On Classification in Automobile Insurance

Abstract

Automobile insurance rates are based on classifications of policies according to a number of variables such as age, marital status, occupation, use of vehicle, accident record, place of residence, type of automobile, etc. A common rate is established for all insureds assigned to the same class, and this rate is a function of the expected claim costs and expenses per policy in the given class. In practice, a number of different classification systems may be in use at any one time. One insurance company, for example, may distinguish male and female drivers who are more than 25 years old, while another company may classify both sexes into a single age class of over-25; one company may use the occupation of the principal driver as a classification variable, while another may ignore it entirely; and so on. Any classification system may be used, if it results in a set of classes among which there are significant differences with respect to expected claim costs and expenses. One issue that appears not to have been carefully considered concerns the number of classes into which policies are classified whatever the classification variables happen to be. To put the question simply, suppose that an insurance company has the choice of either charging the same rate to all its policyholders, or dividing them into a number of classes and charging each class a different rate. To make the situation even simpler initially, suppose that the firm enjoys a captive market (as is effectively the case in British Columbia or Manitoba) so that the number of insureds would remain the same regardless of the choice. Which alternative should be preferred? Does the choice depend on the number of classes, the number of insureds in each class, the length of the company's experience, the degree of homogeneity or variability of claims in each class, or the criterion of optimality used? The literature is not clear on these questions. It appears to suggest that the greater the number of classes and the smaller number of insureds in each class, the greater the variability and uncertainty of premiums and profits. Also, one is left with the impression that the greater the number of classes, the more