Abstract

Risk classification is an important actuarial process for insurance companies. It allows for the underwriting of the best risks, through an appropriate choice of classification variables, and helps set fair premiums in rate-making. Currently, insurance companies mainly use ad-hoc methods for risk classification, more often based on the type of expenses covered than on the distribution of the corresponding losses. The selection of classification variables is also, in general, based on rate-making variables rather than on an optimal choice criteria based on statistical methods. It is known that logistic regression is among the many sophisticated statistical methods used by the banking industry in order to select credit rating variables. Extending the method to insurance risks seems only natural. Insurance risks are not usually classified in only two categories, good and bad, as can be the case in credit rating, but in a larger number of classes. Here we consider the generalization of the model to extend the use of logistic regression to insurance risk classification. Since insurance data presents catastrophic losses and heavy tailed claim distributions, a robust estimation analysis is very important. It is carefully studied here.