Generalized reflected BSDEs driven by a Levy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Ren, Yong¹  El Otmani, Mohamed² 

[1] Univ Tasmania, Sch Math, Hobart, Tas 7001, Australia

[2] Univ Abdelmalek Essaadi, Fac Polydisciplinaire Larache, Larache 92004, Morocco

关键词: Reflected BSDEs;    Generalized BSDEs;    Teugels martingale;    Levy process;    Viscosity solution;   

DOI  :  10.1016/j.cam.2009.09.037

来源: Elsevier

【 摘 要 】

In this paper, we derive the existence and Uniqueness Of the Solution for a class of generalized reflected backward stochastic differential equations (GRBSDEs in short) driven by a Levy process,which involve the integral with respect to a continuous process by means of the Snell envelope, the penalization method and the fixed point theorem. In addition, we obtain the comparison theorem for the solutions of the GRBSDEs. As an application, we give a probabilistic formula for the viscosity solution of an obstacle problem for a class of partial differential-integral equations (PDIEs in short) with a nonlinear Neumann boundary condition. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

【 授权许可】

Free