Convergence of the deep BSDE method for coupled FBSDEs-Reference-Cited by-同舟云学术

Convergence of the deep BSDE method for coupled FBSDEs

Published:2020-07-22 Issue:1 Volume:5 Page:
ISSN:2367-0126
Container-title:Probability, Uncertainty and Quantitative Risk
language:en
Short-container-title:Probab Uncertain Quant Risk

Author:

Han Jiequn,Long Jihao

Abstract

Abstract The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). This article lays a theoretical foundation for the deep BSDE method in the general case of coupled FBSDEs. In particular, a posteriori error estimation of the solution is provided and it is proved that the error converges to zero given the universal approximation capability of neural networks. Numerical results are presented to demonstrate the accuracy of the analyzed algorithm in solving high-dimensional coupled FBSDEs.

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Medicine

Link

http://link.springer.com/content/pdf/10.1186/s41546-020-00047-w.pdf

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