Recursions for the Individual Risk Model

Abstract

In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straightforward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.

Inequalities for the De Pril approximation to the distribution of the number of policies with claims

“…Sundt (2002) and Sundt & Vernic (2009) give surveys of the theory of recursions for aggregate claims distributions. Dhaene et al (2006) and Sundt & Vernic (2006) compare recursions for aggregate claims distributions within an individual setting.…”