Well-posedness and regularity of mean-field backward doubly stochastic Volterra integral equations and applications to dynamic risk measures

TL;DR

This paper develops the theoretical foundation for mean-field backward doubly stochastic Volterra integral equations, establishing well-posedness, regularity, and comparison theorems, with applications to dynamic risk measures.

Contribution

It introduces the well-posedness and regularity results for MF-BDSVIEs and applies these to analyze properties of dynamic risk measures.

Findings

Proved well-posedness of M-solutions for MF-BDSVIEs

Established comparison theorem for these equations

Derived regularity results using Malliavin calculus

Abstract

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.