Convergence of a Deep BSDE solver with jumps

TL;DR

This paper analyzes the numerical error of a deep learning-based method for solving forward-backward stochastic differential equations with jumps, extending previous work to include jump processes and providing error estimates.

Contribution

It extends the deep BSDE solver analysis to include jumps and offers both a priori and a posteriori error estimates for these complex equations.

Findings

Error bounds for finite activity jumps

Error bounds for infinite activity jumps

Extension of deep BSDE solver analysis to jump processes

Abstract

We study the error arising in the numerical approximation of FBSDEs and related PIDEs by means of a deep learning-based method. Our results focus on decoupled FBSDEs with jumps and extend the seminal work of HAn and Long (2020) analyzing the numerical error of the deep BSDE solver proposed in E et al. (2017). We provide a priori and a posteriori error estimates for the finite and infinite activity case.