The Annals of Applied Probability

The asymptotic elasticity of utility functions and optimal investment in incomplete markets

D. Kramkov and W. Schachermayer

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Abstract

The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less than 1.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 3 (1999), 904-950.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962818

Digital Object Identifier
doi:10.1214/aoap/1029962818

Mathematical Reviews number (MathSciNet)
MR1722287

Zentralblatt MATH identifier
0967.91017

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

Keywords
Utility maximization incomplete markets asymptotic elasticity of utility functions Legendre transformation duality theory

Citation

Kramkov, D.; Schachermayer, W. The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9 (1999), no. 3, 904--950. doi:10.1214/aoap/1029962818. https://projecteuclid.org/euclid.aoap/1029962818


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