Abstract
This paper studies a peer-to-peer (P2P) insurance scheme where participants share the first layer of their respective losses while the higher layer is transferred to a (re-)insurer. The conditional mean risk sharing rule proposed by Denuit and Dhaene (Insur Math Econ 51:265–270, 2012) appears to be a very convenient way to distribute retained losses among participants, as shown by Denuit (ASTIN Bull 49:591–617, 2019). The amount of contributions paid by participants is determined by splitting it into the price of the stop-loss protection limiting the community’s total payout and an appropriate provision for the coverage of the lower layer which is mutualized inside the P2P community. As an application, the paper considers the case of a P2P insurance scheme when losses are modeled by independent compound Poisson sums with integer-valued severities (resulting from discretization). Some extensions are also discussed.
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Acknowledgements
The author is grateful to Professor Jan Dhaene for having provided him with his unpublished lecture notes co-authored with Daniel Linders, where a detailed treatment of the general case discussed in Sect. 4.1 can be found. The author also would like to express his deepest gratitude to two anonymous referees whose constructive comments have been extremely useful to improve a previous version of the present work.
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Denuit, M. Investing in your own and peers’ risks: the simple analytics of P2P insurance. Eur. Actuar. J. 10, 335–359 (2020). https://doi.org/10.1007/s13385-020-00238-x
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DOI: https://doi.org/10.1007/s13385-020-00238-x