报告题目：Mean Field Game of Optimal Tracking Portfolio
时 间：2026年06月10日（星期三）08：30
地 点：理工南楼621
主 办：数学与统计学院
参加对象：相关专业师生
报告摘要：This talk discusses the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the n-player model, each agent aims to minimize the expected largest shortfall of the wealth with reference to the benchmark process, which is modeled by a linear combination of the population's average wealth process and a market index process. With a continuum of agents, we formulate the MFG problem with a reflected state process. We establish the existence of the mean field equilibrium (MFE) using the partial differential equation (PDE) approach. Firstly, by applying the dual transform, the best response control of the representative agent can be characterized in analytical form in terms of a dual reflected diffusion process. As a novel contribution, we verify the consistency condition of the MFE in separated domains with the help of the duality relationship and properties of the dual process. Moreover, based on the MFE, we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large.
报告人简介：薄立军，西安电子科技大学数学与统计学院教授，概率与数理统计专业博导、本科毕业于西安电子科技大学数学系、分别于2006年和2009年获南开大学概率论与数理统计专业理学硕士和理学博士学位。主持国家自然科学基金面上项目3项、陕西数理基础科学研究重点项目、中科院前沿科学重点研究计划项目；获2024年度陕西省自然科学奖二等奖、2023年度陕西高校科技奖特等奖；2025年度陕西省教学成果奖二等奖。 在概率统计、随机控制和金融数学等领域权威学术期刊《Ann. Appl. Prob.》《Automatica》《Math. Oper. Res.》《Production Oper. Manag.》(UTD 24)《Math. Finan.》《Science China: Math.》《SIAM J. Contr. Optim.》《SIAM J. Finan. Math.》等发表论文70余篇。出版教材《随机过程》《哈佛概率公开课》（译著）《最优化模型》（译著）和《高等概率论》（科学出版社“十四五”高等学校本科规划教材）。