Confidence intervals for the proportional hazard reinsurance premium for heavy-tailed claims
Résumé
Estimation of an adequate premium in presence of extreme events is of crucial importance for reinsurance companies. In this paper, we consider the statistical issue of constructing confidence intervals for the proportional hazard premium (PHP) under high-excess loss layer. A straightforward confidence interval is based on the asymptotic normal approximation of the PHP. However, its coverage accuracy can be unsatisfactory. In this paper, we propose two other methods, namely, the likelihood ratio method and the data tilting method. We establish their asympotic properties. Then, we assess their finite-sample performance via simulations. Finally, we apply the proposed methods on two real data sets (Danish fire losses and Algerian car insurance claims). Our investigations suggest that the data tilting method provides the best results.
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