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Deferred Correction Methods for Forward Backward Stochastic Differential Equations

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic analysis

Published online by Cambridge University Press:  09 May 2017

Tao Tang ,
Weidong Zhao  and
Tao Zhou
Tao Tang*
Affiliation:
Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China; and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Weidong Zhao*
Affiliation:
School of Mathematics & Finance Institute, Shandong University, Jinan 250100, China
Tao Zhou*
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email addresses:tangt@sustc.edu.cn (T. Tang), wdzhao@sdu.edu.cn (W. D. Zhao), tzhou@lsec.cc.ac.cn (T. Zhou)
*Corresponding author. Email addresses:tangt@sustc.edu.cn (T. Tang), wdzhao@sdu.edu.cn (W. D. Zhao), tzhou@lsec.cc.ac.cn (T. Zhou)
*Corresponding author. Email addresses:tangt@sustc.edu.cn (T. Tang), wdzhao@sdu.edu.cn (W. D. Zhao), tzhou@lsec.cc.ac.cn (T. Zhou)
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Abstract

The deferred correction (DC) method is a classical method for solving ordinary differential equations; one of its key features is to iteratively use lower order numerical methods so that high-order numerical scheme can be obtained. The main advantage of the DC approach is its simplicity and robustness. In this paper, the DC idea will be adopted to solve forward backward stochastic differential equations (FBSDEs) which have practical importance in many applications. Noted that it is difficult to design high-order and relatively “clean” numerical schemes for FBSDEs due to the involvement of randomness and the coupling of the FSDEs and BSDEs. This paper will describe how to use the simplest Euler method in each DC step–leading to simple computational complexity–to achieve high order rate of convergence.

Keywords

Deferred correction methodforward backward stochastic differential equationsEuler methodhigh-order scheme

MSC classification

Secondary: 60H35: Computational methods for stochastic equations 65C20: Models, numerical methods 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 2 , May 2017 , pp. 222 - 242
Copyright
Copyright © Global-Science Press 2017 

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