Afrika Statistika

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

Brahim Brahimi, Fatima Meddi, and Abdelhakim Necir

Full-text: Open access


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

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

First available in Project Euclid: 1 February 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

Export citation