Anticipated mean-field backward stochastic differential equations with jumps

TL;DR

This paper establishes fundamental theoretical results for a class of anticipated mean-field backward stochastic differential equations with jumps, including existence, uniqueness, and comparison theorems.

Contribution

It introduces and proves key properties of anticipated mean-field BSDEs with jumps, advancing the mathematical understanding of these complex stochastic systems.

Findings

Proved existence and uniqueness of solutions.

Established a comparison theorem.

Extended the theory to include jumps.

Abstract

In this paper we prove the existence and uniqueness theorem, comparison theorem of a class of anticipated mean-field backward stochastic differential equations with jumps.