Numerical Algorithms to Determine Tariff Classes

In rate making process the statistical information on claim experience are combined with observable variables describing the risks, in order to build a tariff. The observable variables considered in the tariff structure are called tariff variables and the premium for a new risk is estimated from the observed values of these variables. In this process, many statistical methods and mathematical algorithms are applied to select the variables and to build the tariff. Many tariff methods require the values of the tariff variables to be collected in classes. Even if it is not necessary, commercial reasons often suggest making use of a low number of tariff classes. For instance, if “age of the insured” is a motor vehicle insurance tariff variable, it may be better to classify the risks into age classes instead of considering the single ages. Obviously, a question arises: which values of the tariff variable should be grouped together and which not, and also how many classes should be formed. In this paper some methods that can be used to collect these values in classes are illustrated. We suppose to have selected a set of tariff variables. For each of these variables, according to notation in [9], we call basic classes the elements of the finest partition of its values (e.g. the age of the insured in whole years) and we call tariff classes the clusters grouping the basic classes for rate making purposes. The determination of tariff classes can be viewed as a clustering problem. Cluster analysis techniques (for an extensive review see [1], [10], [12]) have a wide range of applications but, as pointed out in [9], they are rarely applied in insurance field. However, suitable adaptations allow their application to collect the basic classes and form homogenous groups, according to one or more characteristic variables describing the claim experience. In the following, for the sake of simplicity and unless otherwise stated, we will consider only one characteristic variable. Turning back to the variable “age of the insured”, the claim experience can be described, for instance, by the claim frequency. Ages with “quite similar” claim frequency will be allocated in the same