Necessary and Sufficient Conditions in the Problem of Optimal Investment in Incomplete Markets

Following Ann. Appl. Probab. 9 (1999) 904-950 we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In the previous p...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	The Annals of Applied Probability. - Institute of Mathematical Statistics. - 13(2003), 4, Seite 1504-1516
1. Verfasser:	Kramkov, D. (VerfasserIn)
Weitere Verfasser:	Schachermayer, W.
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2003
Zugriff auf das übergeordnete Werk:	The Annals of Applied Probability
Schlagworte:	Primary 90A09 Secondary 90C26 Utility maximization Incomplete markets Legendre transformation Duality theory Mathematics Economics Philosophy


LEADER	01000caa a22002652 4500
001	JST008424195
003	DE-627
005	20240619172232.0
007	cr uuu---uuuuu
008	150323s2003 xx \|\|\|\|\|o 00\| \|\|eng c
035			\|a (DE-627)JST008424195
035			\|a (JST)1193185
040			\|a DE-627 \|b ger \|c DE-627 \|e rakwb
041			\|a eng
084			\|a 90A10 \|2 MSC
100	1		\|a Kramkov, D. \|e verfasserin \|4 aut
245	1	0	\|a Necessary and Sufficient Conditions in the Problem of Optimal Investment in Incomplete Markets
264		1	\|c 2003
336			\|a Text \|b txt \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a Following Ann. Appl. Probab. 9 (1999) 904-950 we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In the previous paper we proved that a minimal condition on the utility function alone, that is, a minimal market independent condition, is that the asymptotic elasticity of the utility function is strictly less than 1. In this paper we show that a necessary and sufficient condition on both, the utility function and the model, is that the value function of the dual problem is finite.
540			\|a Copyright 2003 The Institute of Mathematical Statistics
650		4	\|a Primary 90A09
650		4	\|a Secondary 90C26
650		4	\|a Utility maximization
650		4	\|a Incomplete markets
650		4	\|a Legendre transformation
650		4	\|a Duality theory
650		4	\|a Mathematics \|x Mathematical procedures \|x Mathematical optimization \|x Optimal solutions
650		4	\|a Economics \|x Microeconomics \|x Economic utility \|x Utility functions
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Financial markets \|x Market conditions \|x Incomplete markets
650		4	\|a Mathematics
650		4	\|a Economics \|x Economic research \|x Economic analysis \|x Economic value
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Philosophy \|x Logic \|x Metalogic \|x Logical truth \|x Sufficient conditions
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial investments
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Financial markets \|x Market conditions
655		4	\|a research-article
700	1		\|a Schachermayer, W. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t The Annals of Applied Probability \|d Institute of Mathematical Statistics \|g 13(2003), 4, Seite 1504-1516 \|w (DE-627)270937838 \|w (DE-600)1478737-4 \|x 10505164 \|7 nnns
773	1	8	\|g volume:13 \|g year:2003 \|g number:4 \|g pages:1504-1516
856	4	0	\|u https://www.jstor.org/stable/1193185 \|3 Volltext
912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_JST
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_374
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2932
912			\|a GBV_ILN_2947
912			\|a GBV_ILN_2949
912			\|a GBV_ILN_2950
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4346
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 13 \|j 2003 \|e 4 \|h 1504-1516