The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 13, Number 4 (2003), 1504-1516.
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 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.
Ann. Appl. Probab., Volume 13, Number 4 (2003), 1504-1516.
First available in Project Euclid: 25 November 2003
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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