Zimu Zhu

Title: Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems

Abstract: The seminal paper Han, Jentzen, E (PNAS 2018) propose a new machine learning method to numerically compute high dimensional parabolic PDE. However, their numerical scheme is not adapted to optimal stopping problem, which is quite common in financial markets. In a recent paper by Haojie Wang et al, they propose a new numerical scheme, which we call backward deep BSDE method, which can compute optimal stopping problem. In this talk, we offer a theoretical foundation for the backward deep BSDE method. We show that (1) a posteriori error estimation of the solution is given, namely, the error of the numerical solution could be bounded by the loss function. (2) An upper bound of the loss function is given, which could be sufficiently small subject to universal approximation. Several numerical examples will also be given. The talk is based on a joint work with Ruimeng Hu.