A comparison for numerical approaches to determine the severity of losses

Here we present a comparison of the performance of several numerical methods to determine the probability density of the total severity when a model is known. One method is based on the maximum entropy principle applied to fractional moments. The other is a probabilistic method based on the knowledge of enough integer moments. These two methods are based on the possibility of having a reliable model for the total severity that allows for the computation of the Laplace transform of the total severity. Two other methods are also considered for comparison purposes, one being the direct inversion of the Laplace transform by Fourier methods and the other a standard summation of densities of partial losses.