主 讲 人：余翔，香港理工大学应用数学系副教授

报告时间：2025年4月17日上午10：00—11：00

报告地点：览秀楼105学术报告厅

报告摘要: This paper studies a Merton's optimal portfolio and consumption problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a relaxed tracking formulation such that the wealth process compensated by a fictitious capital injection outperforms the benchmark at all times. The fund manager aims to maximize the expected utility of consumption deducted by the cost of the capital injection, where the latter term can also be regarded as the expected largest shortfall of the wealth with reference to the benchmark. By considering an auxiliary state process, we formulate an equivalent stochastic control problem with state reflections at zero. For general utility functions and Ito benchmark process, we rigorously develop a convex duality theorem, new to the literature, to the stochastic control problem with state reflections in which our dual process also exhibits reflections from above at a constant barrier. For power utility and geometric Brownian motion benchmark process, we can further derive the optimal portfolio and consumption in feedback form using the new duality theorem, allowing us to discuss some interesting financial implications induced by the additional risk-taking from the capital injection and the goal of tracking.

主讲人简介： 余翔，香港理工大学应用数学系副教授。2007 年在华中科技大学获得数学学士学位，2012 年在德克萨斯大学奥斯汀分校获得数学博士学位。研究方向包括数学金融、应用概率与随机分析、随机控制与优化。他最近的研究重点是一些路径依赖的最优投资和消费问题、两层平均场博弈、时间不一致的最优停止问题、新风险模型中的最优分红、具有学习方法的随机控制和最优停止等。相关成果发表在 《Mathematical Finance》, 《Finance and Stochastics》,  《Annals of Applied Probability》, 《Mathematics of Operations Research》, 《SIAM Journal on Control and Optimization》等期刊上。