讲座题目：Finite-Horizon Optimal Consumption and Investment Problem with Endogenously Updating Consumption Bounds
主讲人：杨舟 教授
主持人：张楠 副教授
开始时间：2025-11-14 10:00
讲座地址：普陀校区理科大楼A1514
主办单位：统计学院
报告人简介：
杨舟，华南师范大学数学科学学院，教授，博士导师。主要从事金融数学和随机控制方面的研究，主要研究方向为：美式衍生产品定价、最优投资组合、最优停时问题、金融中的自由边界问题。部分研究成果发表于FINANC STOCH、MATH OPER RES、SIAM J CONTROL OPTIM、SIAM J FINANC MATH、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊。曾主持六项国家基金和多项省部级基金。
报告内容：
This paper addresses the finite-horizon utility maximization problem faced by an agent who dynamically updates their consumption bounds, determined by a minimum consumption level process. The agent derives utility from both the consumption process and the minimum consumption level, incurring a proportional utility cost with each adjustment. Using the dual-martingale approach, we formulate the dual problem as a finite-horizon two-sided singular control problem. By exploring the relationship between singular control and switching control, we transform the dual problem into a set of optimal switching problems, which we then simplify to a single parabolic double obstacle problem. Employing advanced and non-trivial PDE techniques, we thoroughly delineate the analytical properties of the double obstacle problem and its two free boundaries. From this analysis, we construct the optimal singular control for the dual problem using a carefully selected set of switching controls. We conclude by establishing a duality theorem and deriving the optimal strategies in feedback form.
