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, comparison, and stability results . Moreover, we study the link between the reflected forward backward SDEs and 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 convex or concave in the z-variable.
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, comparison, 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 convex or concave in the z-variable.
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. Moreover, we study the link between the reflected forward backward SDEs and
, and consider the optimal stopping for quadratic g-evaluations. As an application of our results we analyze