Quadratic mean-field reflected BSDEs

Abstract

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