Quadratic reflected BSDEs with unbounded obstacles
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.
Volume (Year): 122 (2012)
Issue (Month): 4 ()
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- Bayraktar, Erhan & Yao, Song, 2011.
"Optimal stopping for non-linear expectations--Part II,"
Stochastic Processes and their Applications,
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