Numerical simulation of BSDEs using empirical regression methods: theory and practice

TL;DR

This paper develops a regression-based numerical algorithm for solving backward stochastic differential equations (BSDEs), providing explicit error bounds and demonstrating effectiveness up to 10 dimensions.

Contribution

It introduces a new regression-based simulation algorithm for BSDEs with explicit error bounds, applicable to general filtrations and reflected BSDEs.

Findings

Algorithm achieves accurate solutions in dimension 10.

Provides explicit error bounds for the numerical method.

Demonstrates competitiveness in computational complexity.

Abstract

This article deals with the numerical resolution of backward stochastic differential equations. Firstly, we consider a rather general case where the filtration is generated by a Brownian motion and a Poisson random measure. We provide a simulation algorithm based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo simulations. We state fully explicit error bounds. Secondly, restricting to the case of a Brownian filtration, we consider reflected BSDEs and adapt the previous algorithm to that situation. The complexity of the algorithm is very competitive and allows us to treat numerical results in dimension 10.