IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v112y2023icp23-32.html
   My bibliography  Save this article

Conditional mean risk sharing of losses at occurrence time in the compound Poisson surplus model

Author

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

Abstract

This paper proposes a new risk-sharing procedure, framed into the classical insurance surplus process. Compared to the standard setting where total losses are shared at the end of the period, losses are allocated among participants at their occurrence time in the proposed model. The conditional mean risk-sharing rule proposed by Denuit and Dhaene (2012) is applied to this end. The analysis adopts two different points of views: a collective one for the pool and an individual one for sharing losses and adjusting the amounts of contributions among participants. These two views are compatible under the compound Poisson risk process. Guarantees can also be added by partnering with an insurer.

Suggested Citation

  • Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of losses at occurrence time in the compound Poisson surplus model," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 23-32.
    • Handle: RePEc:eee:insuma:v:112:y:2023:i:c:p:23-32
    DOI: 10.1016/j.insmatheco.2023.05.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016766872300046X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2023.05.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Eric C. K. Cheung & Hayden Lau & Gordon E. Willmot & Jae-Kyung Woo, 2023. "Finite-time ruin probabilities using bivariate Laguerre series," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(2), pages 153-190, February.
    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 & Robert, Christian Y., 2021. "Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    4. Lefèvre, Claude & Trufin, Julien & Zuyderhoff, Pierre, 2017. "Some comparison results for finite-time ruin probabilities in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 143-149.
    5. Denuit, Michel & Robert, Christian Y., 2022. "Collaborative Insurance with Stop-Loss Protection and Team Partitioning," LIDAM Reprints ISBA 2022014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Claude Lefèvre & Stéphane Loisel, 2008. "On finite-time ruin probabilities for classical risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2008(1), pages 41-60.
    7. Michel Denuit & Christian Y. Robert, 2022. "Collaborative Insurance with Stop-Loss Protection and Team Partitioning," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(1), pages 143-160, January.
    8. Denuit, Michel & Robert, Christian Y., 2021. "Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction," LIDAM Reprints ISBA 2021029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Maeda Yuji & Suzawa Yoshihiko & Scordis Nicos A, 2011. "Shareholder Value: The Case of Japanese Captive Insurers," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 5(1), pages 1-24, March.
    10. Stéphane Loisel, 2005. "Differentiation of some functionals of multidimensional risk processes and determination of optimal reserve allocation," Post-Print hal-00397287, HAL.
    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. 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)

    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., 2022. "Dynamic conditional mean risk sharing in the compound Poisson surplus model," LIDAM Discussion Papers ISBA 2022034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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.
    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).
    4. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.
    5. 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).
    6. 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.
    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. 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).
    9. 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).
    10. 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.
    11. 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).
    12. 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).
    13. 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).
    14. 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.
    15. 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).
    16. Matthias Nadler & Felix Bekemeier & Fabian Schar, 2022. "DeFi Risk Transfer: Towards A Fully Decentralized Insurance Protocol," Papers 2212.10308, arXiv.org.
    17. Mohamed Amine Lkabous & Jean-François Renaud, 2018. "A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model," Risks, MDPI, vol. 6(3), pages 1-11, August.
    18. Chateauneuf, Alain & Mostoufi, Mina & Vyncke, David, 2015. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 73-78.
    19. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2021. "Mortality credits within large survivor funds," LIDAM Discussion Papers ISBA 2021038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.

    More about this item

    Keywords

    Risk pooling; Conditional mean risk sharing; Ruin probability; Mutual exclusivity;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:eee:insuma:v:112:y:2023:i:c:p:23-32. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.