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

Release time:2024-10-25

Impact Factor:1.3

DOI number:10.1016/j.jmaa.2024.128089

Journal:J. Math. Anal. Appl.

Key Words:Mean-field backward doubly;stochastic Volterra integral equation;Regularity of M-solutions;Malliavin calculus;Comparison theorem;Dynamic risk measure

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 MF-BDSVIEs, 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.

Co-author:Jinbiao Wu

First Author:Bixuan Yang

Indexed by:Journal paper

Correspondence Author:Tiexin Guo

Document Code:128089

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Volume:535

ISSN No.:0022-247X

Translation or Not:no

Date of Publication:2024-01-08

Included Journals:SCI

Links to published journals:https://www.sciencedirect.com/science/article/pii/S0022247X24000106