Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-01T07:06:21.200Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Exact Calculation of the Aggregate Claims Distribution in the Individual Life Model

Published online by Cambridge University Press:  29 August 2014

Karl-Heinz Waldmann
Karl-Heinz Waldmann*
Affiliation:
Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe
*
Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, Postf. 6980, D-76128 Karlsruhe.
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.

An iteration scheme is derived for calculating the aggregate claims distribution in the individual life model. The (exact) procedure is an efficient reformulation of De Pril's (1986) algorithm, considerably reducing both the number of arithmetic operations to be carried out and the number of data to be kept at each step of iteration. Scaling functions are used to stabilize the algorithm in case of a portfolio with a large number of policies. Some numerical results are displayed to demonstrate the efficiency of the method.

Keywords

Individual life modelaggregate claims distributionDe Pril algorithm
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 1 , May 1994 , pp. 89 - 96
Copyright
Copyright © International Actuarial Association 1994

References

REFERENCES

Beard, R. E., Pentikäinen, T. and Pesonen, E. (1984) Risk Theory. 3rd edition. Chapman and Hall, London.CrossRefGoogle Scholar
De Pril, N. (1986) On the exact computation of the aggregate claims distribution in the individual life model. ASTIN Bulletin 16, 109–112.CrossRefGoogle Scholar
De Pril, N. (1988) Improved Approximations for the Aggregate Claims Distribution of a Life Insurance Portfolio. Scan. Actuarial J. 1988, 61–68.CrossRefGoogle Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph 8, Philadelphia.Google Scholar
Kuon, S., Reich, A. and Reimers, L. (1987) Panjer vs. Kornya vs. De Pril: A comparison from a practical point of view. ASTIN Bulletin 17, 183–191.CrossRefGoogle Scholar
Panjer, H. H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
Panjer, H. H. and Willmot, G. E. (1986) Computational aspects of recursive evaluation of compound distributions. Insurance: Mathematics and Economics 5, 113–116.Google Scholar
Panjer, H.H. and Wang, S. (1993) On the Stability of Recursive Algorithms. ASTIN Bulletin, to appear.Google Scholar
Reimers, L. (1988) Letter to the Editor. ASTIN Bulletin 18, 113–114.CrossRefGoogle Scholar
Ross, S.M. (1983) Stochastic Processes. John Wiley, New York.Google Scholar