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REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS

Part of: Stochastic analysis

Published online by Cambridge University Press:  04 December 2009

YONG REN  and
XILIANG FAN
YONG REN*
Affiliation:
School of Mathematics, University of Tasmania, GPO Box 252C-37, Hobart, Tasmania 7001, Australia (email: brightry@hotmail.com)
XILIANG FAN
Affiliation:
Department of Mathematics, Anhui Normal University, Wuhu 241000, China (email: lanjunzi@mail.ahnu.edu.cn)
*
✉For correspondence; e-mail: brightry@hotmail.com
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Abstract

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In this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.

Keywords

reflected backward stochastic differential equationpartial differential–integral inclusionLévy processTeugels martingalepenalization method

MSC classification

Secondary: 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 4 , April 2009 , pp. 486 - 500
Copyright
Copyright © Australian Mathematical Society 2009

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