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  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 on 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. 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 .
R
z variable
z-variable
A
parabolic
R
on the z variable
in the z-variable