  This paper aims to solve a super-hedging problem along with insurance
re-payment under running risk management constraints. The initial endowment for
the super-heding problem is characterized by a class of mean reflected backward
stochastic differential equation driven by a marked point process (MPP) and a
Brownian motion. By Lipschitz assumptions on the generators and proper
integrability on the terminal value, we give the well-posedness of this kind of
BSDEs by combining a representation theorem with the fixed point argument.
