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Reflected Generalized BSDEs with Random Time and Applications

Volume 14, Number 1 (2012), 83 - 105

Reflected Generalized BSDEs with Random Time and Applications

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Abstract

In this paper, 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 case, 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.