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arXiv · 2308.07029

A discretization scheme for path-dependent FBSDEs and PDEs

Jiuk Jang·Hyungbin Park
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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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BibTeXRIS

Jiuk Jang, Hyungbin Park. 2023-08-14. A discretization scheme for path-dependent FBSDEs and PDEs. https://arxiv.org/abs/2308.07029

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