A discretization scheme for path-dependent FBSDEs and PDEs
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.
Cite
@article{arxiv.2308.07029,
title = {A discretization scheme for path-dependent FBSDEs and PDEs},
author = {Jiuk Jang and Hyungbin Park},
journal= {arXiv preprint arXiv:2308.07029},
year = {2025}
}