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Conditional Tail Expectation Decomposition and Conditional Mean Risk Sharing for Dependent and Conditionally Independent Losses

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  • Michel Denuit

    (Institute of Statistics, Biostatistics and Actuarial Science - ISBA Louvain Institute of Data Analysis and Modeling - LIDAM UCLouvain)

  • Christian Y. Robert

    (Laboratory in Finance and Insurance - LFA CREST - Center for Research in Economics and Statistics ENSAE)

Abstract

Conditional tail expectations are often used in risk measurement and capital allocation. Conditional mean risk sharing appears to be effective in collaborative insurance, to distribute total losses among participants. This paper develops analytical results for risk allocation among different, correlated units based on conditional tail expectations and conditional mean risk sharing. Results available in the literature for independent risks are extended to correlated ones, in a unified way. The approach is applied to mixture models with correlated latent factors that are often used in practice. Conditional Monte Carlo simulation procedures are proposed in that setting.

Suggested Citation

  • Michel Denuit & Christian Y. Robert, 2022. "Conditional Tail Expectation Decomposition and Conditional Mean Risk Sharing for Dependent and Conditionally Independent Losses," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1953-1985, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09888-0
    DOI: 10.1007/s11009-021-09888-0
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    References listed on IDEAS

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    10. Denuit, Michel M. & Mesfioui, Mhamed, 2017. "Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 1-5.
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    15. Denuit, Michel, 2021. "Reply to Jiandong Ren on Their Discussion on the Paper Titled “Size-Biased Risk Measures of Compound Sums”," LIDAM Reprints ISBA 2021054, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Denuit, Michel & Kiriliouk, Anna & Segers, Johan, 2015. "Max-factor individual risk models with application to credit portfolios," LIDAM Reprints ISBA 2015011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    18. 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.
    19. Gupta, Rameshwar D. & Richards, Donald St.P., 1987. "Multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 233-256, December.
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    Cited by:

    1. 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.
    2. Denuit, Michel & Ortega-Jimenez, Patricia & Robert, Christian Y., 2024. "No-sabotage under conditional mean risk sharing of dependent-by-mixture insurance losses," LIDAM Discussion Papers ISBA 2024019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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