Multiple Pareto index regression with application to large claim costs
Résumé
In insurance and reinsurance, an important interest is modeling extreme claim costs. For this motivation, Pareto distributions have been successfully applied in extreme value analysis. Under a single-parameter Pareto distribution of a response variable, we propose a new approach to estimate the Pareto index. We assume that the Pareto index is an unspecified function that depends on multiple indices induced by covariates, which constitutes ’a single-parameter Pareto index regression in multiple-index model’. We obtain the parameter estimators by using an approximate maximum likelihood estimation (aMLE) method where the likelihood function for the Exponential distribution approximates the corresponding function of the Pareto distribution through the log-transformation of the response variable. The number of indices is determined by a cross-validation technique. We show our approach by a simulation argument and its application to claim cost data, and discuss its practical performance.
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