  In this paper, the theory of mean-field backward doubly stochastic Volterra
integral equations (MF-BDSVIEs) is studied. First, we derive the well-posedness
of M-solutions to MFBDSVIEs, and prove the comparison theorem for such a type
of equations. Furthermore, the regularity result of the M-solution for
MF-BDSVIEs is established by virtue of Malliavin calculus. Finally, as an
application of the comparison theorem, we obtain the properties of dynamic risk
measures governed by MF-BDSVIEs.
