EXPONENTIAL UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY FOR UNBOUNDED ENDOWMENTS

• 成果类型: Article
• 署名作者: Bartl, Daniel
• 署名单位: University of Konstanz
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1428
• 发表日期: 2019
• 页码: 577-612
• 关键词: optimal investment; DISCRETE-TIME; Risk measures; Duality; portfolio

摘要

We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martingale measures holds true, and that the problem satisfies the dynamic programming principle (in case of no options). Further, it is shown that the value of the utility maximization problem converges to the robust superhedging price as the risk aversion parameter gets large, and examples of nondominated probabilistic models are discussed.