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

• 成果类型: Article
• 署名作者: Kramkov, D; Schachermayer, W
• 署名单位: Carnegie Mellon University; Technische Universitat Wien
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 1504-1516
• 关键词: fundamental theorem; PORTFOLIO POLICIES; consumption

摘要

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.