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

Published online by Cambridge University Press:  20 July 2016

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:[email protected] (Y. Fu), [email protected] (J. Yang), [email protected] (W. Zhao)
*Corresponding author. Email addresses:[email protected] (Y. Fu), [email protected] (J. Yang), [email protected] (W. Zhao)
*Corresponding author. Email addresses:[email protected] (Y. Fu), [email protected] (J. Yang), [email protected] (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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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