报告题目：Indefinite linear–quadratic mean-field game and optimal control problem with partial information

报 告 人： 聂天洋教授 山东大学

报告时间：2026年9月4日10：00-11：00

报告地点： 腾讯会议：781-825-385

校内联系人：韩月才 [email protected]

报告摘要：

  We investigate an indefinite linear-quadratic partially observed mean field game with common noise, incorporating both state-average and control-average effects. In our model, each agent’s state is observed through both individual and public observations. It is noteworthy that the weighting matrices in both the cost functional are allowed to be indefinite. We derive the optimal decentralized strategies using the Hamiltonian approach and establish the well-posedness of the resulting Hamiltonian system by employing a relaxed compensator. The associated consistency condition and the feedback representation of decentralized strategies are also established, and we demonstrate that the set of decentralized strategies forms an ε-Nash equilibrium. We also investigate mean-field linear–quadratic optimal control problem in the indefinite case with partial information. By employing the backward separation approach, we derive the optimal control from a Hamiltonian system without requiring a monotonicity condition. The feedback representation of optimal control is provided by the indefinite Riccati equations. As an application, we solve a mean variance portfolio selection problem. The talk is based on the joint work with Dr. Tian Chen, Prof. Guangchen Wang, Prof. Zhen Wu and Mr. Weiye Wu.

报告人简介：

  聂天洋，山东大学娱乐城 教授，博士生导师，副院长，入选教育部高层次人才奖励计划。研究方向为倒向随机微分方程、随机控制和金融数学等，研究成果发表在Math. Finance, Finance Stoch., SIAM J. Control Optim., Math. Oper. Res.等高水平期刊。主持国家重点研发计划课题、国家基金委优秀青年基金和山东省杰出青年基金等项目，独立获得山东省自然科学奖和山东省青年科技奖等。担任中国工业与应用数学学会智能控制与博弈专业委员会（筹）主任，山东省随机系统控制理论与科学计算重点实验室（筹）主任。