On a family of risk measures based on largest claims

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

Insurance: Mathematics and Economics, 2019, vol. 86, issue C, 92-97

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.

Keywords: Risk measure; Premium principle; Order statistics; Stop-loss order; Excess-wealth order; Reinsurance (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:86:y:2019:i:c:p:92-97

DOI: 10.1016/j.insmatheco.2019.02.003

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