A class of quadratic reflected BSDEs with singular coefficients

In this paper, we study the existence and uniqueness of the solution to a reflected backward stochastic differential equation (RBSDE) with the generator g(t,y,z)=GfF(t,y,z)+f(y)|z|², where $ f(y) $ is a locally integrable function defined on an open interval D, and GfF(t,y,z) is induced by f and a Lipschitz continuous function F. Both the solution Yₜ and the obstacle Lₜ of this RBSDE take values in D. As applications, we provide a probabilistic interpretation of an obstacle problem for a quadratic PDE with a singular term, whose solution takes values in D, and study an optimal stopping problem for the payoff of American options under general utilities.