勷勤数学•专家报告

题      目：Linear–quadratic mean-field game for stochastic systems with partial observation

报  告  人：李娜 教授  (邀请人：杨舟)

                                   山东财经大学

时      间：4月29日  11：30-12：30

地     点：数科院西楼二楼会议室

报告人简介:

          李娜，二级教授，博士生导师，国家级青年人才，山东省高校优秀青创团队带头人，山东财经大学首批特聘教授，统计与数学学院副院长；担任中国自动化学会TCCT随机系统控制分委会委员、中国数学会会员、山东省大数据研究会理事、《Math Review》评论员。主要研究方向为随机优化，金融数学，金融统计，随机分析。近年来，取得一系列高水平研究成果，发表在包括控制论领域国际三大顶级期刊《SIAM Journal on Control and Optimization》、《Automatica》、《IEEE Transactions on Automatic Control》等国际著名学术期刊；先后主持国家自然科学基金项目3项、山东省自然科学基金项目2项、山东省高等学校科技项目2项；曾获山东省教育系统优秀共产党员称号、山东省高等学校科学技术奖二等奖1项、山东省省级教学成果二等奖3项、山东省青年教师教学比赛三等奖1项、山东财经大学研究生教学成果奖一等奖1项、山东财经大学青年教师讲课比赛二等奖1项；主持教育部产学合作协同育人项目2项、山东省研究生教育优质课程1门。

摘      要：

      This paper is concerned with a class of linear–quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by the individual noise, and all agents are coupled together via the control average term. By studying the associated mean-field game and using the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward–backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. Thanks to the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related ε-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

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