On the Two-Times Differentiability of the Value Functions in the Problem of Optimal Investment in Incomplete Markets

We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the solutions to these problems with respect to their initial values....

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	The Annals of Applied Probability. - Institute of Mathematical Statistics. - 16(2006), 3, Seite 1352-1384
1. Verfasser:	Kramkov, Dmitry (VerfasserIn)
Weitere Verfasser:	Sîrbu, Mihai
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2006
Zugriff auf das übergeordnete Werk:	The Annals of Applied Probability
Schlagworte:	Utility maximization Incomplete markets Legendre transformation Duality theory Risk aversion Risk tolerance Mathematics Economics Business Philosophy


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100	1		\|a Kramkov, Dmitry \|e verfasserin \|4 aut
245	1	0	\|a On the Two-Times Differentiability of the Value Functions in the Problem of Optimal Investment in Incomplete Markets
264		1	\|c 2006
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520			\|a We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the solutions to these problems with respect to their initial values. We show that the key conditions for the results to hold true are that the relative risk aversion coefficient of the utility function is uniformly bounded away from zero and infinity, and that the prices of traded securities are sigma-bounded under the numéraire given by the optimal wealth process.
540			\|a Copyright 2006 The Institute of Mathematical Statistics
650		4	\|a Utility maximization
650		4	\|a Incomplete markets
650		4	\|a Legendre transformation
650		4	\|a Duality theory
650		4	\|a Risk aversion
650		4	\|a Risk tolerance
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Economics \|x Microeconomics \|x Economic utility \|x Utility functions
650		4	\|a Business \|x Business economics \|x Corporate finance \|x Financial modeling
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Probabilities
650		4	\|a Economics \|x Economic disciplines \|x Socioeconomics \|x Wealth
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial analysis \|x Risk management \|x Risk aversion
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Financial markets \|x Market conditions \|x Incomplete markets
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial instruments \|x Financial securities \|x Capital stocks \|x Stock prices
650		4	\|a Philosophy \|x Logic \|x Metalogic \|x Logical truth \|x Sufficient conditions
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Economics \|x Microeconomics \|x Economic utility \|x Utility functions
650		4	\|a Business \|x Business economics \|x Corporate finance \|x Financial modeling
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Probabilities
650		4	\|a Economics \|x Economic disciplines \|x Socioeconomics \|x Wealth
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial analysis \|x Risk management \|x Risk aversion
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Financial markets \|x Market conditions \|x Incomplete markets
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial instruments \|x Financial securities \|x Capital stocks \|x Stock prices
650		4	\|a Philosophy \|x Logic \|x Metalogic \|x Logical truth \|x Sufficient conditions
655		4	\|a research-article
700	1		\|a Sîrbu, Mihai \|e verfasserin \|4 aut
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773	1	8	\|g volume:16 \|g year:2006 \|g number:3 \|g pages:1352-1384
856	4	0	\|u https://www.jstor.org/stable/25442800 \|3 Volltext
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