Minimum Bias, Generalized Linear Models, and Credibility in the Context of Predictive Modeling

By Christopher Gerald Gross, Jonathan Palmer Evans

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Abstract

When predictive performance testing, rather than testing model assumptions, is used for validation, the need for detailed model specification is greatly reduced. Minimum bias models trade some degree of statistical independence in data points in exchange for statistically much more tame distributions underlying individual data points. A combination of multiplicative minimum bias and credibility methods for predictively modeling losses (pure premiums, claim counts, average severity, etc.) based on explanatory risk characteristics is defined. Advantages of this model include grounding in long-standing and conceptually lucid methods with minimal assumptions. An empirical case study is presented with comparisons between multiplicative minimum bias and a typical generalized linear model (GLM). Comparison is also made with methods of incorporating credibility into a GLM.

Keywords: predictive modeling, minimum bias, credibility, ratemaking, generalized linear models

Citation

Gross, Christopher Gerald, and Jonathan Palmer Evans, "Minimum Bias, Generalized Linear Models, and Credibility in the Context of Predictive Modeling," Variance 12:1, 2018, pp. 13-38.

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Mission Statement

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.