Exponential growth BSDE driven by a marked point process

TL;DR

This paper studies the existence and uniqueness of exponential growth backward stochastic differential equations driven by a marked point process, including mean-reflected variants, under unbounded terminal conditions using fixed-point and approximation methods.

Contribution

It introduces new solvability results for exponential growth BSDEs driven by MPPs, including mean-reflected cases, under unbounded terminal conditions.

Findings

Established well-posedness of exponential growth BSDEs driven by MPPs

Proved solvability of mean-reflected exponential growth BSDEs

Applied fixed-point and $ heta$-method techniques

Abstract

In this study, we investigate the well-posedness of exponential growth backward stochastic differential equations (BSDEs) driven by a marked point process (MPP) under unbounded terminal conditions. Our analysis utilizes a fixed-point argument, the $\theta$-method, and an approximation procedure. Additionally, we establish the solvability of mean-reflected exponential growth BSDEs driven by the MPP using the $\theta$-method.