Generalized Reflected BSDE and an Obstacle Problem for PDEs with a Nonlinear Neumann Boundary Condition |
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| Authors: | Yong Ren Ningmao Xia |
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| Institution: | 1. Department of Mathematics , East China University of Science and Technology , Shanghai , China;2. Department of Mathematics , Anhui Normal University , Wuhu , Anhui Province , China brightry@hotmail.com;4. Department of Mathematics , East China University of Science and Technology , Shanghai , China |
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| Abstract: | Abstract In this article, we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equation involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary, in using the penalization method. We also give a characterization of the solution as the value function of an optimal stopping time problem. Then we give a probabilistic formula for the viscosity solution of an obstacle problem for PDEs with a nonlinear Neumann boundary condition. |
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| Keywords: | Backward stochastic differential equation Penalization method Viscosity solution |
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