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The fundamental theorem of mutual insurance

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  • Albrecht, Peter
  • Huggenberger, Markus

Abstract

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.

Suggested Citation

  • Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    • Handle: RePEc:eee:insuma:v:75:y:2017:i:c:p:180-188
    DOI: 10.1016/j.insmatheco.2017.06.002
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    Cited by:

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    4. Denuit, Michel & Robert, Christian Y., 2020. "Risk reduction by conditional mean risk sharing with application to collaborative insurance," LIDAM Discussion Papers ISBA 2020024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Matthias Nadler & Felix Bekemeier & Fabian Schar, 2022. "DeFi Risk Transfer: Towards A Fully Decentralized Insurance Protocol," Papers 2212.10308, arXiv.org.
    6. Schmeiser, Hato & Orozco-Garcia, Carolina, 2021. "The merits of pooling claims: Mutual vs. stock insurers," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 92-104.
    7. 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).
    8. Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    9. Roland Eisen, 2021. "Vulnerability and mutual insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 46(2), pages 224-235, April.

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    More about this item

    Keywords

    Pooling risks; Exchangeability; Reversed martingales; Choquet expected utility; Distortion risk measures;
    All these keywords.

    JEL classification:

    • D - Microeconomics
    • G - Financial Economics

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