Hierarchical Insurance Claims Modeling

• 成果类型: Article
• 署名作者: Frees, Edward W.; Valdez, Emiliano A.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Connecticut
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214508000000823
• 发表日期: 2008
• 页码: 1457-1469
• 关键词: credibility

摘要

This work describes statistical modeling of detailed. microlevel automobile insurance records. We consider 1993-2001 data a from it 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 oil the type of insurance claim such as whether the claim is due to injury to a third party, property damage to it third party, or claims for damage to the insured. as well its 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 it negative binomial regression model for assessing claim frequency. The driver's gender, age, and no claims discount, its 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 it 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 it 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.