Numerical Algorithms for 1-d Backward Stochastic Differential Equations: Convergence and Simulations

TL;DR

This paper investigates various numerical algorithms for 1-dimensional backward stochastic differential equations, proving their convergence and demonstrating their effectiveness through simulations.

Contribution

It introduces implicit and explicit schemes for BSDE and reflected BSDE, and establishes their convergence within a random walk framework.

Findings

Algorithms converge under specified conditions

Simulation results validate theoretical convergence

Different types of BSDEs are effectively solved

Abstract

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.