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Kernel-type estimator of the reinsurance premium for heavy-tailed loss distributions |
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| Institution: | 1. Dpto. de Métodos Estadísticos, Universidad de Zaragoza, María de Luna 3, 50018 Zaragoza, Spain;2. Dpto. de Estadística e Investigación Operativa, Universidad de Sevilla, Avda. Reina Mercedes s.n., 41012 Sevilla, Spain;1. University Carlos III of Madrid, C/Madrid, 126, 28903 Getafe, Madrid, Spain;2. University of Alcalá, Pl. de la Victoria, 2, 28802 Alcalá de Henares, Madrid, Spain;3. University Complutense of Madrid, Somosaguas, 28223 Pozuelo de Alarcón, Madrid, Spain;1. Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan;2. Department of Mathematics, University of Education, Okara Campus, Okara 56300, Pakistan |
| Abstract: | In this paper, we generalize the classical estimator of the reinsurance premium for heavy-tailed loss distributions with a kernel-type estimator. Since this estimator exhibits a bias, we propose its bias-reduced version by using a least-squares method. The asymptotic normality of the proposed estimators is established under suitable assumptions. A small simulation study is carried out to prove the performance of our approach. |
| Keywords: | Proportional hazard premium Reinsurance treaty Bias reduction Kernel estimator Hill estimator Extreme quantile Heavy tails |
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