Brahimi, Brahim; Meddi, Fatima; Necir, Abdelhakim Bias-corrected estimation in distortion risk premiums for heavy-tailed losses. (English) Zbl 1258.91095 Afr. Stat. 7, No. 1, 474-490 (2012). Summary: Recently A. Necir and D. Meraghni [Insur. Math. Econ. 45, No. 1, 49–58 (2009; Zbl 1231.91221)] 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 G. Matthys and J. Beirlant [Stat. Sin. 13, No. 3, 853–880 (2003; Zbl 1028.62038)]. Cited in 3 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 62G32 Statistics of extreme values; tail inference 62G30 Order statistics; empirical distribution functions 62G05 Nonparametric estimation Keywords:bias reduction; high quantiles; Hill estimator; Lévy-stable distribution; L-statistics; order statistics; second order regular variation; tail index; risk measure Citations:Zbl 1231.91221; Zbl 1028.62038 PDF BibTeX XML Cite \textit{B. Brahimi} et al., Afr. Stat. 7, 474--490 (2012; Zbl 1258.91095) Full Text: Euclid OpenURL