Convergence of the deep BSDE method for coupled FBSDEs

Jiequn Han; Jihao Long

doi:10.1186/s41546-020-00047-w

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2020, Volume 5: 5. Doi: 10.1186/s41546-020-00047-w

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Convergence of the deep BSDE method for coupled FBSDEs

Jiequn Han¹ and
Jihao Long²

1. Department of Mathematics, Princeton University, Princeton 08544, NJ, USA
2. School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China

Received: September 25, 2019

Early access: July 2020

Published: September 2020

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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.

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