Report
Matrix-form recursions for a family of compound distributions
X Wu, S Li
ASTIN Bulletin | Published : 2010
Abstract
In this paper, we aim to evaluate the distribution of the aggregate claims in the collective risk model. The claim count distribution is firstly assumed to belong to a generalised (a,b,0) family. A matrix form recursive formula is then derived to evaluate the related compound distribution when individual claim amounts follow a discrete distribution on non-negative integers. The corresponding formula is also given for continuous individual claim amounts. Secondly, we pay particular attention to the recursive formula for compound phase-type distributions, since only certain types of discrete phase-type distributions belong to the generalised (a,b,0) family. Similar recursive formulae are obtai..
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Awarded by Faculty of Business and Economics, the University of Melbourne
Funding Acknowledgements
The authors are grateful to two referees whose constructive comments have definitely 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 a Faculty of Business and Economics research grant (F9A), the University of Melbourne.