山东大学吴臻教授学术报告

报告题目：Mean Field Games and Control via Forward Backward Stochastic Differential Equations

报告地点：博学楼416会议室

报告时间：2025年7月15日下午16:00-17:30

报告人：吴臻  教授

主持人：贾文生  教授

摘要：Mean field theory provides a powerful framework for analyzing large-scale interacting particle systems, with broad applications in game and control theory. In suchsystem, competitive optimization by individual particles leads to N-particle games, while cooperative optimization yields social optima problems. Due to the high dimensionality and coupling among particles, direct analysis of such systems is often intractable. A common approach is to consider the limit behavior of a representative particle, leading to mean field game and mean field control problems. These limiting problems are typically characterized by infinite-dimensional partial differential equations such as the master equation and the Hamilton–Jacobi equation. Two main approaches are used to study their well-posedness: the probabilistic method and the analytical PDE approach. This talk focuses on the probabilistic method, utilizing the theory of forward backward stochastic differential equations (FBSDEs) to address linear-quadratic mean field games with non-monotone data and linear-quadratic mean field control problems with non-convex data. It can be shown that the corresponding master equation and the Hamilton–Jacobi equation admit unique classical solution. The propagation of chaos property for the related trajectories can also be proved.

报告人简介：吴臻，山东大学数学学院教授，教育部“长江学者”特聘教授，国家杰出青年科学基金获得者，泰山学者攀登计划专家。现任山东大学常务副校长兼数学学院院长，中国数学会副理事长，国家自然科学基金委员会数理学部第九届专家咨询委员会委员，数学天元基金第十届学术领导小组副组长，教育部大学数学教学指导委员会委员，山东数学会理事长，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，曾任国际控制理论权威期刊SIAM J. Control Optim.编委，现任国家基金委英文期刊Fundamental Research 数学物理领域编委，SCI 学术期刊ESAIM-Control Optim. Calc. Var.、Statist. Probab. Lett.、国际学术期刊Probab. Uncertain. Quant. Risk 和Part. Diff.Equa. Appl.编委。曾获中国数学会第十七届陈省身数学奖，首位获山东省自然科学奖一等奖，作为主要完成人5次获得国家教学成果奖，获首届国家优秀教材二等奖，2次获山东省教学成果特等奖。主持国家重点研发计划项目、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。