A Convergent Linear Regression Method for Forward-Backward Stochastic Differential Equations with Jumps

TL;DR

This paper presents a convergent linear regression-based numerical method for solving forward-backward stochastic differential equations with jumps, demonstrating good practical applicability through numerical experiments.

Contribution

The paper introduces a new class of convergent numerical methods using basis function regression for FBSDEJs, which was not previously available.

Findings

Method shows strong convergence properties

Numerical experiments confirm practical effectiveness

Applicable to a broad class of FBSDEJs

Abstract

In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ hereafter). Numerical experiment shows good applicability of the proposed method.