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

Author

Listed:
  • Denuit, Michel

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

  • Dhaene, Jan
  • Robert, Christian Y.

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

  • Denuit, Michel & Dhaene, Jan & Robert, Christian Y., 2022. "Risk-sharing rules and their properties, with applications to peer‐to‐peer insurance," LIDAM Reprints ISBA 2022026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2022026
    DOI: https://doi.org/10.1111/jori.12385
    Note: In: Journal of Risk and Insurance, 2022, vol. 89(3), p. 615-667
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    Cited by:

    1. Fallou Niakh & Arthur Charpentier & Caroline Hillairet & Philipp Ratz, 2025. "Disaster Risk Financing through Taxation: A Framework for Regional Participation in Collective Risk-Sharing," Papers 2506.18895, arXiv.org.
    2. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2025. "Efficient evaluation of risk allocations," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 119-136.
    3. Feng, Runhuan & Liu, Ming & Zhang, Ning, 2024. "A unified theory of decentralized insurance," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 157-178.
    4. 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.
    5. H'el`ene Cossette & Benjamin C^ot'e & Alexandre Dubeau & Etienne Marceau, 2024. "On a risk model with tree-structured Poisson Markov random field frequency, with application to rainfall events," Papers 2412.00607, arXiv.org, revised Jan 2026.
    6. Tim J. Boonen & Wing Fung Chong & Mario Ghossoub, 2024. "Pareto‐efficient risk sharing in centralized insurance markets with application to flood risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 91(2), pages 449-488, June.
    7. Matthias Nadler & Felix Bekemeier & Fabian Schar, 2022. "DeFi Risk Transfer: Towards A Fully Decentralized Insurance Protocol," Papers 2212.10308, arXiv.org.
    8. Hanbali, Hamza, 2025. "Mean-variance longevity risk-sharing for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 207-235.
    9. Bohan Li & Wenyuan Li & Kenneth Tsz Hin Ng & Sheung Chi Phillip Yam, 2025. "Mean Field Analysis of Mutual Insurance Market," Papers 2511.12292, arXiv.org.
    10. Denuit, Michel & Dhaene, Jan & Ghossoub, Mario & Robert, Christian Y., 2025. "Comonotonicity and Pareto optimality, with application to collaborative insurance," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 1-16.
    11. 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.
    12. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    13. 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).
    14. Jan Dhaene & Rodrigue Kazzi & Emiliano A. Valdez, 2024. "Axiomatic characterizations of some simple risk-sharing rules," Papers 2411.06240, arXiv.org, revised Nov 2024.
    15. Michel Denuit & Christian Y. Robert, 2024. "Conditional Mean Risk Sharing of Independent Discrete Losses in Large Pools," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-22, December.
    16. Denuit, Michel & Ortega-Jimenez, Patricia & Robert, Christian Y., 2024. "No-sabotage under conditional mean risk sharing of dependent-by-mixture insurance losses," LIDAM Discussion Papers ISBA 2024019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Dhaene, Jan & Milevsky, Moshe A., 2024. "Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 238-250.
    18. Michiko Ogaku, 2025. "Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium," Papers 2505.04122, arXiv.org, revised Aug 2025.
    19. Zhanyi Jiao & Steven Kou & Yang Liu & Ruodu Wang, 2022. "An axiomatic theory for anonymized risk sharing," Papers 2208.07533, arXiv.org, revised May 2023.
    20. 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.
    21. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.
    22. Jan Dhaene & Atibhav Chaudhry & Ka Chun Cheung & Austin Riis-Due, 2025. "Compensation-based risk-sharing," Papers 2510.19511, arXiv.org, revised Nov 2025.
    23. Darko Medved, 2025. "Dynamic pricing and solvency of peer-to-peer insurance: a framework for transparency, risk sharing, and financial sustainability," Risk Management, Palgrave Macmillan, vol. 27(3), pages 1-20, September.
    24. Feng Runhuan & Liang Zongxia & Song Yilun, 2025. "Decentralized Annuity: A Quest for the Holy Grail of Lifetime Financial Security," Papers 2502.13742, arXiv.org.
    25. Mario Ghossoub & Giulio Principi & Ruodu Wang, 2024. "Allocation Mechanisms in Decentralized Exchange Markets with Frictions," Papers 2404.10900, arXiv.org.

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