Aggregate loss model with Poisson-Tweedie frequency

Aggregate loss models are used by insurers to make operational decisions, set insurance premiums, optimize reinsurance and manage risk. The aggregate loss is the summation of all random losses that occurred in a period, and it is a function of both the loss severity and the loss frequency. The need for a flexible model in fitting severity has been well studied in the literature. We extend this work by introducing the Poisson-Tweedie distribution family for the frequency distribution. The Poisson-Tweedie distribution family contains many of the commonly used distributions for modelling loss frequency, thus making loss frequency fitting more flexible and reducing the chance of model misspecification. Using simulation, we show that the sensitivity of percentile based risk measures to different specifications of the frequency distribution. We then apply our proposed model to the Transportation Security Administration (TSA) claims data to demonstrate modelling capacity of the Poisson-Tweedie distribution.