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Optimal reinsurance with multiple reinsurers: Distortion risk measures, distortion premium principles, and heterogeneous beliefs

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  • Boonen, Tim J.
  • Ghossoub, Mario

Abstract

This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets, and heterogeneous beliefs. An insurer minimizes a distortion risk measure, while seeking reinsurance with finitely many reinsurers. The reinsurers use distortion premium principles, and they are allowed to have heterogeneous beliefs regarding the underlying probability distribution. We provide a characterization of optimal reinsurance indemnities, and we show that they are of a layer-insurance type. This is done both with and without a budget constraint, i.e., an upper bound constraint on the aggregate premium. Moreover, the optimal reinsurance indemnities enable us to identify a representative reinsurer in both situations. Finally, two examples with the Conditional Value-at-Risk illustrate our results.

Suggested Citation

  • Boonen, Tim J. & Ghossoub, Mario, 2021. "Optimal reinsurance with multiple reinsurers: Distortion risk measures, distortion premium principles, and heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 23-37.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pa:p:23-37
    DOI: 10.1016/j.insmatheco.2020.06.008
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    References listed on IDEAS

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    Cited by:

    1. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    2. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.

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    More about this item

    Keywords

    Optimal reinsurance design; Distortion risk measures; Distortion premium principle; Heterogeneous beliefs; Multiple reinsurers;
    All these keywords.

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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