Fitting and Predicting Heavy Tailed Insurance Data

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Predicting the severity of insurance claims is not difficult when there is correspondence between the observed data and a chosen parametric model. However, for heavy tailed insurance data it is hard to find a parametric model that is sophisticated enough to both predict the tail behavior and fit the body of the data. In the litterature it seems to be a skew attention towards prediction when modeling heavy tailed data and analyzing the fit of the chosen model is given little or no attention. In the paper it is shown that doing so introduces a risk of choosing a distributional model that might predict well but has a poor fit in comparison to other models. By comparing the goodness-of-fit of eligible models it is easier to convince managers and auditors of the superior characteristics of a specific model. In the paper, the prediction and goodness-of-fit of both parametric and semi-parametric density estimators are compared on simulated data as well as on real heavy tailed data from a large general insurer. Also an additional density estimator is introduced which is specially developed for goodness-of-fit and it is argued that this is a favorable choice when modeling heavy tailed data.