Generalized Reflected BSDE and an Obstacle Problem for PDEs with a Nonlinear Neumann Boundary Condition
- 22 September 2006
- journal article
- research article
- Published by Taylor & Francis Ltd in Stochastic Analysis and Applications
- Vol. 24 (5), 1013-1033
- https://doi.org/10.1080/07362990600870454
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.Keywords
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