Commun. Comput. Phys., 15 (2014), pp. 618-646.


A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations

Weidong Zhao 1, Wei Zhang 1, Lili Ju 2*

1 School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China.
2 Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA; Beijing Computational Science Research Center, Beijing 100084, P.R. China.

Received 28 January 2013; Accepted (in revised version) 19 August 2013
Available online 1 November 2013
doi:10.4208/cicp.280113.190813a

Abstract

In this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed method under general situations. Then we present error estimates for each of the specific cases when some classical numerical schemes for solving the forward SDE are taken in the method; in particular, we prove that the proposed method is second-order accurate if used together with the order-2.0 weak Taylor scheme for the SDE. Some examples are also given to numerically demonstrate the accuracy of the proposed method and verify the theoretical results.

AMS subject classifications: 60H35, 60H10, 65C20, 65C30

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Key words: Decoupled forward-backward stochastic differential equations, numerical scheme, error estimates.

*Corresponding author.
Email: wdzhao@sdu.edu.cn (W. Zhao), weizhang0313@163.com (W. Zhang), ju@math.sc.edu (L. Ju)
 

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