Regularity of Solutions of Mean-Field $G$-SDEs

Abstract

We study regularity properties of the unique solution of a mean-field $G$-SDE. More precisely, we consider a mean-field $G$-SDE with square-integrable random initial condition and establish its first and second order Fréchet differentiability in the random initial condition and specify the $G$-SDEs of the respective Fréchet derivatives.