Optimal control of McKean-Vlasov systems
under partial observation
and hidden Markov switching
报告专家：Huyên Pham教授（巴黎综合理工学院）
报告时间：2026年4月16日（星期四）上午10:00-11:30
报告地点：数学学院西202
报告摘要：
We study a class of mean-field control problems under partial observation. The controlled dynamics are of McKean-Vlasov type and are subject to regime switching driven by a hidden Markov chain. The observation process depends on the control and on the joint distribution of the state and control, which prevents the direct application of standard filtering techniques. The main contribution of this paper is to show how this distribution dependence can be handled within a change-of-probability framework, leading to a well-posed separated control problem. We derive a Zakai equation with a specific structure for the unnormalized filter, and show that the corresponding value function satisfies a dynamic programming principle. This yields a Bellman equation posed on a convex subset of a Wasserstein space, characterizing the optimal control problem under partial observation.
专家简介：
Huyên Pham，巴黎综合理工学院教授。研究领域包括随机分析与控制、数量金融和机器学习，发表了超过 110 篇学术论文，并著有《连续时间随机控制与优化及其金融应用》一书。曾是巴舍利耶金融学会的副主席，目前担任控制论顶刊《SIAM J Control Optim》的主编及《Applied Math. Optim.》的联合主编，也是金融数学顶刊《Math. Finance》的编委等。于 2006 年被任命为法国大学研究院（IUF）成员，2007 年荣获法国科学院颁发的路易·巴舍利耶奖，并于 2016 年在第九届巴舍利耶金融学会世界大会、2018 年在第六届亚洲数量金融会议上担任大会特邀报告人。
邀请人：张旭
