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Matrix-Form Recursions for a Family of Compound Distributions

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  • Wu, Xueyuan
  • Li, Shuanming

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 obtained for discrete and continuous individual claim amount distributions. Finally, numerical examples are presented for three counting distributions.

Suggested Citation

  • Wu, Xueyuan & Li, Shuanming, 2010. "Matrix-Form Recursions for a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 351-368, May.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:01:p:351-368_00
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