Utility maximization in incomplete markets

• 成果类型: Article
• 署名作者: Hu, Y; Imkeller, P; Müller, M
• 署名单位: Universite de Rennes; Humboldt University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000188
• 发表日期: 2005
• 页码: 1691-1712
• 关键词: consumption; portfolio

摘要

We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under these constraints are identified as stochastic processes which usually are supermartingales, and even martingales for particular strategies. These strategies are seen to be optimal, and the corresponding value functions determined simply by the initial values of the supermartingates. We separately treat the cases of exponential, power and logarithmic utility.