Afrika Statistika

Bias-corrected estimation in distortion risk premiums for heavy-tailed losses

Brahim Brahimi, Fatima Meddi, and Abdelhakim Necir

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Abstract

Recently Necir and Meraghni (2009) proposed an asymptotically normal estimator for distortion risk premiums when losses follow heavy-tailed distributions. In this paper, we propose a bias-corrected estimator of this class of risk premiums and establish its asymptotic normality. Our considerations are based on the high quantile estimator given by Matthys and Beirlant 2003.

Article information

Source
Afr. Stat., Volume 7, Number 1 (2012), 474-490.

Dates
First available in Project Euclid: 1 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.as/1359744270

Mathematical Reviews number (MathSciNet)
MR3034391

Zentralblatt MATH identifier
1258.91095

Subjects
Primary: 91B30: Risk theory, insurance 62G32: Statistics of extreme values; tail inference
Secondary: 62G30: Order statistics; empirical distribution functions 62G05: Estimation

Keywords
Bias reduction High quantiles Hill estimator Lévy-stable distribution L-statistics Order statistics Second order regular variation Tail index Risk Measure

Citation

Brahimi, Brahim; Meddi, Fatima; Necir, Abdelhakim. Bias-corrected estimation in distortion risk premiums for heavy-tailed losses. Afr. Stat. 7 (2012), no. 1, 474--490. https://projecteuclid.org/euclid.as/1359744270


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