A novel second order scheme with one step for forward backward stochastic differential equations

TL;DR

This paper introduces a new explicit second order one-step scheme for solving forward backward stochastic differential equations, demonstrating stability, second-order convergence, and validated by numerical experiments.

Contribution

The paper proposes a novel explicit second order one-step scheme for FBSDEs, including stability analysis and convergence proof, with Crank-Nicolson as a special case.

Findings

The scheme achieves second-order convergence.

Theoretical stability results are established.

Numerical experiments confirm the effectiveness.

Abstract

In this paper, we present a novel explicit second order scheme with one step for solving the forward backward stochastic differential equations, with the Crank-Nicolson method as a specific instance within our proposed framework. We first present a rigorous stability result, followed by precise error estimates that confirm the proposed novel scheme achieves second-order convergence. The theoretical results for the proposed methods are supported by numerical experiments.