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Using a distortion risk premium principle, we consider estimation of the reinsurance premium when claim amounts are heavy-tailed. We propose two methods to estimate the reinsurance premium. The first one is a non-parametric estimator based directly on the empirical distribution, and the second one is a semi-parametric estimator. Under some regularity conditions, asymptotic normalities of the two estimators are established, and an algorithm for calculating confidence bounds is presented. Further, finite sample behaviors of the two estimators are compared by simulation studies.
Xiong et al. (Fri,) studied this question.