Quadratic Reflected BSDEs with Unbounded Obstacles
Stochastic Processes and their Applications, 122 (4), 1155-1203, 2012
60 Pages Posted: 15 Feb 2014 Last revised: 10 Jul 2016
Date Written: May 19, 2010
In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator f has quadratic growth in the z-variable. In particular, we obtain existence, uniqueness, and stability results, and consider the optimal stopping for quadratic g-evaluations. As an application of our results we analyze the obstacle problem for semi-linear parabolic PDEs in which the non-linearity appears as the square of the gradient. Finally, we prove a comparison theorem for these obstacle problems when the generator is concave in the z-variable.
Keywords: Quadratic reflected backward stochastic differential equations, concave generator, Legenre-Fenchel duality, optimal stopping problems for quadratic g-evaluations, theta-difference method, stability, obstacle problems for semi-linear parabolic PDEs, viscosity solutions.
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