-846	502	12	in	in	ADP
ejpam-846	502	13	the	the	DET
ejpam-846	502	14	long	long	ADJ
ejpam-846	502	15	and	and	CCONJ
ejpam-846	502	16	short	short	ADJ
ejpam-846	502	17	positions	position	NOUN
ejpam-846	502	18	.	.	PUNCT
ejpam-846	503	1	17	17	NUM
ejpam-846	503	2	%	%	NOUN
ejpam-846	503	3	19	19	NUM
ejpam-846	503	4	%	%	NOUN
ejpam-846	503	5	n	n	NUM
ejpam-846	503	6	jan	jan	PROPN
ejpam-846	503	7	jun	jun	PROPN
ejpam-846	503	8	,	,	PUNCT
ejpam-846	503	9	2010	2010	NUM
ejpam-846	503	10	(	(	PUNCT
ejpam-846	503	11	monthly	monthly	ADV
ejpam-846	503	12	rebalanced	rebalance	VERB
ejpam-846	503	13	)	)	PUNCT
ejpam-846	503	14	13	13	NUM
ejpam-846	503	15	%	%	NOUN
ejpam-846	503	16	15	15	NUM
ejpam-846	503	17	%	%	NOUN
ejpam-846	503	18	a	a	DET
ejpam-846	503	19	n	n	NOUN
ejpam-846	503	20	n	n	PRON
ejpam-846	503	21	u	u	NOUN
ejpam-846	503	22	a	a	DET
ejpam-846	503	23	li	li	PROPN
ejpam-846	503	24	z	z	PROPN
ejpam-846	503	25	e	e	PROPN
ejpam-846	503	26	d	d	NOUN
ejpam-846	503	27	r	r	NOUN
ejpam-846	503	28	e	e	NOUN
ejpam-846	503	29	t	t	NOUN
ejpam-846	503	30	u	u	NOUN
ejpam-846	503	31	r	r	NOUN
ejpam-846	503	32	n	n	NOUN
ejpam-846	503	33	7	7	NUM
ejpam-846	503	34	%	%	NOUN
ejpam-846	503	35	9	9	NUM
ejpam-846	503	36	%	%	NOUN
ejpam-846	503	37	11	11	NUM
ejpam-846	503	38	%	%	NOUN
ejpam-846	503	39	p	p	NOUN
ejpam-846	503	40	o	o	NOUN
ejpam-846	503	41	r	r	NOUN
ejpam-846	503	42	t	t	NOUN
ejpam-846	503	43	fo	fo	INTJ
ejpam-846	503	44	li	li	PROPN
ejpam-846	503	45	o	o	NOUN
ejpam-846	503	46	5	5	NUM
ejpam-846	503	47	%	%	NOUN
ejpam-846	503	48	10	10	NUM
ejpam-846	503	49	%	%	NOUN
ejpam-846	503	50	15	15	NUM
ejpam-846	503	51	%	%	NOUN
ejpam-846	503	52	20	20	NUM
ejpam-846	503	53	%	%	NOUN
ejpam-846	503	54	25	25	NUM
ejpam-846	503	55	%	%	NOUN
ejpam-846	503	56	30	30	NUM
ejpam-846	503	57	%	%	NOUN
ejpam-846	503	58	portfolio	portfolio	NOUN
ejpam-846	503	59	annualized	annualize	VERB
ejpam-846	503	60	std	std	NOUN
ejpam-846	503	61	deviation	deviation	NOUN
ejpam-846	503	62	target	target	NOUN
ejpam-846	503	63	deviation	deviation	NOUN
ejpam-846	503	64	model	model	NOUN
ejpam-846	503	65	(	(	PUNCT
ejpam-846	503	66	in	in	ADP
ejpam-846	503	67	sample	sample	NOUN
ejpam-846	503	68	)	)	PUNCT
ejpam-846	503	69	mean	mean	ADJ
ejpam-846	503	70	/	/	SYM
ejpam-846	503	71	variance	variance	NOUN
ejpam-846	503	72	model	model	NOUN
ejpam-846	503	73	(	(	PUNCT
ejpam-846	503	74	in	in	ADP
ejpam-846	503	75	sample	sample	NOUN
ejpam-846	503	76	)	)	PUNCT
ejpam-846	503	77	figure	figure	NOUN
ejpam-846	503	78	2	2	NUM
ejpam-846	503	79	:	:	PUNCT
ejpam-846	503	80	in	in	ADP
ejpam-846	503	81	-	-	PUNCT
ejpam-846	503	82	sample	sample	NOUN
ejpam-846	503	83	efficient	efficient	ADJ
ejpam-846	503	84	frontiers	frontier	NOUN
ejpam-846	503	85	for	for	SCONJ
ejpam-846	503	86	approximated	approximate	VERB
ejpam-846	503	87	versus	versus	ADP
ejpam-846	503	88	normal	normal	ADJ
ejpam-846	503	89	returns	return	NOUN
ejpam-846	503	90	.	.	PUNCT
ejpam-846	504	1	how	how	SCONJ
ejpam-846	504	2	do	do	AUX
ejpam-846	504	3	the	the	DET
ejpam-846	504	4	above	above	ADJ
ejpam-846	504	5	optimal	optimal	ADJ
ejpam-846	504	6	strategies	strategy	NOUN
ejpam-846	504	7	perform	perform	VERB
ejpam-846	504	8	in	in	ADP
ejpam-846	504	9	the	the	DET
ejpam-846	504	10	out	out	ADJ
ejpam-846	504	11	-	-	PUNCT
ejpam-846	504	12	of	of	ADP
ejpam-846	504	13	-	-	PUNCT
ejpam-846	504	14	sample	sample	NOUN
ejpam-846	504	15	period	period	NOUN
ejpam-846	504	16	from	from	ADP
ejpam-846	504	17	januaryjune	januaryjune	NOUN
ejpam-846	504	18	of	of	ADP
ejpam-846	504	19	2010	2010	NUM
ejpam-846	504	20	when	when	SCONJ
ejpam-846	504	21	applied	apply	VERB
ejpam-846	504	22	against	against	ADP
ejpam-846	504	23	the	the	DET
ejpam-846	504	24	actual	actual	ADJ
ejpam-846	504	25	observed	observed	ADJ
ejpam-846	504	26	returns	return	NOUN
ejpam-846	504	27	?	?	PUNCT
ejpam-846	505	1	figure	figure	VERB
ejpam-846	505	2	4	4	NUM
ejpam-846	505	3	presents	present	VERB
ejpam-846	505	4	the	the	DET
ejpam-846	505	5	outof	outof	PROPN
ejpam-846	505	6	-	-	PUNCT
ejpam-846	505	7	sample	sample	NOUN
ejpam-846	505	8	aror	aror	NOUN
ejpam-846	505	9	/	/	SYM
ejpam-846	505	10	astd	astd	PROPN
ejpam-846	505	11	relationship	relationship	NOUN
ejpam-846	505	12	.	.	PUNCT
ejpam-846	506	1	although	although	SCONJ
ejpam-846	506	2	the	the	DET
ejpam-846	506	3	mv	mv	PROPN
ejpam-846	506	4	model	model	NOUN
ejpam-846	506	5	optimized	optimize	VERB
ejpam-846	506	6	the	the	DET
ejpam-846	506	7	in	in	ADP
ejpam-846	506	8	-	-	PUNCT
ejpam-846	506	9	sample	sample	NOUN
ejpam-846	506	10	edirisinghe	edirisinghe	PROPN
ejpam-846	506	11	/	/	SYM
ejpam-846	506	12	eur	eur	PROPN
ejpam-846	506	13	.	.	PUNCT
ejpam-846	507	1	j.	j.	PROPN
ejpam-846	507	2	pure	pure	PROPN
ejpam-846	507	3	appl	appl	PROPN
ejpam-846	507	4	.	.	PROPN
ejpam-846	507	5	math	math	PROPN
ejpam-846	507	6	,	,	PUNCT
ejpam-846	507	7	3	3	NUM
ejpam-846	507	8	(	(	PUNCT
ejpam-846	507	9	2010	2010	NUM
ejpam-846	507	10	)	)	PUNCT
ejpam-846	507	11	,	,	PUNCT
ejpam-846	507	12	572	572	NUM
ejpam-846	507	13	-	-	SYM
ejpam-846	507	14	592	592	NUM
ejpam-846	507	15	589	589	NUM
ejpam-846	507	16	50	50	NUM
ejpam-846	507	17	%	%	NOUN
ejpam-846	507	18	30	30	NUM
ejpam-846	507	19	%	%	NOUN
ejpam-846	507	20	35	35	NUM
ejpam-846	507	21	%	%	NOUN
ejpam-846	507	22	40	40	NUM
ejpam-846	507	23	%	%	NOUN
ejpam-846	507	24	45	45	NUM
ejpam-846	507	25	%	%	NOUN
ejpam-846	507	26	lo	lo	NOUN
ejpam-846	508	1	n	n	ADV
ejpam-846	508	2	g	g	NOUN
ejpam-846	509	1	o	o	X
ejpam-846	509	2	r	r	NOUN
ejpam-846	509	3	s	s	NOUN
ejpam-846	509	4	h	h	NOUN
ejpam-846	510	1	o	o	NOUN
ejpam-846	510	2	rt	rt	NOUN
ejpam-846	510	3	5	5	NUM
ejpam-846	510	4	%	%	NOUN
ejpam-846	510	5	10	10	NUM
ejpam-846	510	6	%	%	NOUN
ejpam-846	510	7	15	15	NUM
ejpam-846	510	8	%	%	NOUN
ejpam-846	510	9	20	20	NUM
ejpam-846	510	10	%	%	NOUN
ejpam-846	510	11	25	25	NUM
ejpam-846	510	12	%	%	NOUN
ejpam-846	510	13	a	a	DET
ejpam-846	510	14	v	v	NOUN
ejpam-846	510	15	e	e	NOUN
ejpam-846	510	16	ra	ra	NOUN
ejpam-846	510	17	g	g	PROPN
ejpam-846	510	18	e	e	PROPN
ejpam-846	510	19	p	p	PROPN
ejpam-846	510	20	e	e	PROPN
ejpam-846	510	21	rc	rc	PROPN
ejpam-846	510	22	e	e	PROPN
ejpam-846	510	23	n	n	PROPN
ejpam-846	510	24	t	t	PROPN
ejpam-846	510	25	0	0	NUM
ejpam-846	510	26	%	%	NOUN
ejpam-846	510	27	5	5	NUM
ejpam-846	510	28	%	%	NOUN
ejpam-846	510	29	level	level	NOUN
ejpam-846	510	30	of	of	ADP
ejpam-846	510	31	risk	risk	NOUN
ejpam-846	510	32	aversion	aversion	NOUN
ejpam-846	510	33	(	(	PUNCT
ejpam-846	510	34	)	)	PUNCT
ejpam-846	510	35	td	td	NOUN
ejpam-846	510	36	(	(	PUNCT
ejpam-846	510	37	long	long	ADJ
ejpam-846	510	38	)	)	PUNCT
ejpam-846	510	39	td	td	NOUN
ejpam-846	510	40	(	(	PUNCT
ejpam-846	510	41	short	short	ADJ
ejpam-846	510	42	)	)	PUNCT
ejpam-846	510	43	mv	mv	PROPN
ejpam-846	510	44	(	(	PUNCT
ejpam-846	510	45	long	long	ADV
ejpam-846	510	46	)	)	PUNCT
ejpam-846	510	47	mv	mv	PROPN
ejpam-846	510	48	(	(	PUNCT
ejpam-846	510	49	short	short	ADJ
ejpam-846	510	50	)	)	PUNCT
ejpam-846	510	51	figure	figure	NOUN
ejpam-846	510	52	3	3	NUM
ejpam-846	510	53	:	:	PUNCT
ejpam-846	510	54	portfolio	portfolio	NOUN
ejpam-846	510	55	long	long	ADJ
ejpam-846	510	56	/	/	SYM
ejpam-846	510	57	short	short	ADJ
ejpam-846	510	58	strategies	strategy	NOUN
ejpam-846	510	59	for	for	ADP
ejpam-846	510	60	target	target	NOUN
ejpam-846	510	61	-	-	PUNCT
ejpam-846	510	62	based	base	VERB
ejpam-846	510	63	and	and	CCONJ
ejpam-846	510	64	mean	mean	ADJ
ejpam-846	510	65	-	-	PUNCT
ejpam-846	510	66	var	var	NOUN
ejpam-846	510	67	models	model	NOUN
ejpam-846	510	68	.	.	PUNCT
ejpam-846	511	1	mean	mean	ADJ
ejpam-846	511	2	-	-	PUNCT
ejpam-846	511	3	variance	variance	NOUN
ejpam-846	511	4	trade	trade	NOUN
ejpam-846	511	5	off	off	ADP
ejpam-846	511	6	,	,	PUNCT
ejpam-846	511	7	its	its	PRON
ejpam-846	511	8	actual	actual	ADJ
ejpam-846	511	9	performance	performance	NOUN
ejpam-846	511	10	during	during	ADP
ejpam-846	511	11	the	the	DET
ejpam-846	511	12	6	6	NUM
ejpam-846	511	13	months	month	NOUN
ejpam-846	511	14	in	in	ADP
ejpam-846	511	15	2010	2010	NUM
ejpam-846	511	16	is	be	AUX
ejpam-846	511	17	significantly	significantly	ADV
ejpam-846	511	18	inferior	inferior	ADJ
ejpam-846	511	19	to	to	ADP
ejpam-846	511	20	that	that	PRON
ejpam-846	511	21	of	of	ADP
ejpam-846	511	22	the	the	DET
ejpam-846	511	23	td	td	NOUN
ejpam-846	511	24	model	model	NOUN
ejpam-846	511	25	.	.	PUNCT
ejpam-846	512	1	the	the	DET
ejpam-846	512	2	main	main	ADJ
ejpam-846	512	3	insight	insight	NOUN
ejpam-846	512	4	here	here	ADV
ejpam-846	512	5	is	be	AUX
ejpam-846	512	6	that	that	SCONJ
ejpam-846	512	7	the	the	DET
ejpam-846	512	8	assumption	assumption	NOUN
ejpam-846	512	9	of	of	ADP
ejpam-846	512	10	normally	normally	ADV
ejpam-846	512	11	distributed	distribute	VERB
ejpam-846	512	12	returns	return	NOUN
ejpam-846	512	13	in	in	ADP
ejpam-846	512	14	the	the	DET
ejpam-846	512	15	mv	mv	PROPN
ejpam-846	512	16	model	model	NOUN
ejpam-846	512	17	yielded	yield	VERB
ejpam-846	512	18	a	a	DET
ejpam-846	512	19	diversification	diversification	NOUN
ejpam-846	512	20	strategy	strategy	NOUN
ejpam-846	512	21	that	that	PRON
ejpam-846	512	22	is	be	AUX
ejpam-846	512	23	not	not	PART
ejpam-846	512	24	consistent	consistent	ADJ
ejpam-846	512	25	with	with	ADP
ejpam-846	512	26	the	the	DET
ejpam-846	512	27	actually	actually	ADV
ejpam-846	512	28	observed	observe	VERB
ejpam-846	512	29	returns	return	NOUN
ejpam-846	512	30	.	.	PUNCT
ejpam-846	513	1	on	on	ADP
ejpam-846	513	2	the	the	DET
ejpam-846	513	3	contrary	contrary	NOUN
ejpam-846	513	4	,	,	PUNCT
ejpam-846	513	5	the	the	DET
ejpam-846	513	6	second	second	ADJ
ejpam-846	513	7	moment	moment	NOUN
ejpam-846	513	8	-	-	PUNCT
ejpam-846	513	9	based	base	VERB
ejpam-846	513	10	scenarios	scenario	NOUN
ejpam-846	513	11	allow	allow	VERB
ejpam-846	513	12	for	for	ADP
ejpam-846	513	13	extremal	extremal	ADJ
ejpam-846	513	14	scenarios	scenario	NOUN
ejpam-846	513	15	with	with	ADP
ejpam-846	513	16	higher	high	ADJ
ejpam-846	513	17	probabilities	probability	NOUN
ejpam-846	513	18	(	(	PUNCT
ejpam-846	513	19	than	than	ADP
ejpam-846	513	20	normal	normal	ADJ
ejpam-846	513	21	distributions	distribution	NOUN
ejpam-846	513	22	would	would	AUX
ejpam-846	513	23	allow	allow	VERB
ejpam-846	513	24	)	)	PUNCT
ejpam-846	513	25	,	,	PUNCT
ejpam-846	513	26	and	and	CCONJ
ejpam-846	513	27	accordingly	accordingly	ADV
ejpam-846	513	28	,	,	PUNCT
ejpam-846	513	29	the	the	DET
ejpam-846	513	30	out	out	ADV
ejpam-846	513	31	-	-	PUNCT
ejpam-846	513	32	of	of	ADP
ejpam-846	513	33	-	-	PUNCT
ejpam-846	513	34	sample	sample	NOUN
ejpam-846	513	35	performance	performance	NOUN
ejpam-846	513	36	is	be	AUX
ejpam-846	513	37	much	much	ADV
ejpam-846	513	38	improved	improve	VERB
ejpam-846	513	39	.	.	PUNCT
ejpam-846	514	1	observe	observe	VERB
ejpam-846	514	2	that	that	SCONJ
ejpam-846	514	3	the	the	DET
ejpam-846	514	4	market	market	NOUN
ejpam-846	514	5	itself	itself	PRON
ejpam-846	514	6	(	(	PUNCT
ejpam-846	514	7	s&p	s&p	PROPN
ejpam-846	514	8	500	500	NUM
ejpam-846	514	9	index	index	NOUN
ejpam-846	514	10	)	)	PUNCT
ejpam-846	514	11	performed	perform	VERB
ejpam-846	514	12	quite	quite	ADV
ejpam-846	514	13	poorly	poorly	ADV
ejpam-846	514	14	,	,	PUNCT
ejpam-846	514	15	indicating	indicate	VERB
ejpam-846	514	16	the	the	DET
ejpam-846	514	17	extremal	extremal	ADJ
ejpam-846	514	18	nature	nature	NOUN
ejpam-846	514	19	of	of	ADP
ejpam-846	514	20	the	the	DET
ejpam-846	514	21	actual	actual	ADJ
ejpam-846	514	22	returns	return	NOUN
ejpam-846	514	23	during	during	ADP
ejpam-846	514	24	the	the	DET
ejpam-846	514	25	out	out	ADJ
ejpam-846	514	26	-	-	PUNCT
ejpam-846	514	27	of	of	ADP
ejpam-846	514	28	-	-	PUNCT
ejpam-846	514	29	sample	sample	NOUN
ejpam-846	514	30	period	period	NOUN
ejpam-846	514	31	.	.	PUNCT
ejpam-846	515	1	jan	jan	PROPN
ejpam-846	515	2	jun	jun	PROPN
ejpam-846	515	3	,	,	PUNCT
ejpam-846	515	4	2010	2010	NUM
ejpam-846	515	5	(	(	PUNCT
ejpam-846	515	6	monthly	monthly	ADV
ejpam-846	515	7	rebalanced	rebalance	VERB
ejpam-846	515	8	)	)	PUNCT
ejpam-846	515	9	20	20	NUM
ejpam-846	515	10	%	%	NOUN
ejpam-846	515	11	25	25	NUM
ejpam-846	515	12	%	%	NOUN
ejpam-846	515	13	0	0	NUM
ejpam-846	515	14	%	%	NOUN
ejpam-846	515	15	5	5	NUM
ejpam-846	515	16	%	%	NOUN
ejpam-846	515	17	10	10	NUM
ejpam-846	515	18	%	%	NOUN
ejpam-846	515	19	15	15	NUM
ejpam-846	515	20	%	%	NOUN
ejpam-846	515	21	n	n	CCONJ
ejpam-846	515	22	n	n	PRON
ejpam-846	515	23	u	u	NOUN
ejpam-846	515	24	a	a	DET
ejpam-846	515	25	li	li	PROPN
ejpam-846	515	26	z	z	PROPN
ejpam-846	515	27	e	e	PROPN
ejpam-846	515	28	d	d	NOUN
ejpam-846	515	29	r	r	X
ejpam-846	515	30	e	e	X
ejpam-846	515	31	tu	tu	PROPN
ejpam-846	515	32	r	r	NOUN
ejpam-846	515	33	n	n	NUM
ejpam-846	515	34	15	15	NUM
ejpam-846	515	35	%	%	NOUN
ejpam-846	515	36	10	10	NUM
ejpam-846	515	37	%	%	NOUN
ejpam-846	515	38	5	5	NUM
ejpam-846	515	39	%	%	NOUN
ejpam-846	515	40	0	0	NUM
ejpam-846	515	41	%	%	NOUN
ejpam-846	515	42	6	6	NUM
ejpam-846	515	43	%	%	NOUN
ejpam-846	515	44	8	8	NUM
ejpam-846	515	45	%	%	NOUN
ejpam-846	515	46	10	10	NUM
ejpam-846	515	47	%	%	NOUN
ejpam-846	515	48	12	12	NUM
ejpam-846	515	49	%	%	NOUN
ejpam-846	515	50	14	14	NUM
ejpam-846	515	51	%	%	NOUN
ejpam-846	515	52	16	16	NUM
ejpam-846	515	53	%	%	NOUN
ejpam-846	515	54	18	18	NUM
ejpam-846	515	55	%	%	NOUN
ejpam-846	515	56	20	20	NUM
ejpam-846	515	57	%	%	NOUN
ejpam-846	515	58	22	22	NUM
ejpam-846	515	59	%	%	NOUN
ejpam-846	515	60	p	p	NOUN
ejpam-846	515	61	o	o	NOUN
ejpam-846	515	62	r	r	NOUN
ejpam-846	515	63	t	t	NOUN
ejpam-846	515	64	fo	fo	INTJ
ejpam-846	515	65	li	li	PROPN
ejpam-846	515	66	o	o	PROPN
ejpam-846	515	67	a	a	PRON
ejpam-846	515	68	n	n	NUM
ejpam-846	515	69	20	20	NUM
ejpam-846	515	70	%	%	NOUN
ejpam-846	515	71	portfolio	portfolio	NOUN
ejpam-846	515	72	annualized	annualize	VERB
ejpam-846	515	73	std	std	NOUN
ejpam-846	515	74	deviation	deviation	NOUN
ejpam-846	515	75	target	target	NOUN
ejpam-846	515	76	model	model	NOUN
ejpam-846	515	77	(	(	PUNCT
ejpam-846	515	78	out	out	ADP
ejpam-846	515	79	of	of	ADP
ejpam-846	515	80	sample	sample	NOUN
ejpam-846	515	81	)	)	PUNCT
ejpam-846	515	82	mean	mean	ADJ
ejpam-846	515	83	/	/	SYM
ejpam-846	515	84	var	var	NOUN
ejpam-846	515	85	(	(	PUNCT
ejpam-846	515	86	out	out	ADP
ejpam-846	515	87	of	of	ADP
ejpam-846	515	88	sample	sample	NOUN
ejpam-846	515	89	)	)	PUNCT
ejpam-846	515	90	s&p	s&p	PROPN
ejpam-846	515	91	500	500	NUM
ejpam-846	515	92	index	index	NOUN
ejpam-846	515	93	figure	figure	NOUN
ejpam-846	515	94	4	4	NUM
ejpam-846	515	95	:	:	PUNCT
ejpam-846	515	96	out	out	ADJ
ejpam-846	515	97	-	-	PUNCT
ejpam-846	515	98	of	of	ADP
ejpam-846	515	99	-	-	PUNCT
ejpam-846	515	100	sample	sample	NOUN
ejpam-846	515	101	efficient	efficient	ADJ
ejpam-846	515	102	frontiers	frontier	NOUN
ejpam-846	515	103	for	for	SCONJ
ejpam-846	515	104	approximated	approximate	VERB
ejpam-846	515	105	versus	versus	ADP
ejpam-846	515	106	normal	normal	ADJ
ejpam-846	515	107	returns	return	NOUN
ejpam-846	515	108	.	.	PUNCT
ejpam-846	516	1	the	the	DET
ejpam-846	516	2	maxdd	maxdd	ADJ
ejpam-846	516	3	performance	performance	NOUN
ejpam-846	516	4	metric	metric	NOUN
ejpam-846	516	5	too	too	ADV
ejpam-846	516	6	is	be	AUX
ejpam-846	516	7	quite	quite	ADV
ejpam-846	516	8	inferior	inferior	ADJ
ejpam-846	516	9	for	for	ADP
ejpam-846	516	10	the	the	DET
ejpam-846	516	11	mv	mv	PROPN
ejpam-846	516	12	model	model	NOUN
ejpam-846	516	13	relative	relative	ADJ
ejpam-846	516	14	to	to	ADP
ejpam-846	516	15	the	the	DET
ejpam-846	516	16	td	td	PROPN
ejpam-846	516	17	model	model	NOUN
ejpam-846	516	18	,	,	PUNCT
ejpam-846	516	19	see	see	VERB
ejpam-846	516	20	figure	figure	NOUN
ejpam-846	516	21	5	5	NUM
ejpam-846	516	22	.	.	PUNCT
ejpam-846	516	23	with	with	ADP
ejpam-846	516	24	increasing	increase	VERB
ejpam-846	516	25	maxdd	maxdd	NOUN
ejpam-846	516	26	,	,	PUNCT
ejpam-846	516	27	both	both	DET
ejpam-846	516	28	models	model	NOUN
ejpam-846	516	29	yield	yield	VERB
ejpam-846	516	30	diminished	diminish	VERB
ejpam-846	516	31	portfolio	portfolio	NOUN
ejpam-846	516	32	returns	return	NOUN
ejpam-846	516	33	;	;	PUNCT
ejpam-846	516	34	however	however	ADV
ejpam-846	516	35	,	,	PUNCT
ejpam-846	516	36	for	for	ADP
ejpam-846	516	37	moderate	moderate	ADJ
ejpam-846	516	38	risks	risk	NOUN
ejpam-846	516	39	levels	level	NOUN
ejpam-846	516	40	(	(	PUNCT
ejpam-846	516	41	thus	thus	ADV
ejpam-846	516	42	,	,	PUNCT
ejpam-846	516	43	moderate	moderate	ADJ
ejpam-846	516	44	maxdd	maxdd	ADJ
ejpam-846	516	45	values	value	NOUN
ejpam-846	516	46	)	)	PUNCT
ejpam-846	516	47	,	,	PUNCT
ejpam-846	516	48	the	the	DET
ejpam-846	516	49	performance	performance	NOUN
ejpam-846	516	50	of	of	ADP
ejpam-846	516	51	the	the	DET
ejpam-846	516	52	td	td	NOUN
ejpam-846	516	53	-	-	PUNCT
ejpam-846	516	54	portfolio	portfolio	NOUN
ejpam-846	516	55	is	be	AUX
ejpam-846	516	56	outstanding	outstanding	ADJ
ejpam-846	516	57	.	.	PUNCT
ejpam-846	517	1	also	also	ADV
ejpam-846	517	2	,	,	PUNCT
ejpam-846	517	3	observe	observe	VERB
ejpam-846	517	4	from	from	ADP
ejpam-846	517	5	figures	figure	NOUN
ejpam-846	517	6	4	4	NUM
ejpam-846	517	7	and	and	CCONJ
ejpam-846	517	8	5	5	NUM
ejpam-846	517	9	that	that	PRON
ejpam-846	517	10	increased	increase	VERB
ejpam-846	517	11	standard	standard	ADJ
ejpam-846	517	12	deviation	deviation	NOUN
ejpam-846	517	13	for	for	ADP
ejpam-846	517	14	the	the	DET
ejpam-846	517	15	portfolio	portfolio	NOUN
ejpam-846	517	16	does	do	AUX
ejpam-846	517	17	not	not	PART
ejpam-846	517	18	necessarily	necessarily	ADV
ejpam-846	517	19	imply	imply	VERB
ejpam-846	517	20	increased	increase	VERB
ejpam-846	517	21	draw	draw	NOUN
ejpam-846	517	22	references	reference	NOUN
ejpam-846	517	23	590	590	NUM
ejpam-846	517	24	downs	down	NOUN
ejpam-846	517	25	.	.	PUNCT
ejpam-846	518	1	jan	jan	PROPN
ejpam-846	518	2	jun	jun	PROPN
ejpam-846	518	3	,	,	PUNCT
ejpam-846	518	4	2010	2010	NUM
ejpam-846	518	5	(	(	PUNCT
ejpam-846	518	6	monthly	monthly	ADV
ejpam-846	518	7	rebalanced	rebalance	VERB
ejpam-846	518	8	)	)	PUNCT
ejpam-846	518	9	20	20	NUM
ejpam-846	518	10	%	%	NOUN
ejpam-846	518	11	25	25	NUM
ejpam-846	518	12	%	%	NOUN
ejpam-846	518	13	0	0	NUM
ejpam-846	518	14	%	%	NOUN
ejpam-846	518	15	5	5	NUM
ejpam-846	518	16	%	%	NOUN
ejpam-846	518	17	10	10	NUM
ejpam-846	518	18	%	%	NOUN
ejpam-846	518	19	15	15	NUM
ejpam-846	518	20	%	%	NOUN
ejpam-846	518	21	n	n	CCONJ
ejpam-846	518	22	n	n	PRON
ejpam-846	518	23	u	u	NOUN
ejpam-846	518	24	a	a	DET
ejpam-846	518	25	li	li	X
ejpam-846	518	26	ze	ze	PROPN
ejpam-846	518	27	d	d	NOUN
ejpam-846	518	28	r	r	NOUN
ejpam-846	518	29	e	e	X
ejpam-846	518	30	tu	tu	PROPN
ejpam-846	518	31	rn	rn	PROPN
ejpam-846	518	32	20	20	NUM
ejpam-846	518	33	%	%	NOUN
ejpam-846	518	34	15	15	NUM
ejpam-846	518	35	%	%	NOUN
ejpam-846	518	36	10	10	NUM
ejpam-846	518	37	%	%	NOUN
ejpam-846	518	38	5	5	NUM
ejpam-846	518	39	%	%	NOUN
ejpam-846	518	40	2	2	NUM
ejpam-846	518	41	%	%	NOUN
ejpam-846	518	42	4	4	NUM
ejpam-846	518	43	%	%	NOUN
ejpam-846	518	44	6	6	NUM
ejpam-846	518	45	%	%	NOUN
ejpam-846	518	46	8	8	NUM
ejpam-846	518	47	%	%	NOUN
ejpam-846	518	48	10	10	NUM
ejpam-846	518	49	%	%	NOUN
ejpam-846	518	50	12	12	NUM
ejpam-846	518	51	%	%	NOUN
ejpam-846	518	52	14	14	NUM
ejpam-846	518	53	%	%	NOUN
ejpam-846	518	54	16	16	NUM
ejpam-846	518	55	%	%	NOUN
ejpam-846	518	56	p	p	NOUN
ejpam-846	518	57	o	o	X
ejpam-846	519	1	rt	rt	INTJ
ejpam-846	519	2	fo	fo	INTJ
ejpam-846	519	3	li	li	PROPN
ejpam-846	520	1	o	o	PROPN
ejpam-846	520	2	a	a	DET
ejpam-846	520	3	portfolio	portfolio	NOUN
ejpam-846	520	4	(	(	PUNCT
ejpam-846	520	5	6	6	NUM
ejpam-846	520	6	month	month	NOUN
ejpam-846	520	7	)	)	PUNCT
ejpam-846	520	8	maximum	maximum	ADJ
ejpam-846	520	9	drawdown	drawdown	ADJ
ejpam-846	520	10	target	target	NOUN
ejpam-846	520	11	model	model	NOUN
ejpam-846	520	12	(	(	PUNCT
ejpam-846	520	13	out	out	ADP
ejpam-846	520	14	of	of	ADP
ejpam-846	520	15	sample	sample	NOUN
ejpam-846	520	16	)	)	PUNCT
ejpam-846	520	17	mean	mean	ADJ
ejpam-846	520	18	/	/	SYM
ejpam-846	520	19	var	var	NOUN
ejpam-846	520	20	(	(	PUNCT
ejpam-846	520	21	out	out	ADP
ejpam-846	520	22	of	of	ADP
ejpam-846	520	23	sample	sample	NOUN
ejpam-846	520	24	)	)	PUNCT
ejpam-846	520	25	s&p	s&p	PROPN
ejpam-846	520	26	500	500	NUM
ejpam-846	520	27	index	index	NOUN
ejpam-846	520	28	figure	figure	NOUN
ejpam-846	520	29	5	5	NUM
ejpam-846	520	30	:	:	PUNCT
ejpam-846	520	31	portfolio	portfolio	NOUN
ejpam-846	520	32	return	return	VERB
ejpam-846	520	33	to	to	AUX
ejpam-846	520	34	maximum	maximum	ADV
ejpam-846	520	35	draw	draw	VERB
ejpam-846	520	36	down	down	ADP
ejpam-846	520	37	performance	performance	NOUN
ejpam-846	520	38	.	.	PUNCT
ejpam-846	521	1	6	6	X
ejpam-846	521	2	.	.	X
ejpam-846	521	3	concluding	conclude	VERB
ejpam-846	521	4	remarks	remark	NOUN
ejpam-846	521	5	rather	rather	ADV
ejpam-846	521	6	than	than	ADP
ejpam-846	521	7	focusing	focus	VERB
ejpam-846	521	8	on	on	ADP
ejpam-846	521	9	time	time	NOUN
ejpam-846	521	10	series	series	PROPN
ejpam-846	521	11	modeling	modeling	PROPN
ejpam-846	521	12	,	,	PUNCT
ejpam-846	521	13	this	this	DET
ejpam-846	521	14	paper	paper	NOUN
ejpam-846	521	15	aims	aim	VERB
ejpam-846	521	16	at	at	ADP
ejpam-846	521	17	controlling	control	VERB
ejpam-846	521	18	risks	risk	NOUN
ejpam-846	521	19	directly	directly	ADV
ejpam-846	521	20	via	via	ADP
ejpam-846	521	21	portfolio	portfolio	NOUN
ejpam-846	521	22	optimization	optimization	NOUN
ejpam-846	521	23	,	,	PUNCT
ejpam-846	521	24	recognizing	recognize	VERB
ejpam-846	521	25	that	that	SCONJ
ejpam-846	521	26	scenarios	scenario	NOUN
ejpam-846	521	27	of	of	ADP
ejpam-846	521	28	the	the	DET
ejpam-846	521	29	future	future	NOUN
ejpam-846	521	30	can	can	AUX
ejpam-846	521	31	not	not	PART
ejpam-846	521	32	be	be	AUX
ejpam-846	521	33	known	know	VERB
ejpam-846	521	34	with	with	ADP
ejpam-846	521	35	certainty	certainty	PROPN
ejpam-846	521	36	.	.	PUNCT
ejpam-846	522	1	this	this	PRON
ejpam-846	522	2	is	be	AUX
ejpam-846	522	3	done	do	VERB
ejpam-846	522	4	through	through	ADP
ejpam-846	522	5	incorporating	incorporate	VERB
ejpam-846	522	6	risk	risk	NOUN
ejpam-846	522	7	functions	function	NOUN
ejpam-846	522	8	that	that	PRON
ejpam-846	522	9	involve	involve	VERB
ejpam-846	522	10	computing	compute	VERB
ejpam-846	522	11	expectations	expectation	NOUN
ejpam-846	522	12	in	in	ADP
ejpam-846	522	13	high	high	ADJ
ejpam-846	522	14	dimensions	dimension	NOUN
ejpam-846	522	15	,	,	PUNCT
ejpam-846	522	16	embedded	embed	VERB
ejpam-846	522	17	within	within	ADP
ejpam-846	522	18	an	an	DET
ejpam-846	522	19	outer	outer	ADJ
ejpam-846	522	20	decision	decision	NOUN
ejpam-846	522	21	optimization	optimization	NOUN
ejpam-846	522	22	model	model	NOUN
ejpam-846	522	23	.	.	PUNCT
ejpam-846	523	1	the	the	DET
ejpam-846	523	2	basic	basic	ADJ
ejpam-846	523	3	theory	theory	NOUN
ejpam-846	523	4	of	of	ADP
ejpam-846	523	5	approximating	approximate	VERB
ejpam-846	523	6	expectation	expectation	NOUN
ejpam-846	523	7	functions	function	NOUN
ejpam-846	523	8	using	use	VERB
ejpam-846	523	9	first	first	ADJ
ejpam-846	523	10	and	and	CCONJ
ejpam-846	523	11	second	second	ADJ
ejpam-846	523	12	moments	moment	NOUN
ejpam-846	523	13	utilizes	utilize	VERB
ejpam-846	523	14	the	the	DET
ejpam-846	523	15	generalized	generalized	ADJ
ejpam-846	523	16	moment	moment	NOUN
ejpam-846	523	17	problem	problem	NOUN
ejpam-846	523	18	,	,	PUNCT
ejpam-846	523	19	and	and	CCONJ
ejpam-846	523	20	they	they	PRON
ejpam-846	523	21	are	be	AUX
ejpam-846	523	22	applicable	applicable	ADJ
ejpam-846	523	23	for	for	ADP
ejpam-846	523	24	general	general	ADJ
ejpam-846	523	25	convex	convex	NOUN
ejpam-846	523	26	functions	function	NOUN
ejpam-846	523	27	.	.	PUNCT
ejpam-846	524	1	application	application	NOUN
ejpam-846	524	2	of	of	ADP
ejpam-846	524	3	the	the	DET
ejpam-846	524	4	approximation	approximation	NOUN
ejpam-846	524	5	requires	require	VERB
ejpam-846	524	6	compact	compact	ADJ
ejpam-846	524	7	domains	domain	NOUN
ejpam-846	524	8	and	and	CCONJ
ejpam-846	524	9	simplicial	simplicial	ADJ
ejpam-846	524	10	coverage	coverage	NOUN
ejpam-846	524	11	of	of	ADP
ejpam-846	524	12	such	such	ADJ
ejpam-846	524	13	domains	domain	NOUN
ejpam-846	524	14	of	of	ADP
ejpam-846	524	15	random	random	ADJ
ejpam-846	524	16	vectors	vector	NOUN
ejpam-846	524	17	.	.	PUNCT
ejpam-846	525	1	this	this	PRON
ejpam-846	525	2	can	can	AUX
ejpam-846	525	3	be	be	AUX
ejpam-846	525	4	easily	easily	ADV
ejpam-846	525	5	done	do	VERB
ejpam-846	525	6	for	for	ADP
ejpam-846	525	7	financial	financial	ADJ
ejpam-846	525	8	optimization	optimization	NOUN
ejpam-846	525	9	problems	problem	NOUN
ejpam-846	525	10	when	when	SCONJ
ejpam-846	525	11	return	return	VERB
ejpam-846	525	12	scenarios	scenario	NOUN
ejpam-846	525	13	for	for	ADP
ejpam-846	525	14	the	the	DET
ejpam-846	525	15	future	future	NOUN
ejpam-846	525	16	must	must	AUX
ejpam-846	525	17	be	be	AUX
ejpam-846	525	18	based	base	VERB
ejpam-846	525	19	on	on	ADP
ejpam-846	525	20	historical	historical	ADJ
ejpam-846	525	21	(	(	PUNCT
ejpam-846	525	22	discrete	discrete	NOUN
ejpam-846	525	23	)	)	PUNCT
ejpam-846	525	24	returns	return	NOUN
ejpam-846	525	25	observed	observe	VERB
ejpam-846	525	26	over	over	ADP
ejpam-846	525	27	some	some	DET
ejpam-846	525	28	period	period	NOUN
ejpam-846	525	29	of	of	ADP
ejpam-846	525	30	time	time	NOUN
ejpam-846	525	31	.	.	PUNCT
ejpam-846	526	1	two	two	NUM
ejpam-846	526	2	competing	compete	VERB
ejpam-846	526	3	models	model	NOUN
ejpam-846	526	4	are	be	AUX
ejpam-846	526	5	compared	compare	VERB
ejpam-846	526	6	,	,	PUNCT
ejpam-846	526	7	one	one	NUM
ejpam-846	526	8	in	in	ADP
ejpam-846	526	9	which	which	PRON
ejpam-846	526	10	normality	normality	NOUN
ejpam-846	526	11	is	be	AUX
ejpam-846	526	12	assumed	assume	VERB
ejpam-846	526	13	for	for	ADP
ejpam-846	526	14	random	random	ADJ
ejpam-846	526	15	returns	return	NOUN
ejpam-846	526	16	,	,	PUNCT
ejpam-846	526	17	and	and	CCONJ
ejpam-846	526	18	thus	thus	ADV
ejpam-846	526	19	,	,	PUNCT
ejpam-846	526	20	the	the	DET
ejpam-846	526	21	usual	usual	ADJ
ejpam-846	526	22	mean	mean	ADJ
ejpam-846	526	23	-	-	PUNCT
ejpam-846	526	24	variance	variance	NOUN
ejpam-846	526	25	quadratic	quadratic	ADJ
ejpam-846	526	26	optimization	optimization	NOUN
ejpam-846	526	27	(	(	PUNCT
ejpam-846	526	28	due	due	ADP
ejpam-846	526	29	to	to	ADP
ejpam-846	526	30	markowitz	markowitz	PROPN
ejpam-846	526	31	)	)	PUNCT
ejpam-846	526	32	is	be	AUX
ejpam-846	526	33	applied	apply	VERB
ejpam-846	526	34	for	for	ADP
ejpam-846	526	35	risk	risk	NOUN
ejpam-846	526	36	-	-	PUNCT
ejpam-846	526	37	return	return	NOUN
ejpam-846	526	38	trade	trade	NOUN
ejpam-846	526	39	off	off	ADP
ejpam-846	526	40	.	.	PUNCT
ejpam-846	527	1	second	second	ADJ
ejpam-846	527	2	,	,	PUNCT
ejpam-846	527	3	under	under	ADP
ejpam-846	527	4	no	no	DET
ejpam-846	527	5	such	such	ADJ
ejpam-846	527	6	distributional	distributional	ADJ
ejpam-846	527	7	assumption	assumption	NOUN
ejpam-846	527	8	,	,	PUNCT
ejpam-846	527	9	historical	historical	ADJ
ejpam-846	527	10	returns	return	NOUN
ejpam-846	527	11	are	be	AUX
ejpam-846	527	12	approximated	approximate	VERB
ejpam-846	527	13	with	with	ADP
ejpam-846	527	14	second	second	ADJ
ejpam-846	527	15	moment	moment	NOUN
ejpam-846	527	16	-	-	PUNCT
ejpam-846	527	17	approximated	approximate	VERB
ejpam-846	527	18	discrete	discrete	ADJ
ejpam-846	527	19	scenarios	scenario	NOUN
ejpam-846	527	20	and	and	CCONJ
ejpam-846	527	21	applied	apply	VERB
ejpam-846	527	22	within	within	ADP
ejpam-846	527	23	a	a	DET
ejpam-846	527	24	risk	risk	NOUN
ejpam-846	527	25	function	function	NOUN
ejpam-846	527	26	that	that	PRON
ejpam-846	527	27	is	be	AUX
ejpam-846	527	28	not	not	PART
ejpam-846	527	29	symmetric	symmetric	ADJ
ejpam-846	527	30	,	,	PUNCT
ejpam-846	527	31	in	in	ADP
ejpam-846	527	32	this	this	DET
ejpam-846	527	33	case	case	NOUN
ejpam-846	527	34	,	,	PUNCT
ejpam-846	527	35	a	a	DET
ejpam-846	527	36	target	target	NOUN
ejpam-846	527	37	deficit	deficit	NOUN
ejpam-846	527	38	risk	risk	NOUN
ejpam-846	527	39	model	model	NOUN
ejpam-846	527	40	.	.	PUNCT
ejpam-846	528	1	while	while	SCONJ
ejpam-846	528	2	in	in	ADP
ejpam-846	528	3	-	-	PUNCT
ejpam-846	528	4	sample	sample	NOUN
ejpam-846	528	5	performance	performance	NOUN
ejpam-846	528	6	of	of	ADP
ejpam-846	528	7	the	the	DET
ejpam-846	528	8	mean	mean	ADJ
ejpam-846	528	9	-	-	PUNCT
ejpam-846	528	10	variance	variance	NOUN
ejpam-846	528	11	trade	trade	NOUN
ejpam-846	528	12	off	off	ADP
ejpam-846	528	13	model	model	NOUN
ejpam-846	528	14	is	be	AUX
ejpam-846	528	15	superior	superior	ADJ
ejpam-846	528	16	,	,	PUNCT
ejpam-846	528	17	as	as	ADP
ejpam-846	528	18	for	for	ADP
ejpam-846	528	19	the	the	DET
ejpam-846	528	20	out	out	ADJ
ejpam-846	528	21	-	-	PUNCT
ejpam-846	528	22	of	of	ADP
ejpam-846	528	23	-	-	PUNCT
ejpam-846	528	24	sample	sample	NOUN
ejpam-846	528	25	(	(	PUNCT
ejpam-846	528	26	actual	actual	ADJ
ejpam-846	528	27	)	)	PUNCT
ejpam-846	528	28	performance	performance	NOUN
ejpam-846	528	29	,	,	PUNCT
ejpam-846	528	30	the	the	DET
ejpam-846	528	31	scenario	scenario	NOUN
ejpam-846	528	32	-	-	PUNCT
ejpam-846	528	33	approximated	approximate	VERB
ejpam-846	528	34	target	target	NOUN
ejpam-846	528	35	deficit	deficit	NOUN
ejpam-846	528	36	model	model	NOUN
ejpam-846	528	37	is	be	AUX
ejpam-846	528	38	far	far	ADV
ejpam-846	528	39	superior	superior	ADJ
ejpam-846	528	40	.	.	PUNCT
ejpam-846	529	1	these	these	DET
ejpam-846	529	2	results	result	NOUN
ejpam-846	529	3	corroborate	corroborate	VERB
ejpam-846	529	4	well	well	ADV
ejpam-846	529	5	with	with	ADP
ejpam-846	529	6	the	the	DET
ejpam-846	529	7	well	well	ADV
ejpam-846	529	8	-	-	PUNCT
ejpam-846	529	9	known	know	VERB
ejpam-846	529	10	fact	fact	NOUN
ejpam-846	529	11	that	that	SCONJ
ejpam-846	529	12	stock	stock	NOUN
ejpam-846	529	13	returns	return	NOUN
ejpam-846	529	14	have	have	AUX
ejpam-846	529	15	heavier	heavy	ADJ
ejpam-846	529	16	-	-	PUNCT
ejpam-846	529	17	tails	tail	NOUN
ejpam-846	529	18	and	and	CCONJ
ejpam-846	529	19	discounting	discount	VERB
ejpam-846	529	20	extremal	extremal	ADJ
ejpam-846	529	21	possibilities	possibility	NOUN
ejpam-846	529	22	in	in	ADP
ejpam-846	529	23	returns	return	NOUN
ejpam-846	529	24	can	can	AUX
ejpam-846	529	25	often	often	ADV
ejpam-846	529	26	lead	lead	VERB
ejpam-846	529	27	to	to	ADP
ejpam-846	529	28	significant	significant	ADJ
ejpam-846	529	29	declines	decline	NOUN
ejpam-846	529	30	in	in	ADP
ejpam-846	529	31	fund	fund	NOUN
ejpam-846	529	32	performance	performance	NOUN
ejpam-846	529	33	.	.	PUNCT
ejpam-846	530	1	references	reference	NOUN
ejpam-846	530	2	[	[	X
ejpam-846	530	3	1	1	NUM
ejpam-846	530	4	]	]	X
ejpam-846	530	5	e.j	e.j	PROPN
ejpam-846	530	6	.	.	PROPN
ejpam-846	530	7	anderson	anderson	PROPN
ejpam-846	530	8	and	and	CCONJ
ejpam-846	530	9	p.	p.	PROPN
ejpam-846	530	10	nash	nash	PROPN
ejpam-846	530	11	.	.	PUNCT
ejpam-846	531	1	linear	linear	PROPN
ejpam-846	531	2	programming	programming	NOUN
ejpam-846	531	3	in	in	ADP
ejpam-846	531	4	infinite	infinite	ADJ
ejpam-846	531	5	-	-	PUNCT
ejpam-846	531	6	dimensional	dimensional	ADJ
ejpam-846	531	7	spaces	space	NOUN
ejpam-846	531	8	.	.	PUNCT
ejpam-846	532	1	john	john	PROPN
ejpam-846	532	2	wiley	wiley	PROPN
ejpam-846	532	3	and	and	CCONJ
ejpam-846	532	4	sons	son	NOUN
ejpam-846	532	5	,	,	PUNCT
ejpam-846	532	6	new	new	PROPN
ejpam-846	532	7	york	york	PROPN
ejpam-846	532	8	,	,	PUNCT
ejpam-846	532	9	1987	1987	NUM
ejpam-846	532	10	.	.	PUNCT
ejpam-846	533	1	references	reference	NOUN
ejpam-846	533	2	591	591	NUM
ejpam-846	533	3	[	[	X
ejpam-846	533	4	2	2	NUM
ejpam-846	533	5	]	]	X
ejpam-846	533	6	j.r	j.r	PROPN
ejpam-846	533	7	.	.	PROPN
ejpam-846	533	8	birge	birge	PROPN
ejpam-846	533	9	and	and	CCONJ
ejpam-846	533	10	r.j	r.j	PROPN
ejpam-846	533	11	-	-	PUNCT
ejpam-846	533	12	b.	b.	NOUN
ejpam-846	533	13	wets	wet	NOUN
ejpam-846	533	14	.	.	PUNCT
ejpam-846	534	1	designing	design	VERB
ejpam-846	534	2	approximation	approximation	NOUN
ejpam-846	534	3	schemes	scheme	NOUN
ejpam-846	534	4	for	for	ADP
ejpam-846	534	5	stochastic	stochastic	ADJ
ejpam-846	534	6	optimization	optimization	NOUN
ejpam-846	534	7	problems	problem	NOUN
ejpam-846	534	8	,	,	PUNCT
ejpam-846	534	9	in	in	ADP
ejpam-846	534	10	particular	particular	ADJ
ejpam-846	534	11	for	for	ADP
ejpam-846	534	12	stochastic	stochastic	ADJ
ejpam-846	534	13	programs	program	NOUN
ejpam-846	534	14	with	with	ADP
ejpam-846	534	15	recourse	recourse	NOUN
ejpam-846	534	16	.	.	PUNCT
ejpam-846	535	1	mathematical	mathematical	ADJ
ejpam-846	535	2	programming	programming	NOUN
ejpam-846	535	3	study	study	NOUN
ejpam-846	535	4	,	,	PUNCT
ejpam-846	535	5	27:54–102	27:54–102	NUM
ejpam-846	535	6	,	,	PUNCT
ejpam-846	535	7	1986	1986	NUM
ejpam-846	535	8	.	.	PUNCT
ejpam-846	536	1	[	[	X
ejpam-846	536	2	3	3	X
ejpam-846	536	3	]	]	PUNCT
ejpam-846	536	4	m.	m.	NOUN
ejpam-846	536	5	bychkov	bychkov	NOUN
ejpam-846	536	6	and	and	CCONJ
ejpam-846	536	7	n.c.p	n.c.p	PROPN
ejpam-846	536	8	.	.	PROPN
ejpam-846	536	9	edirisinghe	edirisinghe	PROPN
ejpam-846	536	10	.	.	PUNCT
ejpam-846	537	1	rational	rational	ADJ
ejpam-846	537	2	risk	risk	NOUN
ejpam-846	537	3	measures	measure	NOUN
ejpam-846	537	4	and	and	CCONJ
ejpam-846	537	5	applications	application	NOUN
ejpam-846	537	6	.	.	PUNCT
ejpam-846	538	1	working	work	VERB
ejpam-846	538	2	paper	paper	NOUN
ejpam-846	538	3	,	,	PUNCT
ejpam-846	538	4	university	university	PROPN
ejpam-846	538	5	of	of	ADP
ejpam-846	538	6	tennessee	tennessee	PROPN
ejpam-846	538	7	,	,	PUNCT
ejpam-846	538	8	college	college	NOUN
ejpam-846	538	9	of	of	ADP
ejpam-846	538	10	business	business	NOUN
ejpam-846	538	11	,	,	PUNCT
ejpam-846	538	12	knoxville	knoxville	PROPN
ejpam-846	538	13	,	,	PUNCT
ejpam-846	538	14	tn	tn	PROPN
ejpam-846	538	15	,	,	PUNCT
ejpam-846	538	16	2008	2008	NUM
ejpam-846	538	17	.	.	PUNCT
ejpam-846	539	1	[	[	X
ejpam-846	539	2	4	4	X
ejpam-846	539	3	]	]	X
ejpam-846	539	4	n.c.p	n.c.p	PROPN
ejpam-846	539	5	.	.	PROPN
ejpam-846	539	6	edirisinghe	edirisinghe	PROPN
ejpam-846	539	7	.	.	PUNCT
ejpam-846	540	1	new	new	ADJ
ejpam-846	540	2	second	second	ADJ
ejpam-846	540	3	-	-	PUNCT
ejpam-846	540	4	order	order	NOUN
ejpam-846	540	5	bounds	bound	NOUN
ejpam-846	540	6	on	on	ADP
ejpam-846	540	7	the	the	DET
ejpam-846	540	8	expectation	expectation	NOUN
ejpam-846	540	9	of	of	ADP
ejpam-846	540	10	saddle	saddle	NOUN
ejpam-846	540	11	functions	function	NOUN
ejpam-846	540	12	with	with	ADP
ejpam-846	540	13	applications	application	NOUN
ejpam-846	540	14	to	to	PART
ejpam-846	540	15	stochastic	stochastic	ADJ
ejpam-846	540	16	linear	linear	ADJ
ejpam-846	540	17	programming	programming	NOUN
ejpam-846	540	18	.	.	PUNCT
ejpam-846	541	1	operations	operation	NOUN
ejpam-846	541	2	research	research	NOUN
ejpam-846	541	3	,	,	PUNCT
ejpam-846	541	4	44:909–922	44:909–922	NUM
ejpam-846	541	5	,	,	PUNCT
ejpam-846	541	6	1996	1996	NUM
ejpam-846	541	7	.	.	PUNCT
ejpam-846	542	1	[	[	X
ejpam-846	542	2	5	5	NUM
ejpam-846	542	3	]	]	X
ejpam-846	542	4	n.c.p	n.c.p	PROPN
ejpam-846	542	5	.	.	PROPN
ejpam-846	542	6	edirisinghe	edirisinghe	PROPN
ejpam-846	542	7	.	.	PUNCT
ejpam-846	543	1	integrated	integrate	VERB
ejpam-846	543	2	risk	risk	NOUN
ejpam-846	543	3	control	control	NOUN
ejpam-846	543	4	using	use	VERB
ejpam-846	543	5	stochastic	stochastic	ADJ
ejpam-846	543	6	programming	programming	NOUN
ejpam-846	543	7	alm	alm	NOUN
ejpam-846	543	8	models	model	NOUN
ejpam-846	543	9	for	for	ADP
ejpam-846	543	10	money	money	NOUN
ejpam-846	543	11	management	management	NOUN
ejpam-846	543	12	.	.	PUNCT
ejpam-846	544	1	in	in	ADP
ejpam-846	544	2	s.a	s.a	PROPN
ejpam-846	544	3	.	.	PROPN
ejpam-846	544	4	zenios	zenios	PROPN
ejpam-846	544	5	and	and	CCONJ
ejpam-846	544	6	w.t	w.t	PROPN
ejpam-846	544	7	.	.	PROPN
ejpam-846	544	8	ziemba	ziemba	PROPN
ejpam-846	544	9	,	,	PUNCT
ejpam-846	544	10	editors	editor	NOUN
ejpam-846	544	11	,	,	PUNCT
ejpam-846	544	12	handbook	handbook	NOUN
ejpam-846	544	13	of	of	ADP
ejpam-846	544	14	asset	asset	NOUN
ejpam-846	544	15	and	and	CCONJ
ejpam-846	544	16	liability	liability	NOUN
ejpam-846	544	17	management	management	NOUN
ejpam-846	544	18	,	,	PUNCT
ejpam-846	544	19	volume	volume	NOUN
ejpam-846	544	20	2	2	NUM
ejpam-846	544	21	,	,	PUNCT
ejpam-846	544	22	chapter	chapter	NOUN
ejpam-846	544	23	16	16	NUM
ejpam-846	544	24	,	,	PUNCT
ejpam-846	545	1	pages	page	VERB
ejpam-846	545	2	707–750	707–750	NUM
ejpam-846	545	3	.	.	PUNCT
ejpam-846	546	1	elsevier	elsevier	PROPN
ejpam-846	546	2	science	science	PROPN
ejpam-846	546	3	bv	bv	PROPN
ejpam-846	546	4	,	,	PUNCT
ejpam-846	546	5	2007	2007	NUM
ejpam-846	546	6	.	.	PUNCT
ejpam-846	547	1	[	[	X
ejpam-846	547	2	6	6	NUM
ejpam-846	547	3	]	]	X
ejpam-846	547	4	n.c.p	n.c.p	PROPN
ejpam-846	547	5	.	.	PROPN
ejpam-846	547	6	edirisinghe	edirisinghe	PROPN
ejpam-846	547	7	.	.	PUNCT
ejpam-846	548	1	an	an	DET
ejpam-846	548	2	efficient	efficient	ADJ
ejpam-846	548	3	scheme	scheme	NOUN
ejpam-846	548	4	for	for	ADP
ejpam-846	548	5	computing	compute	VERB
ejpam-846	548	6	a	a	DET
ejpam-846	548	7	compact	compact	ADJ
ejpam-846	548	8	simplex	simplex	NOUN
ejpam-846	548	9	covering	cover	VERB
ejpam-846	548	10	multivariate	multivariate	NOUN
ejpam-846	548	11	points	point	NOUN
ejpam-846	548	12	.	.	PUNCT
ejpam-846	549	1	working	work	VERB
ejpam-846	549	2	paper	paper	NOUN
ejpam-846	549	3	,	,	PUNCT
ejpam-846	549	4	university	university	PROPN
ejpam-846	549	5	of	of	ADP
ejpam-846	549	6	tennessee	tennessee	PROPN
ejpam-846	549	7	,	,	PUNCT
ejpam-846	549	8	college	college	NOUN
ejpam-846	549	9	of	of	ADP
ejpam-846	549	10	business	business	NOUN
ejpam-846	549	11	,	,	PUNCT
ejpam-846	549	12	knoxville	knoxville	PROPN
ejpam-846	549	13	,	,	PUNCT
ejpam-846	549	14	tn	tn	PROPN
ejpam-846	549	15	(	(	PUNCT
ejpam-846	549	16	under	under	ADP
ejpam-846	549	17	review	review	NOUN
ejpam-846	549	18	)	)	PUNCT
ejpam-846	549	19	,	,	PUNCT
ejpam-846	549	20	2009	2009	NUM
ejpam-846	549	21	.	.	PUNCT
ejpam-846	550	1	[	[	X
ejpam-846	550	2	7	7	X
ejpam-846	550	3	]	]	X
ejpam-846	550	4	n.c.p	n.c.p	PROPN
ejpam-846	550	5	.	.	PROPN
ejpam-846	550	6	edirisinghe	edirisinghe	PROPN
ejpam-846	550	7	and	and	CCONJ
ejpam-846	550	8	g	g	NOUN
ejpam-846	550	9	-	-	PUNCT
ejpam-846	550	10	m.	m.	NOUN
ejpam-846	550	11	you	you	PRON
ejpam-846	550	12	.	.	PUNCT
ejpam-846	551	1	second	second	ADJ
ejpam-846	551	2	-	-	PUNCT
ejpam-846	551	3	order	order	NOUN
ejpam-846	551	4	scenario	scenario	NOUN
ejpam-846	551	5	approximation	approximation	NOUN
ejpam-846	551	6	and	and	CCONJ
ejpam-846	551	7	refinement	refinement	NOUN
ejpam-846	551	8	in	in	ADP
ejpam-846	551	9	optimization	optimization	NOUN
ejpam-846	551	10	under	under	ADP
ejpam-846	551	11	uncertainty	uncertainty	NOUN
ejpam-846	551	12	.	.	PUNCT
ejpam-846	552	1	annals	annal	NOUN
ejpam-846	552	2	of	of	ADP
ejpam-846	552	3	operations	operation	NOUN
ejpam-846	552	4	research	research	NOUN
ejpam-846	552	5	,	,	PUNCT
ejpam-846	552	6	19:314–340	19:314–340	NUM
ejpam-846	552	7	,	,	PUNCT
ejpam-846	552	8	1996	1996	NUM
ejpam-846	552	9	.	.	PUNCT
ejpam-846	553	1	[	[	X
ejpam-846	553	2	8	8	NUM
ejpam-846	553	3	]	]	X
ejpam-846	553	4	n.c.p	n.c.p	PROPN
ejpam-846	553	5	.	.	PROPN
ejpam-846	553	6	edirisinghe	edirisinghe	PROPN
ejpam-846	553	7	and	and	CCONJ
ejpam-846	553	8	w.t	w.t	PROPN
ejpam-846	553	9	.	.	PUNCT
ejpam-846	553	10	ziemba	ziemba	PROPN
ejpam-846	553	11	.	.	PUNCT
ejpam-846	554	1	tight	tight	ADJ
ejpam-846	554	2	bounds	bound	NOUN
ejpam-846	554	3	for	for	ADP
ejpam-846	554	4	stochastic	stochastic	ADJ
ejpam-846	554	5	convex	convex	NOUN
ejpam-846	554	6	programs	program	NOUN
ejpam-846	554	7	.	.	PUNCT
ejpam-846	555	1	operations	operation	NOUN
ejpam-846	555	2	research	research	NOUN
ejpam-846	555	3	,	,	PUNCT
ejpam-846	555	4	40:660–677	40:660–677	PROPN
ejpam-846	555	5	,	,	PUNCT
ejpam-846	555	6	1992	1992	NUM
ejpam-846	555	7	.	.	PUNCT
ejpam-846	556	1	[	[	X
ejpam-846	556	2	9	9	NUM
ejpam-846	556	3	]	]	PUNCT
ejpam-846	556	4	k.	k.	PROPN
ejpam-846	556	5	glashoff	glashoff	PROPN
ejpam-846	556	6	and	and	CCONJ
ejpam-846	556	7	s	s	NOUN
ejpam-846	556	8	-	-	PUNCT
ejpam-846	556	9	a.	a.	NOUN
ejpam-846	556	10	gustafson	gustafson	PROPN
ejpam-846	556	11	.	.	PUNCT
ejpam-846	557	1	linear	linear	ADJ
ejpam-846	557	2	optimization	optimization	NOUN
ejpam-846	557	3	and	and	CCONJ
ejpam-846	557	4	approximation	approximation	NOUN
ejpam-846	557	5	.	.	PUNCT
ejpam-846	558	1	springerverlag	springerverlag	PROPN
ejpam-846	558	2	,	,	PUNCT
ejpam-846	558	3	new	new	PROPN
ejpam-846	558	4	york	york	PROPN
ejpam-846	558	5	,	,	PUNCT
ejpam-846	558	6	1983	1983	NUM
ejpam-846	558	7	.	.	PUNCT
ejpam-846	559	1	[	[	X
ejpam-846	559	2	10	10	NUM
ejpam-846	559	3	]	]	X
ejpam-846	559	4	j.l	j.l	PROPN
ejpam-846	559	5	.	.	PROPN
ejpam-846	559	6	jensen	jensen	PROPN
ejpam-846	559	7	.	.	PUNCT
ejpam-846	560	1	sur	sur	PROPN
ejpam-846	560	2	les	les	PROPN
ejpam-846	560	3	fonctions	fonctions	PROPN
ejpam-846	560	4	convexes	convexe	NOUN
ejpam-846	560	5	et	et	NOUN
ejpam-846	560	6	les	les	PROPN
ejpam-846	560	7	inégalités	inégalités	PROPN
ejpam-846	560	8	entre	entre	PROPN
ejpam-846	560	9	les	les	PROPN
ejpam-846	560	10	valeurs	valeurs	PROPN
ejpam-846	560	11	moyennes	moyennes	PROPN
ejpam-846	560	12	.	.	PUNCT
ejpam-846	561	1	acta	acta	PROPN
ejpam-846	561	2	mathematica	mathematica	PROPN
ejpam-846	561	3	,	,	PUNCT
ejpam-846	561	4	30:173–177	30:173–177	NUM
ejpam-846	561	5	,	,	PUNCT
ejpam-846	561	6	1906	1906	NUM
ejpam-846	561	7	.	.	PUNCT
ejpam-846	562	1	[	[	X
ejpam-846	562	2	11	11	NUM
ejpam-846	562	3	]	]	PUNCT
ejpam-846	562	4	p.	p.	PROPN
ejpam-846	562	5	kall	kall	PROPN
ejpam-846	562	6	.	.	PUNCT
ejpam-846	563	1	stochastic	stochastic	ADJ
ejpam-846	563	2	linear	linear	ADJ
ejpam-846	563	3	programming	programming	NOUN
ejpam-846	563	4	.	.	PUNCT
ejpam-846	564	1	springer	springer	NOUN
ejpam-846	564	2	-	-	PUNCT
ejpam-846	564	3	verlag	verlag	PROPN
ejpam-846	564	4	,	,	PUNCT
ejpam-846	564	5	berlin	berlin	PROPN
ejpam-846	564	6	,	,	PUNCT
ejpam-846	564	7	1976	1976	NUM
ejpam-846	564	8	.	.	PUNCT
ejpam-846	565	1	[	[	X
ejpam-846	565	2	12	12	NUM
ejpam-846	565	3	]	]	PUNCT
ejpam-846	565	4	p.	p.	PROPN
ejpam-846	565	5	kall	kall	PROPN
ejpam-846	565	6	.	.	PUNCT
ejpam-846	566	1	stochastic	stochastic	ADJ
ejpam-846	566	2	programming	programming	NOUN
ejpam-846	566	3	with	with	ADP
ejpam-846	566	4	recourse	recourse	NOUN
ejpam-846	566	5	:	:	PUNCT
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ejpam-846	566	7	bounds	bound	NOUN
ejpam-846	566	8	and	and	CCONJ
ejpam-846	566	9	moment	moment	NOUN
ejpam-846	566	10	problems	problem	NOUN
ejpam-846	566	11	.	.	PUNCT
ejpam-846	567	1	in	in	ADP
ejpam-846	567	2	k.	k.	PROPN
ejpam-846	567	3	lommatzsch	lommatzsch	PROPN
ejpam-846	567	4	m.	m.	PROPN
ejpam-846	568	1	vlach	vlach	PROPN
ejpam-846	568	2	k.	k.	PROPN
ejpam-846	568	3	zimmermann	zimmermann	PROPN
ejpam-846	568	4	j.	j.	PROPN
ejpam-846	568	5	guddat	guddat	PROPN
ejpam-846	568	6	,	,	PUNCT
ejpam-846	568	7	p.	p.	PROPN
ejpam-846	568	8	kall	kall	PROPN
ejpam-846	568	9	,	,	PUNCT
ejpam-846	568	10	editor	editor	NOUN
ejpam-846	568	11	,	,	PUNCT
ejpam-846	568	12	advances	advance	NOUN
ejpam-846	568	13	in	in	ADP
ejpam-846	568	14	mathematical	mathematical	ADJ
ejpam-846	568	15	optimization	optimization	NOUN
ejpam-846	568	16	and	and	CCONJ
ejpam-846	568	17	related	related	ADJ
ejpam-846	568	18	topics	topic	NOUN
ejpam-846	568	19	.	.	PUNCT
ejpam-846	569	1	akademie	akademie	PROPN
ejpam-846	569	2	-	-	PUNCT
ejpam-846	569	3	verlag	verlag	PROPN
ejpam-846	569	4	,	,	PUNCT
ejpam-846	569	5	berlin	berlin	PROPN
ejpam-846	569	6	,	,	PUNCT
ejpam-846	569	7	1988	1988	NUM
ejpam-846	569	8	.	.	PUNCT
ejpam-846	570	1	[	[	X
ejpam-846	570	2	13	13	NUM
ejpam-846	570	3	]	]	X
ejpam-846	570	4	a.f	a.f	PROPN
ejpam-846	570	5	.	.	PROPN
ejpam-846	570	6	karr	karr	PROPN
ejpam-846	570	7	.	.	PUNCT
ejpam-846	571	1	extreme	extreme	ADJ
ejpam-846	571	2	points	point	NOUN
ejpam-846	571	3	of	of	ADP
ejpam-846	571	4	certain	certain	ADJ
ejpam-846	571	5	sets	set	NOUN
ejpam-846	571	6	of	of	ADP
ejpam-846	571	7	probability	probability	NOUN
ejpam-846	571	8	measures	measure	NOUN
ejpam-846	571	9	,	,	PUNCT
ejpam-846	571	10	with	with	ADP
ejpam-846	571	11	applications	application	NOUN
ejpam-846	571	12	.	.	PUNCT
ejpam-846	572	1	mathematics	mathematic	NOUN
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ejpam-846	572	3	operations	operation	NOUN
ejpam-846	572	4	research	research	NOUN
ejpam-846	572	5	,	,	PUNCT
ejpam-846	572	6	8:74–85	8:74–85	NUM
ejpam-846	572	7	,	,	PUNCT
ejpam-846	572	8	1983	1983	NUM
ejpam-846	572	9	.	.	PUNCT
ejpam-846	573	1	[	[	X
ejpam-846	573	2	14	14	NUM
ejpam-846	573	3	]	]	X
ejpam-846	573	4	j.	j.	PROPN
ejpam-846	573	5	kemperman	kemperman	PROPN
ejpam-846	573	6	.	.	PUNCT
ejpam-846	574	1	the	the	DET
ejpam-846	574	2	general	general	ADJ
ejpam-846	574	3	moment	moment	NOUN
ejpam-846	574	4	problem	problem	NOUN
ejpam-846	574	5	.	.	PUNCT
ejpam-846	575	1	a	a	DET
ejpam-846	575	2	geometric	geometric	ADJ
ejpam-846	575	3	approach	approach	NOUN
ejpam-846	575	4	.	.	PUNCT
ejpam-846	576	1	annals	annal	NOUN
ejpam-846	576	2	of	of	ADP
ejpam-846	576	3	mathematical	mathematical	ADJ
ejpam-846	576	4	statistics	statistic	NOUN
ejpam-846	576	5	,	,	PUNCT
ejpam-846	576	6	39:93–112	39:93–112	NUM
ejpam-846	576	7	,	,	PUNCT
ejpam-846	576	8	1968	1968	NUM
ejpam-846	576	9	.	.	PUNCT
ejpam-846	577	1	[	[	X
ejpam-846	577	2	15	15	NUM
ejpam-846	577	3	]	]	X
ejpam-846	577	4	h.	h.	PROPN
ejpam-846	577	5	markowitz	markowitz	PROPN
ejpam-846	577	6	.	.	PUNCT
ejpam-846	577	7	portfolio	portfolio	NOUN
ejpam-846	577	8	selection	selection	NOUN
ejpam-846	577	9	efficient	efficient	ADJ
ejpam-846	577	10	diversification	diversification	NOUN
ejpam-846	577	11	of	of	ADP
ejpam-846	577	12	investments	investment	NOUN
ejpam-846	577	13	.	.	PUNCT
ejpam-846	578	1	john	john	PROPN
ejpam-846	578	2	wiley	wiley	PROPN
ejpam-846	578	3	and	and	CCONJ
ejpam-846	578	4	sons	son	NOUN
ejpam-846	578	5	,	,	PUNCT
ejpam-846	578	6	new	new	PROPN
ejpam-846	578	7	york	york	PROPN
ejpam-846	578	8	,	,	PUNCT
ejpam-846	578	9	1959	1959	NUM
ejpam-846	578	10	.	.	PUNCT
ejpam-846	579	1	references	reference	NOUN
ejpam-846	579	2	592	592	NUM
ejpam-846	579	3	[	[	X
ejpam-846	579	4	16	16	NUM
ejpam-846	579	5	]	]	PUNCT
ejpam-846	579	6	w.	w.	PROPN
ejpam-846	579	7	ogryczak	ogryczak	PROPN
ejpam-846	579	8	and	and	CCONJ
ejpam-846	579	9	a.	a.	NOUN
ejpam-846	579	10	ruszczynski	ruszczynski	PROPN
ejpam-846	579	11	.	.	PUNCT
ejpam-846	580	1	dual	dual	ADJ
ejpam-846	580	2	stochastic	stochastic	ADJ
ejpam-846	580	3	dominance	dominance	NOUN
ejpam-846	580	4	and	and	CCONJ
ejpam-846	580	5	related	relate	VERB
ejpam-846	580	6	mean	mean	ADJ
ejpam-846	580	7	-	-	PUNCT
ejpam-846	580	8	risk	risk	NOUN
ejpam-846	580	9	models	model	NOUN
ejpam-846	580	10	.	.	PUNCT
ejpam-846	581	1	siam	siam	PROPN
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ejpam-846	581	3	of	of	ADP
ejpam-846	581	4	optimization	optimization	NOUN
ejpam-846	581	5	,	,	PUNCT
ejpam-846	581	6	13(1):60–78	13(1):60–78	NUM
ejpam-846	581	7	,	,	PUNCT
ejpam-846	581	8	2002	2002	NUM
ejpam-846	581	9	.	.	PUNCT
ejpam-846	582	1	[	[	X
ejpam-846	582	2	17	17	NUM
ejpam-846	582	3	]	]	X
ejpam-846	582	4	j.m	j.m	PROPN
ejpam-846	582	5	.	.	PROPN
ejpam-846	582	6	eber	eber	PROPN
ejpam-846	582	7	p.	p.	PROPN
ejpam-846	582	8	artzner	artzner	NOUN
ejpam-846	582	9	,	,	PUNCT
ejpam-846	582	10	f.	f.	PROPN
ejpam-846	582	11	delbaen	delbaen	PROPN
ejpam-846	582	12	and	and	CCONJ
ejpam-846	582	13	d.	d.	PROPN
ejpam-846	582	14	heath	heath	PROPN
ejpam-846	582	15	.	.	PUNCT
ejpam-846	583	1	coherent	coherent	ADJ
ejpam-846	583	2	measures	measure	NOUN
ejpam-846	583	3	of	of	ADP
ejpam-846	583	4	risk	risk	NOUN
ejpam-846	583	5	.	.	PUNCT
ejpam-846	584	1	mathematical	mathematical	ADJ
ejpam-846	584	2	finance	finance	NOUN
ejpam-846	584	3	,	,	PUNCT
ejpam-846	584	4	9:203–227	9:203–227	NUM
ejpam-846	584	5	,	,	PUNCT
ejpam-846	584	6	1999	1999	NUM
ejpam-846	584	7	.	.	PUNCT
ejpam-846	585	1	[	[	X
ejpam-846	585	2	18	18	NUM
ejpam-846	585	3	]	]	X
ejpam-846	585	4	r.t	r.t	PROPN
ejpam-846	585	5	.	.	PROPN
ejpam-846	585	6	rockafellar	rockafellar	PROPN
ejpam-846	585	7	and	and	CCONJ
ejpam-846	585	8	s.	s.	PROPN
ejpam-846	585	9	uryasev	uryasev	PROPN
ejpam-846	585	10	.	.	PUNCT
ejpam-846	586	1	optimization	optimization	NOUN
ejpam-846	586	2	of	of	ADP
ejpam-846	586	3	conditional	conditional	ADJ
ejpam-846	586	4	value	value	NOUN
ejpam-846	586	5	at	at	ADP
ejpam-846	586	6	risk	risk	NOUN
ejpam-846	586	7	.	.	PUNCT
ejpam-846	587	1	journal	journal	NOUN
ejpam-846	587	2	of	of	ADP
ejpam-846	587	3	risk	risk	NOUN
ejpam-846	587	4	,	,	PUNCT
ejpam-846	587	5	2(3):21–41	2(3):21–41	NUM
ejpam-846	587	6	,	,	PUNCT
ejpam-846	587	7	2000	2000	NUM
ejpam-846	587	8	.	.	PUNCT
ejpam-846	588	1	[	[	X
ejpam-846	588	2	19	19	NUM
ejpam-846	588	3	]	]	X
ejpam-846	588	4	r.j	r.j	PROPN
ejpam-846	588	5	-	-	PUNCT
ejpam-846	588	6	b.	b.	NOUN
ejpam-846	588	7	wets	wet	NOUN
ejpam-846	588	8	.	.	PUNCT
ejpam-846	589	1	stochastic	stochastic	ADJ
ejpam-846	589	2	programs	program	NOUN
ejpam-846	589	3	with	with	ADP
ejpam-846	589	4	fixed	fixed	ADJ
ejpam-846	589	5	recourse	recourse	NOUN
ejpam-846	589	6	:	:	PUNCT
ejpam-846	589	7	the	the	DET
ejpam-846	589	8	equivalent	equivalent	ADJ
ejpam-846	589	9	deterministic	deterministic	ADJ
ejpam-846	589	10	problem	problem	NOUN
ejpam-846	589	11	.	.	PUNCT
ejpam-846	590	1	siam	siam	PROPN
ejpam-846	590	2	review	review	PROPN
ejpam-846	590	3	,	,	PUNCT
ejpam-846	590	4	16:309–339	16:309–339	PROPN
ejpam-846	590	5	,	,	PUNCT
ejpam-846	590	6	1974	1974	NUM
ejpam-846	590	7	.	.	PUNCT
ejpam-846	591	1	[	[	X
ejpam-846	591	2	20	20	NUM
ejpam-846	591	3	]	]	X
ejpam-846	591	4	r.j	r.j	PROPN
ejpam-846	591	5	-	-	PUNCT
ejpam-846	591	6	b.	b.	NOUN
ejpam-846	591	7	wets	wet	NOUN
ejpam-846	591	8	.	.	PUNCT
ejpam-846	592	1	stochastic	stochastic	ADJ
ejpam-846	592	2	programming	programming	NOUN
ejpam-846	592	3	:	:	PUNCT
ejpam-846	592	4	solution	solution	NOUN
ejpam-846	592	5	techniques	technique	NOUN
ejpam-846	592	6	and	and	CCONJ
ejpam-846	592	7	approximation	approximation	NOUN
ejpam-846	592	8	schemes	scheme	NOUN
ejpam-846	592	9	.	.	PUNCT
ejpam-846	593	1	in	in	ADP
ejpam-846	593	2	b.	b.	PROPN
ejpam-846	593	3	korte	korte	PROPN
ejpam-846	593	4	a.	a.	PROPN
ejpam-846	593	5	bachem	bachem	PROPN
ejpam-846	593	6	,	,	PUNCT
ejpam-846	593	7	m.	m.	PROPN
ejpam-846	593	8	groetschel	groetschel	PROPN
ejpam-846	593	9	,	,	PUNCT
ejpam-846	593	10	editor	editor	NOUN
ejpam-846	593	11	,	,	PUNCT
ejpam-846	593	12	mathematical	mathematical	ADJ
ejpam-846	593	13	programming	programming	NOUN
ejpam-846	593	14	:	:	PUNCT
ejpam-846	593	15	state	state	NOUN
ejpam-846	593	16	-	-	PUNCT
ejpam-846	593	17	of	of	ADP
ejpam-846	593	18	-	-	PUNCT
ejpam-846	593	19	the	the	DET
ejpam-846	593	20	-	-	PUNCT
ejpam-846	593	21	art	art	NOUN
ejpam-846	593	22	.	.	PUNCT
ejpam-846	594	1	springer	springer	NOUN
ejpam-846	594	2	-	-	PUNCT
ejpam-846	594	3	verlag	verlag	PROPN
ejpam-846	594	4	,	,	PUNCT
ejpam-846	594	5	berlin	berlin	PROPN
ejpam-846	594	6	,	,	PUNCT
ejpam-846	594	7	1982	1982	NUM
ejpam-846	594	8	.	.	PUNCT
ejpam-846	595	1	[	[	X
ejpam-846	595	2	21	21	NUM
ejpam-846	595	3	]	]	X
ejpam-846	595	4	w.t	w.t	PROPN
ejpam-846	595	5	.	.	PUNCT
ejpam-846	595	6	ziemba	ziemba	PROPN
ejpam-846	595	7	.	.	PUNCT
ejpam-846	596	1	the	the	DET
ejpam-846	596	2	stochastic	stochastic	ADJ
ejpam-846	596	3	programming	programming	NOUN
ejpam-846	596	4	approach	approach	NOUN
ejpam-846	596	5	to	to	ADP
ejpam-846	596	6	asset	asset	NOUN
ejpam-846	596	7	liability	liability	NOUN
ejpam-846	596	8	and	and	CCONJ
ejpam-846	596	9	wealth	wealth	NOUN
ejpam-846	596	10	management	management	NOUN
ejpam-846	596	11	.	.	PUNCT
ejpam-846	597	1	aimr	aimr	NOUN
ejpam-846	597	2	,	,	PUNCT
ejpam-846	597	3	2003	2003	NUM
ejpam-846	597	4	.	.	PUNCT