Numerical schemes for fully coupled mean-field forward backward stochastic differential equations

Abstract

In this paper, based on the nonlinear Feynman-Kac formula and Itô-Taylor schemes for solving mean-field forward stochastic differential equations, we propose numerical schemes for solving fully coupled mean-field forward backward stochastic differential equations. Our numerical experiments show that the schemes are stable, effective, and can be of second-order accuracy when weak second-order schemes are used for solving mean-field forward stochastic differential equations.