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

Rassoul Abdelaziz

EN

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

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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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Rassoul Abdelaziz This is me

Publication Date

June 1, 2015

Submission Date

February 11, 2014

Acceptance Date

-

Published in Issue

Year 2015 Volume: 44 Number: 3

IZ

https://izlik.org/JA79SC25ZM

Cite

RIS / Bibtex

APA

Abdelaziz, R. (2015). An improved estimator of the distortion risk measure for heavy-tailed claims. Hacettepe Journal of Mathematics and Statistics, 44(3), 735-746. https://izlik.org/JA79SC25ZM

AMA

1.Abdelaziz R. An improved estimator of the distortion risk measure for heavy-tailed claims. Hacettepe Journal of Mathematics and Statistics. 2015;44(3):735-746. https://izlik.org/JA79SC25ZM

Chicago

Abdelaziz, Rassoul. 2015. “An Improved Estimator of the Distortion Risk Measure for Heavy-Tailed Claims”. Hacettepe Journal of Mathematics and Statistics 44 (3): 735-46. https://izlik.org/JA79SC25ZM.

EndNote

Abdelaziz R (June 1, 2015) An improved estimator of the distortion risk measure for heavy-tailed claims. Hacettepe Journal of Mathematics and Statistics 44 3 735–746.

IEEE

[1]R. Abdelaziz, “An improved estimator of the distortion risk measure for heavy-tailed claims”, Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 3, pp. 735–746, June 2015, [Online]. Available: https://izlik.org/JA79SC25ZM

ISNAD

Abdelaziz, Rassoul. “An Improved Estimator of the Distortion Risk Measure for Heavy-Tailed Claims”. Hacettepe Journal of Mathematics and Statistics 44/3 (June 1, 2015): 735-746. https://izlik.org/JA79SC25ZM.

JAMA

1.Abdelaziz R. An improved estimator of the distortion risk measure for heavy-tailed claims. Hacettepe Journal of Mathematics and Statistics. 2015;44:735–746.

MLA

Abdelaziz, Rassoul. “An Improved Estimator of the Distortion Risk Measure for Heavy-Tailed Claims”. Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 3, June 2015, pp. 735-46, https://izlik.org/JA79SC25ZM.

Vancouver

1.Rassoul Abdelaziz. An improved estimator of the distortion risk measure for heavy-tailed claims. Hacettepe Journal of Mathematics and Statistics [Internet]. 2015 Jun. 1;44(3):735-46. Available from: https://izlik.org/JA79SC25ZM