Convergence of the Deep BSDE Method for Coupled FBSDEs
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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 provides a theoretical foundation for this algorithm in the general case of coupled FBSDEs. In particular, we provide a posteriori error estimation of the solution and prove the error can converge 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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