A generalized scheme for BSDEs based on derivative approximation and its error estimates

TL;DR

This paper introduces a flexible numerical scheme for solving backward stochastic differential equations using derivative approximation via Lagrange interpolation, with analysis of stability and convergence based on sample point distribution.

Contribution

It proposes a generalized scheme for BSDEs that allows customization of stability and convergence properties through sample point distribution adjustments.

Findings

Scheme's convergence depends on sample point distribution

Different distributions yield schemes with varying stability and convergence

Provided conditions ensure the scheme's convergence

Abstract

In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stability and convergence order. We present a condition for the distribution of sample points to guarantee the convergence of the scheme.