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On Stop-Loss Premiums for the Individual Model

Published online by Cambridge University Press:  29 August 2014

R. Kaas ,
A. E. van Heerwaarden  and
M. J. Goovaerts
R. Kaas*
Affiliation:
University of Amsterdam
A. E. van Heerwaarden*
Affiliation:
University of Amsterdam
M. J. Goovaerts*
Affiliation:
K.U. Leuven andUniversity of Amsterdam
*
Institute for Actuarial Scienceand Econometrics, Jodenbreestraat 23, NL-1011 NH, Amsterdam.
Institute for Actuarial Scienceand Econometrics, Jodenbreestraat 23, NL-1011 NH, Amsterdam.
Institute for Actuarial Scienceand Econometrics, Jodenbreestraat 23, NL-1011 NH, Amsterdam.
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Abstract

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It is shown how the upper bounds for stop-loss premiums (and approximations to tail probabilities) obtained by replacing the individual model for a portfolio of risks by the collective model can be improved upon at the cost of only slightly more computer time. The method used is simply to keep a restricted number of large risks as they are instead of approximating them by a compound Poisson distribution. In a real-life example, the relative error in the stop-loss premium is shown to be reduced drastically by keeping only 10 out of 743 risks unchanged.

Keywords

Stop-loss premiumindividual model
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 1 , April 1988 , pp. 91 - 97
Copyright
Copyright © International Actuarial Association 1988

References

Beriram, J. (1981) Numerische Berechnung von Gesamtschadenverteilungen: Blätter der deutsche Gesellschaft für Versicherungs-Mathematiker XV–2, 175–194.Google Scholar
Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. (1987) Actuarial Mathematics. Society of Actuaries, Itasca, Ill.Google 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
Gerber, H. U. (1984) Error bounds for the compound Poisson approximation. Insurance: Mathematics and Economics 3, 191–194.Google Scholar
Goovaerts, M. J., Haezendonck, J. and De Vylder, F. (1984) Insurance Premiums. North-Holland, Amsterdam.Google Scholar
Kaas, R. (1987) Bounds and Approximations for Some Risk Theoretical Quantities. University of Amsterdam.Google Scholar
Kornya, P. S. (1983) Distribution of aggregate claims in the individual risk theory model. Society of Actuaries: Transactions 35, 823–858.Google Scholar
Kuon, S., Reich, A. and Reimers, L. (1987) Panjer vs Kornya vs De Pril: A comparison from a practical poinl of view. XX ASTIN-Colloquium, Scheveningen.Google Scholar