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Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps

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

Published online by Cambridge University Press:  20 July 2016

Yu Fu ,
Jie Yang  and
Weidong Zhao
Yu Fu*
Affiliation:
School of Mathematics & Institute of Finance, Shandong University, Jinan, Shandong 250100, China
Jie Yang*
Affiliation:
School of Mathematics & Institute of Finance, Shandong University, Jinan, Shandong 250100, China
Weidong Zhao*
Affiliation:
School of Mathematics & Institute of Finance, Shandong University, Jinan, Shandong 250100, China
*
*Corresponding author. Email addresses:nielf0614@126.com (Y. Fu), yangjie218@mail.sdu.edu.cn (J. Yang), wdzhao@sdu.edu.cn (W. Zhao)
*Corresponding author. Email addresses:nielf0614@126.com (Y. Fu), yangjie218@mail.sdu.edu.cn (J. Yang), wdzhao@sdu.edu.cn (W. Zhao)
*Corresponding author. Email addresses:nielf0614@126.com (Y. Fu), yangjie218@mail.sdu.edu.cn (J. Yang), wdzhao@sdu.edu.cn (W. Zhao)
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Abstract

By introducing a new Gaussian process and a new compensated Poisson random measure, we propose an explicit prediction-correction scheme for solving decoupled forward backward stochastic differential equations with jumps (FBSDEJs). For this scheme, we first theoretically obtain a general error estimate result, which implies that the scheme is stable. Then using this result, we rigorously prove that the accuracy of the explicit scheme can be of second order. Finally, we carry out some numerical experiments to verify our theoretical results.

Keywords

Prediction-correction schemedecoupled forward backward stochastic differential equation with jumpsconvergence analysis

MSC classification

Secondary: 60H35: Computational methods for stochastic equations 65C20: Models, numerical methods 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 3 , August 2016 , pp. 253 - 277
Copyright
Copyright © Global-Science Press 2016 

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