Mean-field doubly reflected backward stochastic differential equations

Abstract

<p style='text-indent:20px;'>We study mean-field doubly reflected BSDEs. First, using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-integrable with <inline-formula><tex-math id="M2">\begin{document}$ p = 1 $\end{document}</tex-math></inline-formula> or <inline-formula><tex-math id="M3">\begin{document}$ p>1 $\end{document}</tex-math></inline-formula>. The two cases are treated separately. Next by penalization we show also the existence of the solution. The two methods do not cover the same set of assumptions.</p>