Exponential growth BSDE driven by a marked point process

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.

Keywords

Exponential growth BSDEs / Marked point processes / Mean-reflected BSDEs

Acknowledgements

The authors thank the anonymous referees and editors for their valuable advice and insightful comments, which greatly helped improve the previous version of this paper. This work was partially supported by NSFC (Grant No. 12371473) and by the Tianyuan Fund for Mathematics of NSFC (Grant No. 12326603).

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