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

Mean reflected BSDE driven by a marked point process and application in insurance risk management