Journal article

Matrix-form Recursive Evaluation of the Aggregate Claims Distribution Revisited

Kok Keng Siaw, Xueyuan Wu, David Pitt, Yan Wang

Annals of Actuarial Science | Cambridge University Press (CUP) | Published : 2011

Abstract

AbstractThis paper aims to evaluate the aggregate claims distribution under the collective risk model when the number of claims follows a so-called generalised (a, b, 1) family distribution. The definition of the generalised (a, b, 1) family of distributions is given first, then a simple matrix-form recursion for the compound generalised (a, b, 1) distributions is derived to calculate the aggregate claims distribution with discrete non-negative individual claims. Continuous individual claims are discussed as well and an integral equation of the aggregate claims distribution is developed. Moreover, a recursive formula for calculating the moments of aggregate claims is also obtained in this pa..

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