Quadratic mean-field reflected BSDEs

Abstract

<p style='text-indent:20px;'>In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown <inline-formula><tex-math id="M1">\begin{document}$ z $\end{document}</tex-math></inline-formula>. Using a linearization technique and the BMO martingale theory, we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of the <inline-formula><tex-math id="M2">\begin{document}$ \theta $\end{document}</tex-math></inline-formula> -method, we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave (or convex) with respect to the second unknown <inline-formula><tex-math id="M3">\begin{document}$ z $\end{document}</tex-math></inline-formula>.</p>