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Bias-corrected estimation in distortion risk premiums for heavy-tailed losses. (English) Zbl 1258.91095

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)].

MSC:

91B30 Risk theory, insurance (MSC2010)
62G32 Statistics of extreme values; tail inference
62G30 Order statistics; empirical distribution functions
62G05 Nonparametric estimation
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