{ "115524-21834953": { "datetime_modified":"20231127T130432", "datetime_start":"20231206T160000", "datetime_end":"20231206T170000", "has_end_time":1, "date_start":"2023-12-06", "date_end":"2023-12-06", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems.", "occurrence_title":"", "combined_title":"Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems.: ZImu Zhu of UCSB", "event_subtitle":"ZImu Zhu of UCSB", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"The optimal stopping problem is one of the core problems in financial markets, with broad appli- cations 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 in- spired many applications. However, the method solves backward stochastic differential equations (BSDEs) in a forward manner, which can not be used for optimal stopping prob- lems 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 back- ward 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 suffi- ciently small subject to universal approximations. We give two numerical examples, which present consistent performance with the proved theory. 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