Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions

El Hadji Deme 1, 2 Stephane Girard 2 Armelle Guillou 3
1 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
3 IRMA - Institut de Recherche Mathématique Avancée
Abstract : Many different premium principles have been proposed in the literature. In this paper, we focus on the Proportional Hazard Premium. Its asymptotic normality has been established in the literature under suitable conditions which are not fulfilled in case of heavy tailed distributions. We thus focus on this framework and propose a reduced-bias approach for the classical estimators. A small simulation study is proposed to illustrate the efficiency of our approach.
Keywords : Bias correction Extreme values Heavy-tailed distribution Proportional Hazard Premium Kernel estimators
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El Hadji Deme, Stephane Girard, Armelle Guillou. Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions. Insurance: Mathematics and Economics, Elsevier, 2013, 52 (3), pp.550-559. ⟨10.1016/j.insmatheco.2013.03.010⟩. ⟨hal-00763978⟩

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