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

R  Ezzati; M  Khodabin and Z  Sadati

doi:10.17485/ijst/2014/v7i3.10

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

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2014/v7i3.10

Year: 2014, Volume: 7, Issue: 3, Pages: 271-275

Original Article

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

R. Ezzati^* , M. Khodabin and Z. Sadati

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

*Author for the correspondence:
R. Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
E-mail: [email protected]

Received Date:01 February 2014, Accepted Date:23 February 2014, Published Date:03 March 2014

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.

Keywords: Backward Stochastic Differential Equations, Block Pulse Function, Brownian Motion, Stochastic Operational Matrix