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

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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.

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Acknowledgements

The authors thank two anonymous Referees and the Editor for their constructive comments which helped to improve this paper.

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Authors and Affiliations

  1. Institute of Statistics, Biostatistics and Actuarial Science - ISBA Louvain Institute of Data Analysis and Modeling - LIDAM UCLouvain, Louvain-la-Neuve, Belgium

    Michel Denuit

  2. Laboratory in Finance and Insurance - LFA CREST - Center for Research in Economics and Statistics ENSAE, Paris, France

    Christian Y. Robert

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  1. Michel Denuit
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  2. Christian Y. Robert
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Correspondence to Michel Denuit.

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Denuit, M., Robert, C.Y. Conditional Tail Expectation Decomposition and Conditional Mean Risk Sharing for Dependent and Conditionally Independent Losses. Methodol Comput Appl Probab 24, 1953–1985 (2022). https://doi.org/10.1007/s11009-021-09888-0

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  • DOI: https://doi.org/10.1007/s11009-021-09888-0

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