Most automobile insurance databases contain a large number of policyholders with zero claims. This high frequency of zeros may reflect the fact that some insureds make little use of their vehicle, or that they do not wish to make a claim for small accidents in order to avoid an increase in their premium, but it might also be because of good driving. We analyse information on exposure to risk and driving habits using telematics data from a Pay-as-you-Drive sample of insureds. We include distance travelled per year as part of an offset in a zero-inflated Poisson model to predict the excess of zeros. We show the existence of a learning effect for large values of distance travelled, so that longer driving should result in higher premium, but there should be a discount for drivers that accumulate longer distances over time due to the increased proportion of zero claims. We confirm that speed limit violations and driving in urban areas increase the expected number of accident claims. We discuss how telematics information can be used to design better insurance and to improve traffic safety.

Conventional supervised statistical learning models aim to achieve high accuracy in predicting the value of an outcome measure based on a number of input measures. However, in many applications, some type of action is randomized on the observational units. This is the case, for example, in treatment=control settings, such as those usually encountered in marketing and clinical trial applications. In these situations, we may not necessarily be interested in predicting the outcome itself, but in estimating the expected change in the outcome as a result of the action. This is precisely the idea behind uplift models, which, despite their many practical applications, have received little attention in the literature. In this article, we extend the state-of-theart research in this area by proposing a new approach based on Random Forests. We perform carefully designed experiments using simple simulation models to illustrate some of the properties of the proposed method. In addition, we present evidence on a dataset pertaining to a large Canadian insurer on a customer retention case. The results confirm the effectiveness of the proposed method and show favorable performance relative to other existing uplift modeling approaches.

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Pay-as-you-drive (PAYD), or usage-based automobile insurance (UBI), is a policy agreement tied to vehicle usage. In this paper we analyze the effect of the distance traveled on the risk of accidents among young drivers with a PAYD policy. We use regression models for survival data to estimate how long it takes them to have their first accident at fault during the coverage period. Our empirical application with real data is presented and shows that gender differences are mainly attributable to the intensity of use. Indeed, although gender has a significant effect in explaining the time to the first crash, this effect is no longer significant when the average distance traveled per day is introduced in the model. This suggests that gender differences in the risk of accidents are, to a large extent, attributable to the fact that men drive more often than women. Estimates of the time to the first accident for different driver risk types are presented. We conclude that no gender discrimination is necessary if telematics provides enough information on driving habits.

Customer-side influences on insurance have been relatively ignored in the literature. Using the household as the unit of analysis, this article focuses on the behavior of households having multiple policies of different types with the same insurance company, and who cancel their first policy. How long after the household's cancellation of the first policy does the insurer have to retain the customer and avoid customer defection on all policies to the competition? And, what customer characteristics are associated with customer loyalty? Using logistic regression and survival analysis techniques, an assessment is made of the probability of total customer withdrawal, and the length of time between first cancellation and subsequent customer withdrawal. Using a European database spanning 54 months of household multiple policyholder behavior, the results show that cancellation of one policy is a very strong indicator that other household policies will be canceled. Further, the insurer can have time to react to retain the customer after the first cancellation, however, this time is significantly dependent on the method used to contact the company, household demographics, and the nature of the household's insurance policy portfolio. Surprisingly, core customers having three or more policies in addition to the canceled policy are more vulnerable to total defection on all policies than noncore customers. Further, the potential customer repelling effects of premium increases seem to wear out after 12 months. Strategic implications of the results are presented. Copyright (c) The Journal of Risk and Insurance, 2008.