数学科学学院学术报告[2023] 068号

(高水平大学建设系列报告839号)

报告题目: Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth

报告人：温家强，助理教授，南方科技大学

报告时间：2023.10.19 16:00-17:00pm

讲座地点：汇星楼（科技楼）501

报告内容：In this paper, we study the general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for one-dimensional mean-field BSDEs when the generator grows in Z quadratically and the terminal value is bounded. Second, a comparison theorem for the general mean-field BSDEs is obtained with the Girsanov transform. Third, we prove the convergence of the particle systems to the mean-field BSDEs with quadratic growth, and in addition, the rate of convergence is given. Finally, in this framework, we use the mean-field BSDE to give a probabilistic representation for the viscosity solution of a nonlocal partial differential equation (PDE, for short), as an extended nonlinear Feynman-Kac formula, which yields the existence and uniqueness of the solution to the PDE.

报告人简历：温家强，南方科技大学数学系助理教授。2018年博士毕业于山东大学金融研究院，博士期间曾赴美国UCF联合培养，合作导师为雍炯敏教授；2018年6月至9月在香港理工大学数学系做研究助理；2018年9月至2020年9月在南方科技大学数学系做博士后，导师为熊捷讲席教授。获深圳市海外高层次人才“孔雀计划”C类，美国数学评论评论员。主持国家自然科学青年基金、广东省面上项目和国家博士后面上项目等。温家强的研究方向为倒向随机微分方程、随机最优控制理论和金融数学，论文发表于SIAM J. Control Optim.、ESAIM Control Optim. Calc. Var.、Appl. Math. Optim.、J. Differ. Equations、Stochastics等杂志。

欢迎师生参加！

邀请人：李婧超

数学科学学院

2023年10月17日