Quadratic reflected BSDEs with unbounded obstacles

Erhan Bayraktar and Song Yao

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1155-1203

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, 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.

Keywords: Quadratic reflected backward stochastic differential equations; Concave generator; Legendre–Fenchel duality; Optimal stopping problems for quadratic g-evaluations; θ-difference method; Stability; Obstacle problems for semi-linear parabolic PDEs; Viscosity solutions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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Working Paper: Quadratic Reflected BSDEs with Unbounded Obstacles (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:4:p:1155-1203

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DOI: 10.1016/j.spa.2011.12.013

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