Recursions and fast Fourier transforms for a new bivariate aggregate claims model

Insurance companies typically face multiple sources (types) of claims. Therefore, modelling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In this paper, we first introduce a multivariate aggregate claims model, which allows dependencies among claim numbers as well as dependencies among claim sizes. For this proposed model, we derive recursive formulas for the joint probability functions of different types of claims. In addition, we extend the concept of exponential tilting to the multivariate fast Fourier transform and use it to compute the joint probability functions of the various types of claims. We provide numerical examples to compare the accuracy and efficiency of the two computation methods.