Credibility Prediction Using Collateral Information
By Edward W. Frees, Peng Shi
In property-casualty insurance ratemaking, insurers often have access to external information which could be manual rates from a rating bureau or scores from a commercial predictive model. Such collateral information could be valuable because the insurer might either not have sufficient rating information nor the predictive modeling expertise to produce an effective score.
This paper shows how to blend collateral information with an insurer’s own experience for ratemaking in a predictive modeling framework. Bayesian methods are employed to allow analysts to incorporate their personal knowledge about the precision of the external score. Using conjugate priors, we show that closed-form credibility predictions exist for a variety of distributions, including the Tweedie family. A simulation study is performed to demonstrate the prediction with collateral information in a variety of hypothetical scenarios. We further apply the proposed approach to an automobile insurance dataset from Massachusetts. Both the simulation and empirical studies demonstrate situations where combining external information with internal company information provides lift in the prediction of out-of-sample policies.
Keywords Bayesian inference, automobile ratemaking, generalized linear model