Indefinite LQ Partially Observed Mean-Field Game and Control Problem
报告人： 聂天洋（山东大学）
时间：2026-09-11 15:30-16:30
地点：智华楼四元厅-225
Abstract:
We investigate an indefinite linear-quadratic partially observed mean field game with common noise, incorporating both state-average and control-average effects. It is noteworthy that the weighting matrices in the cost functional are allowed to be indefinite. By employing the backward separation approach, 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. 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. The talk is based on the joint work with Dr. Tian Chen, Prof. Guangchen Wang, Prof. Zhen Wu and Mr. Weiye Wu.
About the Speaker:
聂天洋，山东大学数学学院教授，博士生导师，副院长。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.等期刊。入选教育部长江学者特聘教授，主持国家重点研发计划课题、国家基金委优秀青年基金等，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。
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