Property and Casualty Premiums based on Tweedie Families of Generalized Linear Models

We consider the problem of estimating accurately the pure premium of a property and casualty insurance portfolio when the individual aggregate losses are assumed to follow a compound Poisson distribution with gamma jump sizes. Generalized Linear Models (GLMs) with a Tweedie response distribution are analyzed as a method for this estimation. This approach is compared against the standard practice in the industry of combining estimations obtained separately for the frequency and severity by using GLMs with Poisson and gamma responses, respectively. We show that one important difference between these two methods is the variation of the scale parameter of the compound Poisson-gamma distribution when it is parametrized as an exponential dispersion model. We conclude that both approaches need to be considered during the process of model selection for the pure premium