Stochastic grid bundling method for backward stochastic differential equations

TL;DR

This paper introduces the Stochastic Grid Bundling Method (SGBM) for numerically solving backward stochastic differential equations, combining bundling of Monte Carlo paths with local regression to improve accuracy and efficiency.

Contribution

The paper presents a novel application of SGBM to BSDEs, including an error analysis and numerical validation of the method's effectiveness.

Findings

Established an upper error bound for the local regression.

Conducted a full error analysis for the explicit algorithm.

Numerical experiments demonstrate the method's properties and accuracy.

Abstract

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations (BSDEs). The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving the backward stochastic differential equations will be introduced and an upper error bound is established for the local regression. A full error analysis is also conducted for the explicit version of our algorithm and numerical experiments are performed to demonstrate various properties of our algorithm.