Numerical Solution of Backward Stochastic Differential Equations Driven by Brownian Motion through Block Pulse Functions

Abstract

In this paper, a computational technique is presented for solving a Backward Stochastic Differential Equations (BSDEs) driven by a standard Brownian motion. The proposed method is stated via a stochastic operational matrix based on the Block Pulse Functions (BPFs) in combination with the collocation method. With using this approach, the BSDEs are reduced to a stochastic nonlinear system of 2m equations and 2m unknowns. Then, the error analysis is proved by using some definitions, theorems and assumptions on the BSDEs. Efficiency of this method and good reasonable degree of accuracy is confirmed by some numerical examples.