Credibility Prediction Using Collateral Information

By Edward W. Frees, Peng Shi

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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


Frees, Edward W., and Peng Shi, "Credibility Prediction Using Collateral Information," Variance 11:1, 2018, pp. 45-59.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.