On the Prediction of Automobile Insurance Claims: The Personalization versus Confidence Trade-off

In order to determine an appropriate auto insurance policy premium one needs to take into account the risk associated with the drivers and cars on the policy. The premium is then typically a combination of the administrative and other costs required to support this customer, the profit margin desired by the provider (which in turn depends on the competition) and finally on the expected claims to be made on this policy based on risk. Given multiple features of the policy (age and gender of drivers, value of car, etc.) one can potentially provide personalized insurance policies based specifically on these policy features. However, as the level of personalization increases, the quantity of data available for predicting individual claim rates (the average total claim value per year) decreases and hence the robustness of the estimate decreases. The optimal level of personalization will depend on the number of samples and attributes as well as factors such as the variance of the claim rate for different attributes and the variation of the claim rate across categories of each attribute. We formulate a mathematical model for this trade-off and demonstrate how one can obtain the optimal choice. We demonstrate using illustrative examples as well as with data from an automobile insurance company.

I. Introduction

Traditionally insurance companies determined automobile policy premiums using rate tables computed by Actuaries. Today however, the vast amount of data collected in electronic form can now be used to determine more suitable premiums for a given policy since such data can be used to better predict risk [1]. This form of personalized policies benefit the customer (who pays an amount more in line with their risk) as well as the insurance company (which can now better ensure that it can safely cover claims costs across all of its customers). The typical approach is straightforward. For a given new customer, one can use historical data of past and present customers with similar characteristics (attributes) to better estimate the risk level of the new customer and then use this to determine a premium for their policy. This is similar to the recommender systems used by companies such as Netflix. In that case movies are recommended to an individual based on movies that were enjoyed by customers with similar characteristics. In the case of insurance, one must “recom-mend” a policy that is both desirable to the customer (through personalization) and profitable to the insurance provider.