An efficient third-order scheme for BSDEs based on nonequidistant difference scheme

TL;DR

This paper introduces a highly efficient third-order numerical scheme for solving backward stochastic differential equations, utilizing non-equidistant grids and Gauss-Hermite quadrature to reduce computational complexity and improve accuracy.

Contribution

The paper presents a novel third-order scheme for BSDEs that avoids spatial interpolation and employs non-equidistant points, significantly enhancing computational efficiency.

Findings

The scheme achieves third-order accuracy in numerical experiments.

It reduces computational complexity compared to existing methods.

Numerical examples demonstrate high efficiency and accuracy.

Abstract

In this paper we propose an efficient third-order numerical scheme for backward stochastic differential equations(BSDEs). We use 3-point Gauss-Hermite quadrature rule for approximation of the conditional expectation and avoid spatial interpolation by setting up a fully nested spatial grid and using the approximation of derivatives based on non-equidistant sample points. As a result, the overall computational complexity is reduced significantly. Several examples show that the proposed scheme is of third-order and very efficient.