Quadratic Reflected BSDEs with Unbounded Obstacles

2010/05/19 by Bayraktar, Erhan, Yao, Song
#Analysis of PDEs (math.AP) #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1005.3565

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.

Related

• A class of quadratic reflected BSDEs with singular coefficients
• Well-posedness of quadratic RBSDEs and BSDEs with one-sided growth restrictions
• Quadratic Mean-Field Reflected BSDEs
• Reflected BSDEs and continuous solutions of parabolic obstacle problem for semilinear PDEs in divergence form
• Doubly Reflected BSDEs With Stochastic Quadratic Growth: Around The Predictable Obstacles