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Risk‐sharing rules and their properties, with applications to peer‐to‐peer insurance

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  • Michel Denuit
  • Jan Dhaene
  • Christian Y. Robert

Abstract

This paper offers a systematic treatment of risk‐sharing rules for insurance losses, based on a list of relevant properties. A number of candidate risk‐sharing rules are considered, including the conditional mean risk‐sharing rule proposed in Denuit and Dhaene and the newly introduced quantile risk‐sharing rule. Their compliance with the proposed properties is established. Then, methods for building new risk‐sharing rules are discussed. The results derived in this paper are helpful in the development of peer‐to‐peer insurance (or crowdsurance), as well as to manage contingent risk funds where a given budget is distributed among claimants.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jrinsu:v:89:y:2022:i:3:p:615-667
    DOI: 10.1111/jori.12385
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    1. Göran Skogh & Hong Wu, 2005. "The Diversification Theorem Restated: Risk-pooling Without Assignment of Probabilities," Journal of Risk and Uncertainty, Springer, vol. 31(1), pages 35-51, July.
    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. Renaud Bourlès & Yann Bramoullé & Eduardo Perez-Richet, 2021. "Altruism and Risk Sharing in Networks," Journal of the European Economic Association, European Economic Association, vol. 19(3), pages 1488-1521.
    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. 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.
    6. Paul Embrechts & Haiyan Liu & Tiantian Mao & Ruodu Wang, 2017. "Quantile-Based Risk Sharing with Heterogeneous Beliefs," Swiss Finance Institute Research Paper Series 17-65, Swiss Finance Institute, revised Jan 2018.
    7. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    8. Denuit, Michel & Robert, Christian Y., 2021. "Polynomial series expansions and moment approximations for conditional mean risk sharing of insurance losses," LIDAM Discussion Papers ISBA 2021016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    10. Denuit, Michel & Robert, Christian Y., 2021. "Risk sharing under the dominant peer‐to‐peer property and casualty insurance business models," LIDAM Reprints ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Denuit, Michel & Robert, Christian Y., 2020. "Large-Loss Behavior of Conditional Mean Risk Sharing," LIDAM Reprints ISBA 2020021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Frauke von Bieberstein & Eberhard Feess & José F. Fernando & Florian Kerzenmacher & Jörg Schiller, 2019. "Moral Hazard, Risk Sharing, and the Optimal Pool Size," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(2), pages 297-313, June.
    13. 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.
    14. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    15. 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.
    16. Denuit, Michel & Robert, Christian Y., 2021. "Risk sharing under the dominant peer-to-peer property and casualty insurance business models," LIDAM Discussion Papers ISBA 2021001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, vol. 12(3), pages 423-439, July.
    18. 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.
    19. 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).
    20. repec:dau:papers:123456789/5394 is not listed on IDEAS
    21. 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).
    22. 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).
    23. Denuit, Michel & Robert, Christian Y., 2020. "Large-Loss Behavior Of Conditional Mean Risk Sharing," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 1093-1122, September.
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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. Matthias Nadler & Felix Bekemeier & Fabian Schar, 2022. "DeFi Risk Transfer: Towards A Fully Decentralized Insurance Protocol," Papers 2212.10308, arXiv.org.
    3. Jan L. M. Dhaene & Moshe A. Milevsky, 2024. "Egalitarian pooling and sharing of longevity risk', a.k.a. 'The many ways to skin a tontine cat," Papers 2402.00855, arXiv.org.
    4. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    5. Denuit, Michel & Dhaene, Jan & Ghossoub, Mario & Robert, Christian Y., 2023. "Comonotonicity and Pareto Optimality, with Application to Collaborative Insurance," LIDAM Discussion Papers ISBA 2023005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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).
    7. Zhanyi Jiao & Steven Kou & Yang Liu & Ruodu Wang, 2022. "An axiomatic theory for anonymized risk sharing," Papers 2208.07533, arXiv.org, revised May 2023.
    8. Mario Ghossoub & Michael B. Zhu & Wing Fung Chong, 2024. "Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures," Papers 2409.05103, arXiv.org.
    9. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.
    10. Mario Ghossoub & Giulio Principi & Ruodu Wang, 2024. "Allocation Mechanisms in Decentralized Exchange Markets with Frictions," Papers 2404.10900, arXiv.org.

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