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Risk Classification by Means of Clustering


Bernhard Christian Kübler

Determining risk-adequate insurance premiums is a core issue in actuarial mathematics. This study is specifically concerned with identifying convenient partitions of (general) insurance collectives such that the resulting tariff classes are homogeneous to a maximum extent and – on the other hand – yet large enough to allow for the occurrence of the group balance concept and to end up with reliable estimates of the moments of the claim size distributions. Therefore, the author develops an innovative classification algorithm utilizing a multidimensional cluster approach combined with credibility-theoretical implications. Its construction stems from involving the entire claim information of risks simultaneously and in a suitable manner, and particulary from obtaining optimality regarding the cluster criterions. Under certain conditions, commonly used cross classification schemes are shown to be a particular case of the new approach. Besides desirable theoretical benefits like its generalizing established cross classification systems, an empirical investigation also suggests the practical superiority of the new algorithm.


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6 Empirical Investigation 142


Chapter 6 Empirical Investigation The aim of our research here is to evaluate the quality of MC (algorithm 5.3.1) empirically. Therefore, we compare its perfor- mance to a CC system using data gained from the analysis of military road accidents which occurred in 2007. To this end, we construct a collective which mirrors the set of those members of the Bundeswehr who operated a company car in the considered time period. 6.1 Organization of the Data 6.1.1 Description of the Data Sets Our raw data consist of two parts: (1) Information concerning road accidents associated with stan- dard passenger cars operated by the Bundeswehr in Jan- uary, February, June and July 2007 and (mainly) caused by military staff1. These data were provided by ZMK 1This restriction was made to picture the situation of a third party liability insurance. (Zentrale Militärkraftfahrtstelle), the approval authorities for military vehicles. In the data base of ZMK, informa- tion concerning road accidents are collected according to a special form, the notice of accident (Meldung über den Kraftfahrzeugunfall). (2) Further, the structure of the Bundeswehr according to mil- itary rank and age, more precisely, the absolute frequen- cies of all age-rank-tuples is available (valuation date: De- cember 2007). This was provided by BMVg (Bundesmin- isterium der Verteidigung). The data for July serve to evaluate the performance by means of a prognostive test to be described later of our model, so that we use solely the data from the three months January, February and June...

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