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

Journal article

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.

Authors: Kramkov, D; Schachermayer, W

• Publication status: Published
• Journal: ANNALS OF APPLIED PROBABILITY
• Volume: 13
• Issue: 4
• Pages: 1504-1516
• Publication date: 2003-11-01
• DOI: 10.1214/aoap/1069786508
• ISSN: 1050-5164
• Language: English
• Keywords: duality theory; incomplete markets; utility maximization; Legendre transformation