THE BELLMAN EQUATION FOR POWER UTILITY MAXIMIZATION WITH SEMIMARTINGALES

• 成果类型: Article
• 署名作者: Nutz, Marcel
• 署名单位: Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP776
• 发表日期: 2012
• 页码: 363-406
• 关键词: Incomplete markets; STOCHASTIC-PROCESSES; martingale measure; Optimal investment; portfolio; models

摘要

We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in terms of the opportunity process, which is characterized as the minimal solution of the Bellman equation. We also give verification theorems for this equation.