Some applications of the fast Fourier transform algorithm in insurance mathematics This paper is dedicated to Professor W. S. Jewell on the occasion of his 60th birthday

Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre-Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distributions.