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Risk sharing under the dominant peer‐to‐peer property and casualty insurance business models

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  • Michel Denuit
  • Christian Y. Robert

Abstract

This paper purposes to formalize the three business models dominating peer‐to‐peer (P2P) property and casualty insurance: the self‐governing model, the broker model, and the carrier model. The former one develops outside the insurance market whereas the latter ones may originate from the insurance industry, by partnering with an existing company or by issuing a new generation of participating insurance policies where part of the risk is shared within a community and higher losses, exceeding the community's risk‐bearing capacity are covered by an insurance or reinsurance company. The present paper proposes an actuarial modeling based on conditional mean risk sharing, to support the development of this new P2P insurance offer under each of the three business models. In addition, several specific questions are also addressed in the self‐governing model. Considering an economic agent who has to select the optimal pool for a risk to be shared with other participants, it is shown that uniform comparison of the Lorenz or concentration curves associated to the respective total losses of the pools under consideration allows the agent to decide which pool is preferable.

Suggested Citation

  • Michel Denuit & Christian Y. Robert, 2021. "Risk sharing under the dominant peer‐to‐peer property and casualty insurance business models," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 24(2), pages 181-205, June.
  • Handle: RePEc:bla:rmgtin:v:24:y:2021:i:2:p:181-205
    DOI: 10.1111/rmir.12180
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    References listed on IDEAS

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    1. 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.
    2. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    3. Denuit, Michel, 2010. "Positive dependence of signals," LIDAM Discussion Papers ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Denuit, Michel, 2020. "Investing in your own and peers’ risks: the simple analytics of P2P insurance," LIDAM Reprints ISBA 2020026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Denuit, Michel & Robert, Christian Y., 2021. "From risk sharing to pure premium for a large number of heterogeneous losses," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 116-126.
    7. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    8. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Reprints ISBA 2019046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. 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).
    10. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Reprints ISBA 2019038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Denuit, Michel & Robert, Christian Y., 2021. "From risk sharing to pure premium for a large number of heterogeneous losses," LIDAM Reprints ISBA 2021001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Furman, Edward & Kuznetsov, Alexey & Zitikis, Ričardas, 2018. "Weighted risk capital allocations in the presence of systematic risk," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 75-81.
    13. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.
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    Cited by:

    1. Denuit, Michel & Robert, Christian Y., 2023. "From risk reduction to risk elimination by conditional mean risk sharing of independent losses," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 46-59.
    2. Michel Denuit & Jan Dhaene & Christian Y. Robert, 2022. "Risk‐sharing rules and their properties, with applications to peer‐to‐peer insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 615-667, September.
    3. Denuit, Michel & Robert, Christian Y., 2023. "Endowment contingency funds for mutual aid and public financing," LIDAM Discussion Papers ISBA 2023009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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