Risk aversion asymptotics for power utility maximization

• 成果类型: Article
• 署名作者: Nutz, Marcel
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0334-3
• 发表日期: 2012
• 页码: 703-749
• 关键词: Incomplete markets; OPTIMAL PORTFOLIO; CONVERGENCE; INVESTMENT; WEALTH

摘要

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex analysis and backward stochastic differential equations (BSDEs).