Estimation of the occurrence of extreme events is actually a great interest of risk measures in insurance and finance. Heavy-tailed distributions are used to modelate large claims and losses. In this paper we deal with the empirical estimation of the distortion risk premiums for heavy tailed losses by using extreme value statistics. This approach can produce a potential bias in the estimation. Thus we look at this framework here and propose a reduced-bias approach of the classical estimators already suggested in the literature. A finite sample behavior is investigated, both for simulated data and real insurance data, in order to illustrate the efficiency of our approach.

estimation, risk measures, heavy-tailed distribution, tail index, extreme quantiles, bias reduction.

Received: February 1, 2021; Accepted: April 8, 2021; Published: June 21, 2021

How to cite this article: El Hadji Deme, Mouhamad M. Allaya, Siradhi Deme, Hamza Dhaker and Ali Souleyman Dabye, Estimation of risk measures from heavy tailed distributions, Far East Journal of Theoretical Statistics 62(1) (2021), 35-80. DOI: 10.17654/TS062010035

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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