A Class of Runge-Kutta Methods for Backward Stochastic Differential Equations

Abstract

In this paper, we introduce a class of Runge-Kutta (RK) methods for backward stochastic differential equations (BSDEs). The convergence rate is studied and the corresponding order conditions are obtained. For the conditional expectations involved in the methods, we design an approximation algorithm by combining the characteristics of the methods and replacing the increments of Brownian motion with appropriate discrete random variables. An important feature of our approximation algorithm is that interpolation operations can be avoided. The numerical results of four examples are presented to show that our RK methods provide a good approach for solving the BSDEs.