报告题目：Stochastic Maximum Principle for Extended Mean Field Control Problem with Constraints
时 间：2024年11月7日（星期四）15:00
地 点：理工南楼621
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：概率统计系及其他感兴趣的师生
报告摘要：This talk discusses the extended mean field control problems under general dynamic expectation constraints and/or dynamic pathwise state-control and law constraints. We aim to pioneer the establishment of the stochastic maximum principle (SMP) and the derivation of the backward SDE (BSDE) from the perspective of the constrained optimization using the method of Lagrangian multipliers. To this end, we first propose to embed the constrained extended mean-field control (C-MFC) problems into some abstract optimization problems with constraints on Banach spaces, for which we develop the generalized Fritz-John (FJ) optimality conditions. We then prove the stochastic maximum principle (SMP) for C-MFC problems by transforming the FJ type conditions into an equivalent stochastic first-order condition associated with a general type of constrained forward-backward SDEs (FBSDEs). Contrary to the existing literature, we treat the controlled Mckean-Vlasov SDE as an infinite- dimensional equality constraint such that the BSDE induced by the FJ first-order optimality condition can be interpreted as the generalized Lagrange multiplier to cope with the SDE constraint. Finally, we also present the SMP for stochastic control problems and mean field game problems under similar types of constraints as consequences of our main result for C-MFC problems.
报告人简介： 薄立军，西安电子科技大学教授。本科毕业于西安电子科技大学、硕士和博士毕业于南开大学概率论与数理统计专业，研究方向为随机分析、随机控制与金融数学。先后主持国家自然科学基金面上项目、中科院前沿科学重点研究计划-青年拔尖科学家项目、陕西国家应用数学中心交叉团队培育项目等。目前已在国际公认的概率统计、金融数学、管理和运筹学权威期刊Ann. Appl. Probab.、Stoch. Process. Appl. 、Math. Finan.、SIAM J. Contr. Optim.、SIAM J. Finan. Math.、Math. Opers. Res.、Prod. Oper. Manag. (POM)上发表学术论文70余篇，出版本科和研究生教材四部。