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November 2003 Necessary and sufficient conditions in the problem of optimal investment in incomplete markets
D. Kramkov, W. Schachermayer
Ann. Appl. Probab. 13(4): 1504-1516 (November 2003). DOI: 10.1214/aoap/1069786508

Abstract

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.

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D. Kramkov. W. Schachermayer. "Necessary and sufficient conditions in the problem of optimal investment in incomplete markets." Ann. Appl. Probab. 13 (4) 1504 - 1516, November 2003. https://doi.org/10.1214/aoap/1069786508

Information

Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1091.91036
MathSciNet: MR2023886
Digital Object Identifier: 10.1214/aoap/1069786508

Subjects:
Primary: 90A09 , 90A10
Secondary: 90C26

Keywords: duality theory , incomplete markets , Legendre transformation , utility maximization

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 4 • November 2003
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