数学学科2024系列学术报告之三十二

　　题目：Robust optimal stopping with regime switching

　　报告人：吕思宇

　　时间：2024年11月13日（周三），上午10：00-11：00

　　地点：理学院1-301会议室

　　报告摘要：This work is concerned with an optimal stopping problem in the presence of model uncertainty and regime switching. In this work, the max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical framework for such kind of problem. First, under certain smoothness requirement, a verification theorem consisting of a set of sufficient conditions for robust optimality is established. Then, based on the dynamic programming principle, the value function of the optimal stopping problem is characterized as the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation. Moreover, when the Markov chain has a large state space and exhibits a two-time-scale structure, a singular perturbation approach is utilized to reduce the complexity involved. Finally, an example of choosing the best time to sell a stock is provided. Numerical experiments are reported to illustrate the theoretical results and to gain insights into the implications of model uncertainty and regime switching.

　　This talk is based on a joint work with Prof Zhen Wu (Shandong University), Prof Jie Xiong (SUSTech), and Prof Xin Zhang (Southeast University).

　　报告人简介：

　　吕思宇，东南大学数学学院副教授、硕士生导师。2017年在山东大学数学学院获得博士学位。2015年至2016年在美国佐治亚大学数学系访问学习。多次到香港理工大学、香港城市大学、南方科技大学、复旦大学等从事合作研究。主要研究领域为随机系统的最优控制和微分对策理论及其在金融中的应用，取得了以动态规划方法为特色的创新性成果。在国际重要学术期刊Automatica、Applied Mathematics & Optimization、Annals of Operations Research、Systems & Control Letters等发表多篇论文。主持国家自然科学基金面上项目等多项国家级和省部级科研项目，入选江苏省科协青年科技人才托举工程、东南大学“至善青年学者”支持计划等。