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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

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