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Improved Approximations for the Aggregate Claims Distribution in the Individual Model

Published online by Cambridge University Press:  29 August 2014

Christian Hipp
Christian Hipp*
Affiliation:
University of Cologne
*
Mathematisches Institut der Universität Köln, Weyertal 86, D-5000 Köln 41.
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Abstract

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Kornya-type higher order approximations are derived for the aggregate claims distribution and for stop loss premiums in the individual model with arbitrary positive claims. Absolute error bounds and error bounds based on concentration functions are given. In the Gerber portfolio containing 31 policies, second order approximations lead to an accuracy of 3 × 10−4, and third order approximations to 1.7 ×10−5.

Keywords

Aggregate claims distributioncompound Poisson distributionhigher order approximations
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue 2 , November 1986 , pp. 89 - 100
Copyright
Copyright © International Actuarial Association 1986

References

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