A numerical algorithm for a class of BSDEs via branching process

TL;DR

This paper introduces a novel numerical algorithm for a class of non-Markovian Backward SDEs using branching processes, eliminating the need for backward regression and ensuring convergence through viscosity solutions.

Contribution

It extends existing algorithms for semi-linear PDEs to non-Markovian BSDEs, providing a regression-free, convergent numerical method based on branching processes.

Findings

Algorithm successfully approximates solutions to non-Markovian BSDEs.

Convergence proven using viscosity solutions of path-dependent PDEs.

No backward regression required in the simulation process.

Abstract

We generalize the algorithm for semi-linear parabolic PDEs in Henry-Labord\`ere (2012) to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren, Keller, Touzi and Zhang (2012) and extended in Ekren, Touzi and Zhang (2013).