  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.
