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Between Individual and Collective Model for the Total Claims

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 Science and Econometrics, Jodenbreestraat 23, NL-1011, NH Amsterdam
Institute for Actuarial Science and Econometrics, Jodenbreestraat 23, NL-1011, NH Amsterdam
Institute for Actuarial Science and Econometrics, Jodenbreestraat 23, NL-1011, NH Amsterdam
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Abstract

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This article studies random variables whose stop-loss rank falls between a certain risk (assumed to be integer-valued and non-negative, but not necessarily of life-insurance type) and the compound Poisson approximation to this risk. They consist of a compound Poisson part to which some independent Bernoulli-type variables are added.

Replacing each term in an individual model with such a random variable leads to an approximating model for the total claims on a portfolio of contracts that is computationally almost as attractive as the compound Poisson approximation used in the standard collective model. The resulting stop-loss premiums are much closer to the real values.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 2 , November 1988 , pp. 169 - 174
Copyright
Copyright © International Actuarial Association 1988

References

Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. (1987); Actuarial Mathematics; Society of Actuaries, Itasca, IL.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
De Pril, N. (1988); Improved approximation for the aggregate claims distribution of a life portfolio, Scandinavian Actuarial Journal, to be published.CrossRefGoogle Scholar
Goovaerts, M. J., Haezendonck, J. and De Vylder, F. (1984); Insurance Premiums; North-Holland, Amsterdam.Google Scholar
Hipp, Ch. (1986); Improved Approximations for the Aggregate Claims Distribution in the Individual Model, ASTIN Bulletin 16.2, 89–100.CrossRefGoogle Scholar
Kaas, R. (1987); Bounds and approximations for some risk theoretical quantities; University of Amsterdam.Google Scholar
Kaas, R., Van Heerwaarden, A. E. and Goovaerts, M. J. (1988); On stop-loss premiums for the individual model, ASTIN Bulletin 18, 91–98.CrossRefGoogle 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., Reich, A. and Reimers, L. (1987); PANJER vs KORNYA vs DE PRIL: A Comparison from a Practical Point of View, ASTIN Bulletin 17.2, 183–191.CrossRefGoogle Scholar
Reimers, L. (1988); Letter to the Editor, ASTIN Bulletin 18.2, 113–114.CrossRefGoogle Scholar