On a family of risk measures based on largest claims

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 distribution...

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Bibliographic Details
Published inInsurance, mathematics & economics Vol. 86; pp. 92 - 97
Main Authors Castaño-Martínez, A., Pigueiras, G., Sordo, M.A.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.05.2019
Elsevier Sequoia S.A
Subjects
Distortion
Excess-wealth order
Expected utility
Mixtures
Order statistics
Premium principle
Premiums
Reinsurance
Risk assessment
Risk factors
Risk measure
Stochastic models
Stop-loss order
Risk measure
Reinsurance
Premium principle
Excess-wealth order
G220
Stop-loss order
Order statistics
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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2019.02.003