Quadratic mean-field reflected BSDEs

In this paper,we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown z.Using a linearization technique and the BMO martingale theory,we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle.Then,with the help of theθ-method,we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave(or convex)with respect to the second unknown.