Hierarchical Insurance Claims Modeling

This work describes statistical modeling of detailed, microlevel automobile insurance records. We consider 1993–2001 data from a major insurance company in Singapore. By detailed microlevel records, we mean experience at the individual vehicle level, including vehicle and driver characteristics, insurance coverage, and claims experience, by year. The claims experience consists of detailed information on the type of insurance claim, such as whether the claim is due to injury to a third party, property damage to a third party, or claims for damage to the insured, as well as the corresponding claim amount. We propose a hierarchical model for three components, corresponding to the frequency, type, and severity of claims. The first model is a negative binomial regression model for assessing claim frequency. The driver’s gender, age, and no claims discount, as well as vehicle age and type, turn out to be important variables for predicting the event of a claim. The second is a multinomial logit model to predict the type of insurance claim, whether it is third-party injury, third-party property damage, insured’s own damage or some combination. Year, vehicle age, and vehicle type turn out to be important predictors for this component. Our third model is for the severity component. Here we use a generalized beta of the second kind of long-tailed distribution for claim amounts and also incorporate predictor variables. Year, vehicle age, and person’s age turn out to be important predictors for this component. Not surprisingly, we show a significant dependence among the different claim types; we use a t-copula to account for this dependence. The three-component model provides justification for assessing the importance of a rating variable. When taken together, the integrated model allows more efficient prediction of automobile claims compared with than traditional methods. Using simulation, we demonstrate this by developing predictive distributions and calculating premiums under alternative coverage limitations.