Simulation of BSDEs with jumps by Wiener Chaos Expansion

TL;DR

This paper introduces an algorithm for solving backward stochastic differential equations with jumps using Wiener Chaos Expansion, providing explicit error bounds and demonstrating promising numerical results in speed and accuracy.

Contribution

It extends Wiener Chaos-based methods to BSDEs with jumps, offering a practical forward scheme with explicit error bounds and numerical validation.

Findings

The algorithm efficiently computes conditional expectations via chaos decomposition.

Explicit error bounds are derived with respect to chaos order, time step, and Monte Carlo simulations.

Numerical experiments show high speed and accuracy in solving BSDEs with jumps.

Abstract

We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.