Mean-field reflected BSDEs driven by a marked point process

TL;DR

This paper investigates mean-field reflected backward stochastic differential equations driven by a marked point process, establishing existence and uniqueness results under various conditions using g-expectation and $ heta$-method techniques.

Contribution

It introduces new existence and uniqueness results for MFRBSDEs driven by marked point processes, including cases with exponential growth generators and unbounded terminal conditions.

Findings

Proved existence and uniqueness under Lipschitz conditions.

Extended results to exponential growth generators.

Addressed unbounded terminal conditions.

Abstract

In this paper, we study a class of mean-field reflected backward stochastic differential equations (MFRBSDEs) driven by a marked point process. Based on a g-expectation representation lemma, we give the existence and uniqueness of MFRBSDEs driven by a marked point process under Lipschitz generator conditions. Besides, the well-posedness of this kind of BSDEs with exponential growth generator and unbounded terminal is also provided by $\theta$-method.