Quadratic Reflected BSDEs with Unbounded Obstacles

Details Quadratic Reflected BSDEs with Unbounded Obstacles Quadratic Reflected BSDEs with Unbounded Obstacles

2010-05-19

arxiv.org/abs/1005.3565v4

Mathematics

Probability

Key Words: Quadratic reflected backward stochastic differential equations, convex/concave generator, $\th$-difference method,

Scientific paper

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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