数学科学学院学术报告[2024] 110号

(高水平大学建设系列报告990号)

报告题目: Path-dependent controlled Mean-Field coupled forward-backward SDEs. The associated stochastic maximum principle

报告人： 邢传智  副研究员 （山东大学）

报告时间：2024年11月2日下午14:30-16:00

报告地点： 腾讯会议228279187

报告内容：In the present paper we discuss a new type of mean-field coupled forward-backward stochastic differential equations (MFFBSDEs). The novelty consists in the fact that the coefficients of both the forward as well as the backward SDEs depend not only on the controlled solution processes $(X_t,Y_t,Z_t)$ at the current time $t$, but also on the law of the paths of $(X,Y,u)$ of the solution process and the process by which it is controlled. The existence for such a MFFBSDE which is fully coupled through the law of the paths of $(X,Y)$ in the coefficients of both the forward and the backward equations is proved under rather general assumptions. The main part of the work is devoted to the study of Pontryagin's maximal principle for such a MFFBSDE. The dependence of the coefficients of the law of the paths of the solution processes and their control makes that a completely new and interesting criterion for the optimality of a stochastic control for the MFFBSDE is obtained. Furthermore, we show that this necessary optimality condition is, under the assumption of convexity of the Hamiltonian, also sufficient. The talk is based on joint work with Rainer Buckdahn (UBO, France), Juan Li (SDU, China), Junsong Li (SDU, China).

报告人简历：邢传智，山东大学数学与交叉科学研究中心副研究员，主要研究方向为倒向随机微分方程、随机控制、随机分析。在J. Differ. Equations、J. Math. Anal. Appl.、 Acta Math. Sci.等国际期刊发表多篇学术论文，主持了国家自然科学青年基金，中国博士后科学基金面上资助，山东省自然科学青年基金等项目。

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邀请人：王寒霄

                                            数学科学学院

                                       2024年月10月29日