Journal article
Matrix-form Recursive Evaluation of the Aggregate Claims Distribution Revisited
KK Siaw, X Wu, D Pitt, Y Wang
Annals of Actuarial Science | CAMBRIDGE UNIV PRESS | Published : 2011
Abstract
This 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 paper. Wit..
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Funding Acknowledgements
The authors are grateful to two referees for their very constructive comments that helped raise the level of rigour and clarity of the presentation and lead to a substantial improvement of the paper. This research was funded by the Australian Actuarial Research Grants, sponsored by the Institute of Actuaries of Australia.