Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition |
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Authors: | Yong Ren Mohamed El Otmani |
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Institution: | a School of Mathematics, University of Tasmania, GPO Box 252C-37, Hobart, Tasmania 7001, Australia b Université Abdelmalek Essaadi, Faculté Polydisciplinaire de Larache, Route de Rabat, Km 2 - Larache, BP. 745 - Larache 92004, Morocco |
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Abstract: | 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 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. |
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Keywords: | 60H10 60H20 |
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