Approximations of the Aggregate Loss Distribution

Aggregate Loss Distributions are used extensively in actuarial practice, both in ratemaking and reserving. A number of approaches have been developed to calculate aggregate loss distributions, including the Heckman-Meyers method, Panjer method, Fast Fourier transform, and stochastic simulations. All these methods are based on the assumption that separate loss frequency and loss severe distributions are available. Sometimes, however, it is not practical to obtain frequency and severity distributions separately, and only aggregate information is available for analysis. In this case the assumption about the shape of aggregate loss distribution becomes very important, especially in the "tail" of the distribution. This paper will address the question of what type of probability distribution is the most appropriate to use to approximate an aggregate loss distribution.