The Annals of Applied Probability

Necessary and sufficient conditions in the problem of optimal investment in incomplete markets

D. Kramkov and W. Schachermayer

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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.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 4 (2003), 1504-1516.

Dates
First available in Project Euclid: 25 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1069786508

Digital Object Identifier
doi:10.1214/aoap/1069786508

Mathematical Reviews number (MathSciNet)
MR2023886

Zentralblatt MATH identifier
1091.91036

Subjects
Primary: 90A09 90A10
Secondary: 90C26: Nonconvex programming, global optimization

Keywords
Utility maximization incomplete markets Legendre transformation duality theory

Citation

Kramkov, D.; Schachermayer, W. Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 13 (2003), no. 4, 1504--1516. doi:10.1214/aoap/1069786508. https://projecteuclid.org/euclid.aoap/1069786508


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