Inference in multiplicative pricing

In multiplicative pricing of non-life insurance, we report a simulation study of mean square errors (MSEs) of point estimates by (1) the marginal totals method and (2) the Standard Generalized Linear Model (GLM) method of Poisson claim numbers and gamma distributed claim severities with constant coefficient of variation. MSEs per tariff cell are summed with insurance exposures as weights to give a total MSE. This is smallest for Standard GLM under the multiplicative assumption. But with moderate deviations from parameter multiplicativity, the study indicates that the marginal totals method is typically better in the MSE sense when there are many arguments and many claims, i.e. for mass consumer insurance. A method called MVW for confidence intervals, using only the compound Poisson model, is given for the marginal totals method. These confidence intervals are compared with the ones of Standard GLM and the Tweedie method for risk premiums in a simulation study and are found to be mostly the best. The study reports both cover probabilities, which should be close to 0.95 for 95% confidence intervals, and interval lengths, which should be small. The Tweedie method is found to be never better than Standard GLM.