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On a family of risk measures based on largest claims

Author

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  • Castaño-Martínez, A.
  • Pigueiras, G.
  • Sordo, M.A.

Abstract

Given a set of n≥2 independent and identically distributed claims, the expected average of the n−i largest claims, with 0≤i≤n−1, is shown to be a distortion risk measure with concave distortion function that can be represented in terms of mixtures of tail value-at-risks with beta mixing distributions. This result allows to interpret the tail value-at-risk in terms of the largest claims of a portfolio of independent claims. As an application, we provide sufficient conditions for stochastic comparisons of premiums in the context of large claims reinsurance.

Suggested Citation

  • Castaño-Martínez, A. & Pigueiras, G. & Sordo, M.A., 2019. "On a family of risk measures based on largest claims," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 92-97.
    • Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:92-97
    DOI: 10.1016/j.insmatheco.2019.02.003
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    Cited by:

    1. Barmalzan, Ghobad & Akrami, Abbas & Balakrishnan, Narayanaswamy, 2020. "Stochastic comparisons of the smallest and largest claim amounts with location-scale claim severities," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 341-352.

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    More about this item

    Keywords

    Risk measure; Premium principle; Order statistics; Stop-loss order; Excess-wealth order; Reinsurance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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