Selected problems associated with modeling the biggest compensations in non-life insurance

Abstract

Modelling the highest compensations are very important for insurance companies, as more and more policies now can generate high claims (for example third party liability insurance, property, especially connected to catastrophic events). In modelling extreme values of compensations paid by insurance company it is possible to use different models (exponential, gamma, Pareto distribution are most common) for typical values and different ones for the highest compensations (for example Generalised Pareto distribution). In this case however a problem of choice of the point, in which the change of the way of modelling is taking place appears. The paper is devoted to methods useful in choosing this point, that can be found in literature. Using simple example of the data, these methods can be analysed to find their advantages and disadvantages. All of the presented methods are mainly based on the analysis of graphs of selected parameters, which makes the results obtained are not strict guidelines, however, provide indicative results.