主讲人简介：李娟教授，女、山东大学数学学院教授、博士生导师，2012年获得首届国家优秀青年基金，2013年度获教育部新世纪优秀人才支持计划，2016年获得牛顿高级学者基金项目；2017年获教育部长江学者特聘教授。现任山东大学（威海）数学与统计学院副院长，多个国际SCI期刊的编委。主持多项国家与省部级项目，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。

内容摘要：In this talk we study Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's G-expectation. The dynamics of the controlled state process is given by a stochastic differential equation driven by a G-Brownian motion, whose coefficients depend not only on the control, the controlled state process but also on its law under the G-expectation. Also the associated cost functional is of mean-field type. Under the assumption of a convex control state space we study the stochastic maximum principle, which gives a necessary optimality condition for control processes. Under additional convexity assumptions on the Hamiltonian it is shown that this necessary condition is also a sufficient one. The main difficulty which we have to overcome in our work consists in the differentiation of the G-expectation of parameterized random variables. Based on a joint work with Rainer Buckdahn (UBO, France), Bowen He (SDU, China).

主持人：闫理坦

撰写：李学元