Towards Multivariate Ratemaking: Claim Frequency Analysis Examples

Motivation: Test how changes in level and distribution of exposures affect different ratemaking models. Actuaries are well aware that loss trend can be distorted by changes in exposure level and business mix. They are trained to recognize situations in which these distortions may arise, and how to adjust for them. Multivariate models are another way of handling these distortions. Using claim frequency as an example, the paper illustrates the design of multivariate analyses resistant to changes in exposure level and business mix.

Method: Simulate data in which the predominant sources of variation are changing exposure levels and changes in the distribution of exposures. Determine indicated trend, development, and classification factors using multivariate and univariate models. Compare the results.

Results: Trend, development factors, and relativity indications from 30 samples having different levels of variation in exposure levels and distribution are obtained by different methods.

Conclusions: Multivariate analyses that incorporate all available information are more robust than other analyses when data have significant changes in exposure levels or changes in mix of business.

Availability: Input data sets and model outputs are available at www.casact.org.

Keywords: Ratemaking, Trend and Loss Development, Rating Class Relativities, Generalized Linear Models