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The individual risk model: a compound distribution

Published online by Cambridge University Press:  20 April 2012

R. J. Verrall
R. J. Verrall
Affiliation:
City University, London
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Extract

The two approaches to modelling aggregate claims—the individual and the collective models—have been regarded as arising by considering a portfolio of policies in different ways. The individual risk model (IRM) is derived by considering the claims on individual policies and summing over all policies in the portfolio, while the collective risk model (CRM) is derived from the portfolio as a whole. This is sometimes held to be the main difference between the IRM and the CRM. In fact the IRM can be derived in exactly the same way as the CRM and can be regarded as a compound binomial distribution. This makes a unified treatment of risk models possible, simplifies the calculation of the mean and variance of the IRM, and facilitates the calculation of higher moments.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 116 , Issue 1 , June 1989 , pp. 101 - 107
Copyright
Copyright © Institute and Faculty of Actuaries 1989

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References

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