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Quadratic reflected BSDEs with unbounded obstacles

Authors
Journal
Stochastic Processes and their Applications
0304-4149
Publisher
Elsevier
Volume
122
Issue
4
Identifiers
DOI: 10.1016/j.spa.2011.12.013
Keywords
  • Quadratic Reflected Backward Stochastic Differential Equations
  • Concave Generator
  • Legendre–Fenchel Duality
  • Optimal Stopping Problems For Quadratic [Formula Omitted]-Evaluations
  • [Formula Omitted]-Difference Method
  • Stability
  • Obstacle Problems For Semi-Linear Parabolic Pdes
  • Viscosity Solutions
Disciplines
  • Mathematics

Abstract

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.

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