深圳大学数学科学学院

荔园学者Colloquium第一百二十二期

讲座题目: Optimal control problems with generalized mean-field dynamics and viscosity solution to Master Bellman equation

主讲人：李娟 教授（山东大学）

讲座时间：2025年4月28日上午10：30-11：30

讲座地点：深圳大学粤海校区汇星楼一号教室

内容摘要：We study an optimal control problem of generalized mean-field dynamics with open-loop controls, where the coefficients depend not only on the state processes and controls, but also on the joint law of them. The value function $V$ defined in a conventional way, but it does not satisfy the Dynamic Programming Principle (DPP for short). For this reason we introduce subtly a novel value function $\vartheta$, which is closely related to the original value function $V$, such that, a description of $\vartheta$, as a solution of a partial differential equation (PDE), also characterizes $V$. We establish the DPP for $\vartheta$. By using an intrinsic notion of viscosity solutions, initially introduced in Burzoni, Ignazio, Reppen and Soner (2020) and specifically tailored to our framework, we show that the value function $\vartheta$ is a viscosity solution to a Master Bellman equation on a subset of Wasserstein space of probability measures. The uniqueness of viscosity solution is proved for coefficients which depend on the time and the joint law of the control process and the controlled process.

Based on a joint work with Rainer Buckdahn (UBO, France) and Zhanxin Li (SDU, Weihai).

主讲人简介：李娟，山东大学特聘教授、博士生导师。2003年毕业于山东大学数学学院，获理学博士学位。 主要研究方向为随机分析、随机控制、倒向随机微分方程与金融数学。

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邀请人：数学科学学院（王寒霄）

　 数学科学学院

2025年4月24日