Stop-loss protection for a large P2P insurance pool

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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper examines a peer-to-peer insurance scheme where losses are distributed among participants based on their number, and investigates the asymptotic behavior of individual retention levels, cash-backs, and stop-loss premiums as the number of participants increases. The probability of total loss hitting the stop-loss level is also considered. The results are dependent on the rate of increase in global retention level with the number of participants and the existence of the Esscher transform of losses.