Speedy convolution algorithms and Panjer recursions for phase-type distributions

For phase-type claim size distributions, the Panjer algorithm can be simplified in the sense that the non local term in the recursion can be replaced by a local one, which yields a considerable reduction of computation time. This is done for the discrete case with arithmetic claim size, for the continuous case with a density for the claim size, and finally for the mixed case in which the claim size distribution is a mixture of two distributions, the first arithmetic, the second continuous. In the last two cases, numerical integration can be replaced by the solution of an interacting system of differential equations. (c) 2005 Elsevier B.V. All rights reserved.