Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T17:35:35.968Z Has data issue: false hasContentIssue false
  • English
  • Français

On some Extensions of Panjer's Class of Counting Distributions1

Published online by Cambridge University Press:  29 August 2014

Bjørn Sundt
Bjørn Sundt*
Affiliation:
The Wyatt Company &University of Oslo
*
The Wyatt Company AS, P.O.Box 1508 Vika, N-0117 Oslo, Norway, e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we discuss some properties of counting distributions whose discrete density satisfies a recursion in the form

with pn = 0 for n < 0 and present an algorithm for recursive evaluation of corresponding compound distributions.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 1 , May 1992 , pp. 61 - 80
Copyright
Copyright © International Actuarial Association 1992

Footnotes

1

This paper is dedicated to Professor W.S. Jewell on the occasion of his 60th birthday July 2, 1992.

References

REREFENCES

De Pril, N. (1985) Recursion for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.CrossRefGoogle Scholar
De Pril, N. (1989) The aggregate claims distribution with arbitrary positive claims. ASTIN Bulletin 19, 9–24.CrossRefGoogle Scholar
Feller, W. (1971) An introduction to probability theory and its applications. Vol. II. (2 ed.) Wiley, New York.Google Scholar
Panjer, H. H. (1981) Recursive evaluation of compound distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
Panjer, H. H. and Willmot, G. E. (1984) Computational techniques in reinsurance models. Transactions of the 22nd International Congress of Actuaries 4, 111–120.Google Scholar
Panjer, H. H. and Willmot, G. E. (1986) Computational aspects of recursive evalution of compound distributions. Insurance: Mathematics and Economics 5, 113–116.Google Scholar
Schröter, K. J. (1990) On a class of counting distributions and recursions for related compound distributions. Scandinavian Actuarial Journal, 161–175.CrossRefGoogle Scholar
Sundt, B. (1982) Asymptotic behaviour of compound distributions and stop-loss premiums. ASTIN Bulletin 13, 89–98. Corrigendum. ASTIN Bulletin 15, 44.CrossRefGoogle Scholar
Sundt, B. (1991a) An introduction to non-life insurance mathematics. (2 ed.) Verlag Versicherungswirtschaft e.V., Karlsruhe.Google Scholar
Sundt, B. (1991b) On asymptotic rates on lines in excess of loss reinsurance. Insurance: Mathematics and Economics 10, 61–67.Google Scholar
Sundt, B. and Jewell, W. S. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 27–39.CrossRefGoogle Scholar