Tianyuan Mathematical Center
in Southwest China

Maximum principle for discrete-time stochastic optimal control problems and its applications

报告人：吴臻 山东大学数学学院

报告时间：7月22日15点—16点

报告地点：腾讯会议：871-4159-1553  无密码

摘要：We study one kind of discrete-time stochastic optimal control problems with convex control domains, for which necessary condition in the form of Pontryagin's maximum principle and sufficient condition of optimality are derived. The results can be extended to two kinds of discrete-time stochastic games, and necessary as well as sufficient conditions are obtained for the equilibrium point of the nonzero-sum game and the saddle point of the zero-sum one. We also extend these results to one kind of discrete-time mean-field type stochastic optimal control problems, in which a technique of adjoint operator is used to overcome the difficulties of obtaining adjoint equations and duality relation. Some examples are presented to illustrate the applications of the theoretical results, including a discrete-time investment/consumption choice problem and a discrete-time mean-variance portfolio selection problem. The purpose of this talk is to establish a rigorous version of discrete-time stochastic maximum principle in a clear way and pave a road for further related topics. The talk is based on the works of Z. Wu, F. Zhang, MCRF 2022 and B. Dong, T. Nie, Z. Wu, Automatica 2022.

报告人简介：

吴臻，山东大学数学学院教授，教育部重要人才计划，国家杰出青年基金获得者，泰山学者攀登计划专家。现任山东大学副校长兼数学学院院长、泰山学堂常务副院长。担任国家自然科学基金数学天元基金学术领导小组成员，山东数学会理事长，国际控制理论权威期刊SIAM Journal on Control and Optimization、国家基金委英文期刊Fundamental Research数学物理领域编委、SCI学术期刊Statistics & Probability Letters、国际学术期刊Probability, Uncertainty and Quantitative Risk、Partial Differential Equations and Applications编委。研究领域涉及控制论、概率论和金融数学等，取得了一系列具有突破性和原创性的科研成果，2019年荣获中国数学会第十七届陈省身数学奖，2018年首位获山东省自然科学奖一等奖，作为主要完成人3次获得国家教学成果奖，2次获山东省教学成果特等奖。主持国家基金委重点项目、山东省重大基础研究项目等。为国家“万人计划”首批科技创新领军人才入选者和科技部首批国家创新人才推进计划 “金融数学”重点领域创新团队负责人，入选国家百千万人才工程并获得“有突出贡献中青年专家”荣誉称号，享受国务院政府特殊津贴。