IDEAS home Printed from https://ideas.repec.org/p/aiz/louvad/2020024.html
   My bibliography  Save this paper

Risk reduction by conditional mean risk sharing with application to collaborative insurance

Author

Listed:
  • Denuit, Michel
  • Robert, Christian Y.

Abstract

Consider an economic agent who has to select the optimal pool for a risk to be shared with other participants, adopting the conditional mean risk sharing rule. This paper shows that pointwise 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. The paper then concentrates on independent losses. The monotonicity of the respective contributions of the participants is established with respect to the convex order, showing that increasing the number of participants is always beneficial provided the conditional mean risk sharing rule is used to allocate independent losses among participants. These results are finally applied to collaborative insurance. It is shown that provided individual losses are mutually independent, there always exists a critical number of participants such that collaborative insurance outperforms commercial one.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2020024
    as

    Download full text from publisher

    File URL: https://dial.uclouvain.be/pr/boreal/fr/object/boreal%3A232136/datastream/PDF_01/view
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gian Paolo Clemente & Pierpaolo Marano, 2020. "The broker model for peer-to-peer insurance: an analysis of its value," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(3), pages 457-481, July.
    2. 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).
    3. 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.
    4. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    5. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    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).
    8. 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).
    9. 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).
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. John A. Major & Stephen J. Mildenhall, 2020. "Pricing and Capital Allocation for Multiline Insurance Firms With Finite Assets in an Imperfect Market," Papers 2008.12427, arXiv.org.
    2. 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.
    3. Zhanyi Jiao & Steven Kou & Yang Liu & Ruodu Wang, 2022. "An axiomatic theory for anonymized risk sharing," Papers 2208.07533, arXiv.org, revised May 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Denuit, Michel & Robert, Christian Y., 2021. "Stop-loss protection for a large P2P insurance pool," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 210-233.
    3. 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.
    4. 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.
    5. 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.
    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. Denuit, Michel & Robert, Christian Y., 2020. "Stop-loss protection for a large P2P insurance pool," LIDAM Discussion Papers ISBA 2020028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Matthias Nadler & Felix Bekemeier & Fabian Schar, 2022. "DeFi Risk Transfer: Towards A Fully Decentralized Insurance Protocol," Papers 2212.10308, arXiv.org.
    9. 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).
    10. Denuit, M. & Robert, C.Y., 2020. "From risk sharing to pure premium for a large number of heterogeneous losses," LIDAM Discussion Papers ISBA 2020015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.
    12. 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).
    13. Denuit, Michel & Ortega-Jimenez, Patricia & Robert, Christian Y., 2024. "Conditional expectations given the sum of independent random variables with regularly varying densities," LIDAM Discussion Papers ISBA 2024006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. 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).
    15. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    16. Denuit, M. & Robert, C.Y., 2020. "Ultimate behavior of conditional mean risk sharing for independent compound Panjer-Katz sums with gamma and Pareto severities," LIDAM Discussion Papers ISBA 2020014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Denuit, Michel & Robert, Christian Y., 2020. "Conditional tail expectation decomposition and conditional mean risk sharing for dependent and conditionally independent risks," LIDAM Discussion Papers ISBA 2020018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. 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).
    19. Abdikerimova, Samal & Feng, Runhuan, 2022. "Peer-to-peer multi-risk insurance and mutual aid," European Journal of Operational Research, Elsevier, vol. 299(2), pages 735-749.
    20. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of independent discrete losses in large pools," LIDAM Discussion Papers ISBA 2023010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    More about this item

    Keywords

    conditional expectation ; risk pooling ; Lorenz curve ; concentration curve ; convex order;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aiz:louvad:2020024. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nadja Peiffer (email available below). General contact details of provider: https://edirc.repec.org/data/isuclbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.