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Error Bounds for Compound Poisson Approximations of the Individual Risk Model

Published online by Cambridge University Press:  29 August 2014

Nelson De Pril  and
Jan Dhaene
Nelson De Pril*
Affiliation:
Catholic University of Leuven, Belgium
Jan Dhaene*
Affiliation:
Catholic University of Leuven, Belgium
*
Catholic University of Leuven, Dekenstraat 2, B-3000 Leuven, Belgium.
Catholic University of Leuven, Dekenstraat 2, B-3000 Leuven, Belgium.
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Abstract

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The approximation of the individual risk model by a compound Poisson model plays an important role in computational risk theory. It is thus desirable to have sharp lower and upper bounds for the error resulting from this approximation if the aggregate claims distribution, related probabilities or stop-loss premiums are calculated.

The aim of this paper is to unify the ideas and to extend to a more general setting the work done in this connection by Bühlmann et al. (1977), Gerber (1984) and others. The quality of the presented bounds is discussed and a comparison with the results of Hipp (1985) and Hipp & Michel (1990) is made.

Keywords

Individual risk modelcompound Poisson approximationerror boundstop-loss premium
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 2 , November 1992 , pp. 135 - 148
Copyright
Copyright © International Actuarial Association 1992

References

Bühlmann, H., Gagliardi, B., Gerber, H.U. and Straub, E. (1977) Some inequalities for stop-loss premiums. ASTIN Bulletin 9, 75–83.CrossRefGoogle Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation Monograph No. 8, distributed by Richard D. Irwin, Inc., Homewood, Illinois.Google Scholar
Gerber, H.U. (1984) Error bounds for the compound Poisson approximation. Insurance: Mathematics and Economics 3, 191–194.Google Scholar
Hipp, C. (1985) Approximation of aggregate claims distributions by compound Poisson distributions. Insurance: Mathematics and Economics 4, 227–232. Correction note: Insurance: Mathematics and Economics 6, 165.Google Scholar
Hipp, C. (1986) Improved approximations for the aggregate claims distribution in the individual model. ASTIN Bulletin 16, 89–100.CrossRefGoogle Scholar
Hipp, C. and Michel, R. (1990) Risicotheorie: Stochastische Modelle und Statistische Methoden. Schriftenreihe Angewandte Versicherungsmathematik, Heft 24, Deutsche Gesellschaft für Versicherungsmathematik, distributed by Verlag Versicherungswirtschaft e.V., Karlsruhe.Google Scholar
Kornya, P. S. (1983) Distribution of aggregate claims in the individual risk theory model. Transactions of the Society of Actuaries 35, 823–836. Discussion 837-858.Google Scholar
Kuon, S., Radtke, M. and Reich, A. (1991) The right way to switch from the individual risk model to the collective one. Paper presented at the XXIII ASTIN Colloquium, Stockholm.Google Scholar
Michel, R. (1987) An improved error bound for the compound Poisson approximation. ASTIN Bulletin 17, 165–169.CrossRefGoogle Scholar
Sundt, B. (1991) An Introduction to Non-Life Insurance Mathematics. Veröffentlichungen des Instituts für Versicherungswissenschaft der Universität Mannheim, Bd. 28, 2. Auflage, distributed by Verlag Versicherungswirtschaft e.V., Karlsruhe.Google Scholar