An improved estimator of the distortion risk measure for heavy-tailed claims

Year 2015, Volume: 44 Issue: 3, 735 - 746, 01.06.2015

Rassoul Abdelaziz

Abstract

The main aim of this paper is to propose an alternative estimate of
the distortion risk measure for heavy-tailed claims. Our approach is
based on the result of Balkema and de Haan (1974) [3], and Pickands
(1975) [22] for approximating the tail of the distribution by a generalized Pareto distribution. The asymptotic normality of the new estimator is established, and its performance illustrated by some results
of simulation who shows the advantages of the new estimator over the
estimator based on the classical extreme-value theory. 

Keywords

Premium principle, Distortion risk measure, POT method, Extremes values theory, Generalized Pareto distribution, Loss distribution

References

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