SDE, BSDE under Nonlinear Expectation and Fully Nonlinear Path-dependent Parabolic PDE
In this talk we begin with stochastic differential equations (SDE, or FSDE) and backward stochastic differential equations (BSDE) driven by a d-dimensional G-Brownian motion defined on a nonlinear expectation space. The corresponding BSDE is then a path-solution of the corresponding (deterministic) path-dependent fully nonlinear partial differential equation of second order. This, combined with the powerful deep learning approach, provides an important tool for solving numerical solutions of a system of high dimensional partial differential equations of parabolic type.
Overview
Presenters
Shige Peng, Academician of the Chinese Academy of Sciences, Professor of Mathematics, and Chairman of the Research Center for Mathematics and Interdisciplinary Sciences at Shandong University
Breif Biography
Shige Peng, Academician of the Chinese Academy of Sciences, Professor of Mathematics, and chairman of the Research Center for Mathematics and Interdisciplinary Sciences at Shandong University. He has made pioneering and fundamental contributions in the fields of backward stochastic differential equations, nonlinear Feynman-Kac equations, and nonlinear expectations. In 2010, he was invited to give a plenary lecture at the 26th International Congress of Mathematicians. He was also awarded to be Princeton Global Scholar 2011-2013.