Classifying the Tails of Loss Distributions

Of the several classifications which actuaries have proposed for the heaviness of loss-distribution tails, none has been generally accepted. Here we will show that the ultimate settlement rate, or asymptotic failure rate, provides a natural tripartite division into light, medium, and heavy tails. We prove that all the positive moments of light-and medium-tailed distributions are finite. Within the heavy-tailed distributions, we will define very heavy-tailed and super heavy-tailed, and we will explain how the power and exponential transformations are the basis for these subdivisions. An appendix relates extreme value theory to our findings.

Keywords: loss distribution, ultimate settlement rate, power transform, exponential transform, extreme value theory