Simulation of BSDEs by Wiener chaos expansion

TL;DR

This paper introduces a Wiener chaos expansion-based algorithm for solving backward stochastic differential equations (BSDEs), utilizing Picard's iterations and Malliavin calculus, with explicit error bounds and promising numerical results.

Contribution

The paper presents a novel algorithm combining Wiener chaos expansion with Picard's iterations for BSDEs, including explicit error bounds and efficient computation methods.

Findings

The algorithm achieves high speed and accuracy in numerical experiments.

Explicit error bounds are derived for chaos order and time discretization.

Numerical results demonstrate the method's effectiveness in solving BSDEs.

Abstract

We present an algorithm to solve BSDEs based on Wiener chaos expansion and Picard's iterations. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. We use the Malliavin derivative to compute $Z$. Concerning the error, we derive explicit bounds with respect to the number of chaos and the discretization time step. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.