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

2023/10/11 by Bixuan Yang, Yang, Bixuan, Jinbiao Wu +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2310.07319

openalex publication_date 2023/10/11 · openalex created_date 2023/10/14 · openalex updated_date 2026/07/28

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.

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