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Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition
journal contribution
posted on 2023-05-17, 00:53 authored by Ren, Yong, Otmani, MEIn 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 Lévy 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 © 2009.
History
Publication title
Journal of Computational and Applied MathematicsVolume
233Issue
8Pagination
2027-2043ISSN
0377-0427Department/School
School of Natural SciencesPublisher
Elsevier Science BVPlace of publication
Amsterdam, NetherlandsRepository Status
- Restricted