Hierarchical Insurance Claims Modeling

This work describes statistical modeling of detailed, micro-level automobile insurance records. We consider 1993-2001 data from a major insurance company in Singapore. By detailed micro-level records, we refer to 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 …rst 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 long-tailed distribution for claim amounts and also incorporate predictor variables. Year, vehicle age and a person’s age turn out to be important predictors for this component. Not surprisingly, we show that there is a signi…cant dependence among the di¤erent claim types; we use a t-copula to account for this dependence. The three component model provides justi…cation for assessing the importance of a rating variable. When taken together, the integrated model allows an actuary to predict automobile claims more e¢ ciently than traditional methods. Using simulation, we demonstrate this by developing predictive distributions and calculating premiums under alternative reinsurance coverages. Keywords: Long-tail regression and copulas. yThe authors acknowledge the research assistance of Mitchell Wills, Shi Peng and Katrien Antonio. The …rst author thanks the National Science Foundation (Grant Number SES0436274) and the Assurant Health Insurance Professorship for funding to support this research. The second author thanks the Australian Research Council through the Discovery Grant DP0345036 and the UNSW Actuarial Foundation of the Institute of Actuaries of Australia for …nancial support. Please do not quote without the authors’permission.