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.
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. https://doi.org/10.1214/aoap/1069786508
Information