Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T19:45:28.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Multivariate Compound Poisson Distributions and Infinite Divisibility

Published online by Cambridge University Press:  29 August 2014

Bjørn Sundt
Bjørn Sundt*
Affiliation:
Vital Forsikring ASA
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 note we give a multivariate extension of the proof of Ospina & Gerber (1987) of the result of Feller (1968) that a univariate distribution on the non-negative integers is infinitely divisible if and only if it can be expressed as a compound Poisson distribution.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 30 , Issue 2 , November 2000 , pp. 305 - 308
Copyright
Copyright © International Actuarial Association 2000

References

De Pril, N. (1985) Recursions for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.CrossRefGoogle Scholar
Feller, W. (1968) An introduction to probability theory and its applications. Vol. 1 (3. ed.) Wiley, New York.Google Scholar
Horn, R. A. & Steutel, F. W. (1978) On multivariate infinitely divisible distributions. Stochastic Processes and their Applications 6, 139–151.CrossRefGoogle Scholar
Ospina, A.V. & Gerber, H.U. (1987) A simple proof of Feller's characterization of the compound Poisson distributions. Insurance: Mathematics and Economics 6, 63–64.Google Scholar
Panjer, H. H. (1980) The aggregate claims distribution and stop-loss reinsurance. Transactions of the Society of Actuaries 32, 523–535.Google Scholar
Sundt, B. (1999) On multivariate Panjer recursions. ASTIN Bulletin 29, 29–45.CrossRefGoogle Scholar