Individual and aggregate loss models are important concepts in nonlife insurance mathematics. This work presents some basic ideas with compound model framework. Compound model allows the use of analytical model for aggregate losses. Compound Poisson model has computational benefits and is in favor of actuaries. Compound Poisson-gamma-model is part of the Tweedie family with parameter p between 1 and 2. This model has many useful applications. Although it does not have closed form for its CDF it has the benefit with connectedness to the risk theory.
Typically claims frequency is modelled by Poisson distribution and claim severity by gamma distribution. Sometimes claims frequency is overdispersed and the Poisson-Tweedie models are called upon. Important example is Poisson-Inverse Gaussian distribution. Tweedie models and Poisson-Tweedie models have ubiquitous presence among actuarial applications. Compound Poisson-gamma has also useful applications in several branch of science. Tweedie convergence theorem shows that for many probability distributions Tweedie distributions act as a foci of convergence. Because Tweedie models are a subset of exponential dispersion models the results that applies to exponential dispersion models are also applicable to Tweedie models.
Some crucial methods regarding calculation of collective risk model is presented. Convolution can be calculated by Fourier transform or more exactly by Fast Fourier Transform (FFT). It has been shown that this is faster option compared to the Panjer's recursion.