Quadratic Reflected BSDEs with Unbounded Obstacles

Erhan Bayraktar and Song Yao

Papers from arXiv.org

Abstract: 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.

Date: 2010-05, Revised 2011-03
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Citations: View citations in EconPapers (1)

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Journal Article: Quadratic reflected BSDEs with unbounded obstacles (2012)
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