Practical Risk Theory for Actuaries.

Modeling the Risk Process in the XploRe Computing Environment

“…The derivation of claim size distributions from the loss data could be considered to be a separate discipline in its own [7]. The objective is to find a distribution function F which fits the observed data in a satisfactory manner.…”

“…The first parameter controls the thickness of the tail: the smaller the α, the heavier the tail. Empirical experience has shown that the Pareto formula is often an appropriate model for the claim size distribution, particularly when exceptionally large claims may occur [4,7]. However, there is a need to find heavy tailed distributions which offer yet greater flexibility.…”

Pure Risk Premiums under Deductibles

“…The function is a very useful tool for testing the goodness of fit of an analytic distribution function to the observed claim size distribution function, see e.g. [3].…”

“…[3]. The objective is to find a distribution function F which fits the observed data in a satisfactory manner.…”

“…[3] and [6]). If we want to describe in detail the reasons for introducing deductibles we have to mention the following properties of a deductible:…”