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Conditional mean risk sharing for dependent risks using graphical models

Author

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  • Denuit, Michel

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

  • Robert, Christian Y.

Abstract

Conditional mean risk sharing appears to be e_ective in collaborative insurance to distribute total losses among participants. This paper develops analytical results for this risk sharing rule when risks are zero-augmented random variables whose joint occurrences distributions and claim amount distributions are based on network structures and may be characterized by graphical models. More speci_cally we consider the Ising model for occurrences and decomposable graphical models for the claim amount structures. Such models are typically useful for modeling operational risk or cyber security risk.

Suggested Citation

  • Denuit, Michel & Robert, Christian Y., 2020. "Conditional mean risk sharing for dependent risks using graphical models," LIDAM Discussion Papers ISBA 2020029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2020029
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    References listed on IDEAS

    as
    1. 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.
    2. Roland R. Ramsahai, 2020. "Connecting actuarial judgment to probabilistic learning techniques with graph theory," Papers 2007.15475, arXiv.org.
    3. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    4. 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).
    5. Danae Politou & Paolo Giudici, 2009. "Modelling Operational Risk Losses with Graphical Models and Copula Functions," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 65-93, March.
    6. 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).
    7. 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).
    8. Lin, Peng & Neil, Martin & Fenton, Norman, 2014. "Risk aggregation in the presence of discrete causally connected random variables," Annals of Actuarial Science, Cambridge University Press, vol. 8(2), pages 298-319, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Graphical models ; Ising model ; decomposable graphs ; size-biased transform;
    All these keywords.

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