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A discretization scheme for path-dependent FBSDEs and PDEs

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  • Jiuk Jang
  • Hyungbin Park

Abstract

This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key contribution of our approach is a novel estimator for the martingale integrand in the FBSDE, specifically designed to handle path-dependence more reliably than existing methods. We derive a concentration inequality that quantifies the statistical error of this estimator in a Monte Carlo framework. Based on these results, we investigate a supervised learning method with neural networks for solving path-dependent PDEs. The proposed algorithm is fully implementable and adaptable to a broad class of path-dependent problems.

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  • Jiuk Jang & Hyungbin Park, 2023. "A discretization scheme for path-dependent FBSDEs and PDEs," Papers 2308.07029, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2308.07029
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    1. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
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