On mean-variance optimal reinsurance-investment strategies in dynamic contagion claims models

We consider the reinsurance-investment problem under the mean variance criterion in a dynamic contagion model that takes into account self and externally excited claim clustering effects. We find explicit time-consistent reinsurance-investment strategies for a generalized proportional contract in which only losses above a certain level are reinsured. This greater flexibility in the contract mitigates the possible drawback of the primary insurer ceding too much at the expense of profitability, while still ensuring that the higher risks are shared with the reinsurance counterparty.