The Computation of Aggregate Loss Distributions
by John P. Robertson
Abstract: Paul R. Halmos recently hailed the fast Fourier transform as one of the 22 most significant developments in mathematics in the last 7.5 years. This paper provides an application of this tool to the computation of aggregate loss distributions from arbitrary frequency and severity distributions. All necessary mathematics is developed in the paper, complete algorithms arc given, and examples are provided. Sufficient details are given to allow implementation in any computer language, and sample APL computer language routines are given. The final section includes a discussion of excess loss distributions where computation is not limited to the fast Fourier transform based algorithm.
Published in: Proceedings of the Casualty Actuarial Society, Vol. 79, No. 1, (1992), pp. 57-133.