Reflected generalized BSDEs with random time and applications

2010/11/14 by Auguste Aman, Aman, Auguste, Abouo Elouaflin +3
Mathematics · #60H20 #60H30 #60H99 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H20 #msc:60H30 #msc:60H99

paper · pdf · doi:10.48550/arxiv.1011.3223

20 pages

arxiv created 2010/11/14 · arxiv updated 2010/11/16

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. Next, as an application, we get an American pricing option in infinite horizon and we give a probabilistic formula for the viscosity solution of an obstacle problem for elliptic PDEs with a nonlinear Neumann boundary condition.

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