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

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  • 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
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    References listed on IDEAS

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    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 & 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 & 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).
    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. 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).
    6. 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.
    7. 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).
    8. 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.
    9. Stéphane Loisel, 2005. "Differentiation of some functionals of multidimensional risk processes and determination of optimal reserve allocation," Post-Print hal-00397287, HAL.
    10. 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.
    11. 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.
    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)

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    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

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