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Modified Recursions for a Class of Compound Distributions

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  • Waldmann, Karl-Heinz

Abstract

Recursions are derived for a class of compound distributions having a claim frequency distribution of the well known (a,b)-type. The probability mass function on which the recursions are usually based is replaced by the distribution function in order to obtain increasing iterates. A monotone transformation is suggested to avoid an underflow in the initial stages of the iteration. The faster increase of the transformed iterates is diminished by use of a scaling function. Further, an adaptive weighting depending on the initial value and the increase of the iterates is derived. It enables us to manage an arbitrary large portfolio. Some numerical results are displayed demonstrating the efficiency of the different methods. The computation of the stop-loss premiums using these methods are indicated. Finally, related iteration schemes based on the cumulative distribution function are outlined.

Suggested Citation

  • Waldmann, Karl-Heinz, 1996. "Modified Recursions for a Class of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 213-224, November.
    • Handle: RePEc:cup:astinb:v:26:y:1996:i:02:p:213-224_00
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    Cited by:

    1. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    2. Chadjiconstantinidis, Stathis & Pitselis, Georgios, 2009. "Further improved recursions for a class of compound Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 278-286, April.
    3. S. Chadjiconstantinidis & M. V. Koutras & F. S. Milienos, 2023. "The distribution of extended discrete random sums and its application to waiting time distributions," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.

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