One-dimensional reflected BSDEs with quadratic growth generators

Shiqiu Zheng, Lidong Zhang, Xiangbo Meng

Published 2021-10-13, updated 2022-02-02Version 3

In this paper, we study the existence, uniqueness and comparison theorem for solutions of one-dimensional reflected backward stochastic differential equations (RBSDEs) with one continuous obstacle. The generators of such RBSDEs have a quadratic growth in $z$, with the quadratic term taking the form $f(y)|z|^2$, where the function $f$ is defined on an open interval $D$ and local integral. The corresponding results on BSDEs are also obtained. Our proofs mainly depend on a transformation based on $f$ and a domination method based on RBSDEs with two obstacles. As applications, we give a probabilistic interpretation of an obstacle problem for a quadratic PDE with local integral coefficient, and study an optimal stopping problem for the payoff of American options.