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Reflected generalized BSDEs with random time and applications. (English) Zbl 1279.60083

Summary: We aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a infinite horizon. In both cases, we establish an existence and uniqueness result. As application, we give a characterization of an American pricing option in infinite horizon; and we also give a probabilistic formula for the viscosity solution of an obstacle problem for elliptic PDEs with a nonlinear Neumann boundary condition.

MSC:

60H20 Stochastic integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H99 Stochastic analysis
91G80 Financial applications of other theories

References:

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