江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Convergence of the backward deep BSDE method with applications to optimal stopping problems
报告人：朱子木 助理教授 香港科技大学（广州）
报告时间：2025年2月20日（周四）16:00-17:00
报告地点：数学学院A310
报告摘要：The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [Han, Jentzen and E, PNAS, 115(34):8505-8510, 2018] has shown great power in solving high-dimensional forward-backward stochastic differential equations (FBSDEs), and inspired many applications. However, the method solves backward stochastic differential equations (BSDEs) in a forward manner, which can not be used for optimal stopping problems that in general require running BSDE backwardly. To overcome this difficulty, a recent paper [Wang, Chen, Sudjianto, Liu and Shen, arXiv:1807.06622, 2018] proposed the backward deep BSDE method to solve the optimal stopping problem. In this paper, we provide the rigorous theory for the backward deep BSDE method. Specifically, 1. We derive the a posteriori error estimation, i.e., the error of the numerical solution can be bounded by the training loss function; and; 2. We give an upper bound of the loss function, which can be sufficiently small subject to universal approximations. We give two numerical examples, which present consistent performance with the proved theory. This is a joint work with C.Gao, S.Gao and R.Hu.
报告人简介：朱子木，香港科技大学（广州）金融科技学域助理教授。南加州大学应用数学博士。加州大学圣塔芭芭拉分校统计系博士后。研究方向为随机控制，数学金融，委托代理问题，机器学习。在Mathematics of Operation Research，SIAM Journal on Financial Mathematics, Annals of Finance等杂志上发表学术论文。