%0 Journal Article 
%A Castaño Martínez, Antonia
%A Pigueiras Voces, Gema
%A Sordo Díaz, Miguel Ángel
%T On a family of risk measures based on largest claims
%D 2019
%@ 0167-6687
%U http://hdl.handle.net/10498/33388
%X 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.
%K risk measure
%K premium principle
%K order statistics
%K stop-loss order
%K excess-wealth order
%K reinsurance
%~ Universidad de Cádiz