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From risk sharing to risk transfer: the analytics of collaborative insurance

Author

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  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Robert, Christian Y.

Abstract

Denuit (2019, 2020b) demonstrated that conditional mean risk sharing introduced by Denuit and Dhaene (2012) is the appropriate theoretical tool to share losses in collaborative P2P insurance schemes. Denuit and Robert (2020a,b,c) studied this risk sharing mechanism and established several attractive properties including linear approximations when total losses or the number of participants get large. It is also shown there that the conditional expectation defining the conditional mean risk sharing is asymptotically increasing in the total loss (under mild technical assumptions). This ensures that the risk exchange is Pareto-optimal and that all participants have an interest to keep total losses as small as possible. In this paper, we design a exible system where entry prices can be made attractive compared to the premium of a regular, commercial insurance contract. Participants can also be grouped according to some meaningful criterion, resulting in a hierarchical decomposition of the community. The particular case where realized losses are allocated in proportion of the pure premiums is studied. This applies to losses obeying infinitely divisible distributions, such as compound Poisson or compound Negative Binomial ones as long as severities are identically distributed. Also, participants can just opt for such a proportional mean risk sharing, for simplicity.

Suggested Citation

  • Denuit, Michel & Robert, Christian Y., 2020. "From risk sharing to risk transfer: the analytics of collaborative insurance," LIDAM Discussion Papers ISBA 2020017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2020017
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    References listed on IDEAS

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    2. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
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    4. Denuit, Michel, 2019. "Size-Biased Transform And Conditional Mean Risk Sharing, With Application To P2p Insurance And Tontines," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 591-617, September.
    5. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    6. Denuit, Michel, 2010. "Positive dependence of signals," LIDAM Discussion Papers ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Discussion Papers ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    10. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
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    1. Runhuan Feng & Chongda Liu & Stephen Taylor, 2023. "Peer-to-peer risk sharing with an application to flood risk pooling," Annals of Operations Research, Springer, vol. 321(1), pages 813-842, February.

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    More about this item

    Keywords

    Peer-to-Peer (P2P) insurance ; conditional mean risk sharing ; size-biased transform ; comonotonicity;
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