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A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations

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

Published online by Cambridge University Press:  24 May 2016

Weidong Zhao ,
Wei Zhang  and
Lili Ju
Weidong Zhao*
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China
Wei Zhang*
Affiliation:
College of Applied Sciences, Beijing University of Technology, Beijing, 100022, P. R. China
Lili Ju*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
*
*Corresponding author. Email addresses:wdzhao@sdu.edu.cn(W. Zhao), weizhang0313@bjut.edu.cn(W. Zhang), ju@math.sc.edu(L. Ju)
*Corresponding author. Email addresses:wdzhao@sdu.edu.cn(W. Zhao), weizhang0313@bjut.edu.cn(W. Zhang), ju@math.sc.edu(L. Ju)
*Corresponding author. Email addresses:wdzhao@sdu.edu.cn(W. Zhao), weizhang0313@bjut.edu.cn(W. Zhang), ju@math.sc.edu(L. Ju)
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Abstract

Upon a set of backward orthogonal polynomials, we propose a novel multi-step numerical scheme for solving the decoupled forward-backward stochastic differential equations (FBSDEs). Under Lipschtiz conditions on the coefficients of the FBSDEs, we first get a general error estimate result which implies zero-stability of the proposed scheme, and then we further prove that the convergence rate of the scheme can be of high order for Markovian FBSDEs. Some numerical experiments are presented to demonstrate the accuracy of the proposed multi-step scheme and to numerically verify the theoretical results.

Keywords

Decoupled forward-backward stochastic differential equationsbackward orthogonal polynomialsmulti-step numerical schemeerror estimatenumerical analysis

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 9 , Issue 2 , May 2016 , pp. 262 - 288
Copyright
Copyright © Global-Science Press 2016 

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