Classification Ratemaking Using Decision Trees

Introduction Manual rating of specific risks begin with a base rate, which is then modified by appropriate relativity factors depending on characteristics of each risk. Classical methods of deriving indicated relativities, are described by McClenahan (1996) and Finger (1996). A number of different modeling procedures are described in Brown's (1988) "minimum bias" paper and Venter's (1990) review of Brown's paper. These methods generally rely on the "multiplicative" or "additive" assumptions, which may not be reasonable for all types of risk. In this paper an alternative method of calculating indicated relativities is described, and demonstrated using a commercial Business Owners' Product (BOP) data set. relativities are compared with observed relativities, thereby demonstrating the extent of suitability of this method. It should be stressed that the intent here is entirely demonstration of a procedure. For actual practical implementation, modification would be required. First a few words about the ten-ninology and the data set. Relativities are based on grouping of risks with similar risk characteristics. This is essentially a classification problem. The purpose of any classification procedure is partitioning of objects-in our case risks-into demonstrably more homogeneous groups. For the BOP data we seek groups of risks with significantly differing claim frequencies, severities, pure premiums or loss ratios. Typically partitioning is based on a number of risk factors, which for BOP Distinctions must be made between these rating factors, which are used to group risks together and variables such as frequency, severity, pure premium or loss ratio, which 254 must be estimated partially based on these risk factors. The former are independent or predictor variables while the latter are dependent variables. Both of these variables may be assumed to be either categorical or vary continuously in a given interval. The statistics used as the basis of classification depends on whether the dependent and/or the independent variables are categorical or interval scale. For risk classification the independent variables are typically categorical. For example the BOP data includes losses for three different coverages, in 51 different risk states, and with 178 different ISO territory codes, 6 different ISO construction codes, etc. It is customary to say that the classification variable-risk state-has 51 different levels. Similarly, there axe six levels of ISO construction code, etc. The BOP data set under consideration includes 27,854 claims with accident years 1997 through 2000, and 9011 claims with accident year 2001. These are broken down by: Number of Levels Risk …