Open Access
Translator Disclaimer
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


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.


Download Citation

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.


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

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

Primary: 90A09 , 90A10
Secondary: 90C26

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

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 4 • November 2003
Back to Top