2011
DOI: 10.1017/s1748499511000042
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Matrix-form Recursive Evaluation of the Aggregate Claims Distribution Revisited

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 … Show more

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Cited by 1 publication
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“…Finally, we note that PH distributions have rational generating functions, and this is the basis for the adaptation in Eisele (2006) of Panjer's algorithm to the case where N is PH. A comparison of the complexity and numerical stability of the algorithms in Eisele (2006), Ren (2010), Wu & Li (2010) and Siaw et al (2011) is outside the scope of the present paper.…”
Section: Introductionmentioning
confidence: 99%
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“…Finally, we note that PH distributions have rational generating functions, and this is the basis for the adaptation in Eisele (2006) of Panjer's algorithm to the case where N is PH. A comparison of the complexity and numerical stability of the algorithms in Eisele (2006), Ren (2010), Wu & Li (2010) and Siaw et al (2011) is outside the scope of the present paper.…”
Section: Introductionmentioning
confidence: 99%
“…In Section 2, we show that the series P n!0 P n is a key quantity and that, for all practical purposes, it is necessary that the spectral radius of A be strictly less than one in order for the series to converge. Before doing so, we briefly address the issue of the choice of representation, as the one we adopt is slightly different from the representation in Wu & Li (2010) and Siaw et al (2011). Sophie Hautphenne, Guy Latouche, Giang T. Nguyen Next, we assume in Section 3 that A and B commute.…”
Section: Introductionmentioning
confidence: 99%
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