【数学与统计及交叉学科前沿论坛------高端学术讲座第132场】

报告题目：Robust Portfolio Selection under State-dependent Confidence Set

报告人: 关国卉 中国人民大学统计学院

报告时间: 11月22日星期五 14:30-15:30

报告地点: 阜成路校区综合楼501会议室

报告摘要: This talk studies the robust portfolio selection problem under a state-dependent confidence set. The investor invests in a financial market with a risk-free asset and a risky asset. The ambiguity-averse investor faces uncertainty over the drift of the risky asset and updates posterior beliefs by Bayesian learning. The investor holds the belief that the unknown drift falls within a confidence set at a certain confidence level. The confidence set varies with both the observed state and time. By maximizing the expected CARA utility of terminal wealth under the worst-case scenario of the unknown drift, we derive and solve the associated Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. The robust optimal investment strategy is obtained in a semi-analytical form based on a partial differential equation (PDE). We validate the existence and uniqueness of the PDE and demonstrate the optimality of the solution in the verification theorem. The robust optimal investment strategy consists of two components: myopic demand in the worst-case scenario and hedging demand. The robust optimal investment strategy is categorized into three regions: buying, selling, and small trading. Ambiguity aversion results in a more conservative robust optimal investment strategy. Additionally, with learning, the investor's uncertainty about the drift decreases over time, leading to increased risk exposure to the risky asset.

报告人简介：关国卉，中国人民大学统计学院副教授，应用统计科学研究中心研究员。主要研究领域包括最优再保险，最优资产配置和养老金管理等。在Mathematics of Operations Research， European Journal of Operational Research，Journal of Economic Dynamics and Control，Insurance: Mathematics and Economics、Scandinavian Actuarial Journal、、数理统计与管理等期刊发表多篇论文，主持两项国家自科项目，博士后基金面上一等资助等。