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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

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