Abstract: Robust portfolio selection has become a popular problem in recent years. In this paper, we study the optimal investment problem for an individual who carries a constant consumption rate but worries about the  model ambiguity of the financial market. Instead of using a conventional value function such as the utility of terminal wealth maximization, here, we focus on the purpose of risk control and seek to minimize the probability of lifetime ruin. This study is motivated by the work of Bayraktar and Zhang (2015), except that we use a standardized penalty for ambiguity aversion. The reason for taking a standardized penalty is to convert the penalty to units of the value function, which makes the difference meaningful in the definition of the value function. The advantage of taking a standardized penalty is that the closed-form solutions to both the robust investment policy and the value function can be obtained.  By employing the dynamic programming principle, we derive the Hamilton-Jacobi-Bellman (HJB) equation satisfied by the value function, thereby obtaining the closed-form solutions for both  the robust investment strategy and the value function. More interestingly, we use the ``Ambiguity Derived Ratio" to characterize the existence of model ambiguity which significantly affects the optimal investment policy. Finally, several numerical examples are given to illustrate our results.

Bio: 周明，研究员，博士生导师，北美准精算师（ASA），中国精算师协会正会员。曾在加拿大滑铁卢大学统计与精算系做博士后1年，美国德克萨斯大学达拉斯分校管理学院做访问学者1年，先后多次访问香港大学、香港理工大学等进行合作研究。目前主要研究方向为资产负债管理、风险分析与决策。在《Quantitative Finance》《Insurance: Mathematics and Economics》《Astin Bulletin》《Journal of Applied Probability》《中国科学》等国内外知名期刊发表学术论文30余篇，主持国家、省部级等各类项目10余项。