Stop-loss protection for a large P2P insurance pool

Abstract

This paper considers a peer-to-peer (P2P) insurance scheme where the higher layer is transferred to a (re-)insurer and retained losses are distributed among participants according to the conditional mean risk sharing rule proposed by Denuit and Dhaene (2012). The global retention level of the pool of participants grows proportionally with their number. We study the asymptotic behavior of the individual retention levels, as well as individual cash-backs and stop-loss premiums, as the number of participants increases. The probability that the total loss hits the upper layer protected by the stop-loss treaty is also considered. The results depend on the proportional rate of increase of the global retention level with the number of participants, as well as on the existence of the Esscher transform of the losses brought to the pool.