A Class of Reduced Bias Estimators of Distortion Risk Measures under Dependence Serials with Heavy-Tailed Marginals

In this paper, we introduce a class of semi-parametric estimators of the distortion risk premiums for dependent insurance losses with heavy-tailed marginals. Our approach is based on the kernel estimation of the tail index and extreme quantiles under the first and second orders regularly varying assumptions for stationary insured risks with heavy-tailed distribution under dependence serials. Moreover, we illustrate the behaviour of our proposed estimator and give a comparison between this estimator and the classical one in terms of the absolute bias and the root median squared error.