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Predictive Stop-Loss Premiums

Published online by Cambridge University Press:  29 August 2014

Werner Hürlimann
Werner Hürlimann*
Affiliation:
Switzerland
*
Allgemeine Mathematik, Winterthur-Leben, Römerstrasse 17, CH-8401 Winterthur.
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Abstract

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Based on a representation of the aggregate claims random variable as linear combination of counting random variables, a linear multivariate Bayesian model of risk theory is defined. In case of the classical risk theoretical assumptions, that is conditional Poisson likelihood counting variates and Gamma structural density, the model is shown to identify with a Bayesian version of the collective model of risk theory. An interesting multivariate credibility formula for the predictive mean is derived. A new type of recursive algorithm, called three-stage nested recursive scheme, allows to evaluate the predictive density and associated predictive stop-loss premiums in an effective way.

Keywords

Aggregate claimsstop-lossBayesian modellingcollective risk theoryrecursive algorithm
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 1 , May 1993 , pp. 55 - 76
Copyright
Copyright © International Actuarial Association 1993

References

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