Over-Dispersed Claim Counts Regression Models and Their Applications in Auto Insurance

Poisson regression model is widely used in auto claim count models for ratemaking practice. But as the actual claim count data often appears to be over-dispersed (i.e. variance is larger than mean), the Poisson regression model may not produce reasonable results. The paper fist compares several mixed Poisson regression models that may be used to account for overdispersion in claim count data, including Negative Binomial regression(NB), Poisson-inverse Gaussian regression(PIG), Poisson-Lognormal regression(PLN), generalized Poisson regression(GP). Then the paper proposes two new regression models that may also be used for over-dispersed claim count data, namely mixed binomial regression(MB) and mixed negative binomial regression(MNB). Finally the paper applies all these models to an actual auto claim count data and compares the results.