Optimal investments for robust utility functionals in complete market models

• 成果类型: Article
• 署名作者: Schied, A
• 署名单位: Technical University of Berlin
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1040.0138
• 发表日期: 2005
• 页码: 750-764
• 关键词: expected utility; minimax tests; probability

摘要

This paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model, where the robust utility functional is defined by a set Q of probability measures. Our main result shows that this problem can often be reduced to determining a least favorable measure Q(0) is an element of Q, which is universal in the sense that it does not depend on the particular utility function. The robust problem is thus equivalent to a standard utility-maximization problem with respect to the subjective probability measure Q(0). By using the Huber-Strassen theorem from robust statistics, it is shown that Q(0) always exists if Q is the sigma-core of a 2-alternating capacity. Besides other examples, we also discuss the problem of robust utility maximization with uncertain drift in a Black-Scholes market and the case of weak information.