An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations

Abstract

This paper proposes an explicit method for the coupled forward backward stochastic differential equations (FBSDEs). Our method combines skillfully a weak second order stochastic Runge-Kutta method for solving forward equations with a two-step method for solving backward equations. We give a convergence theorem for the proposed method when the FBSDEs is weakly coupled (the forward equations are independent of the variable Z). Finally, some numerical results are presented, and the numerical results show that our method still works well even if the forward equations depend on Z.