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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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    1. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    2. 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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    5. Denuit, Michel & Mesfioui, Mhamed, 2017. "Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization," LIDAM Reprints ISBA 2017002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Edward Furman & Ričardas Zitikis, 2007. "“An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets”, Zinoviy Landsman and Michael Sherris, January 2007," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 174-176.
    7. Denuit, Michel & Kiriliouk, Anna & Segers, Johan, 2015. "Max-factor individual risk models with application to credit portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 162-172.
    8. 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).
    9. 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).
    10. Michel Denuit, 2021. "Reply to Edward Furman, Yisub Kye, and Jianxi Su on Their Discussion on the Paper Titled “Size-Biased Risk Measures of Compound Sums”," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(4), pages 637-638, November.
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    14. 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.
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    18. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
    19. 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).
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    22. Edward Furman & Ričardas Zitikis, 2009. "Weighted Pricing Functionals With Applications to Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 483-496.
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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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