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A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves

Published online by Cambridge University Press:  29 August 2014

Thomas Mack
Thomas Mack*
Affiliation:
Munich Re, Munich, FRG
*
Münchener Rückversicherungs-Gesellschaft, Königinstr. 107, D-8000 München 40, FRG.
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Abstract

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It is shown that there is a connection between rating in automobile insurance and the estimation of IBNR claims amounts because automobile insurance tariffs are mostly cross-classified by at least two variables (e.g. territory and driver class) and IBNR claims run-off triangles are always cross-classified by the two variables accident year and development year. Therefore, by translating the most well-known automobile rating methods into the claims reserving situation, some known and some unknown claims reserving methods are obtained. For instance, the automobile rating method of Bailey and Simon produces a new claims reserving method, whereas the model leading to the rating method called “marginal totals” produces the well-known IBNR claims estimation method called “chain ladder”. A drawback of this model is the fact that it is designed for the number of claims and not for the total claims amount for which it is usually applied.

As an alternative for both, rating and claims reserving, we describe a simple but realistic parametric model for the total claims amount which is based on the Gamma distribution and has the advantage of providing the possibility of assessing the goodness-of-fit and calculating the estimation error. This method is not very well known in automobile insurance—although a satisfactory application is reported—and seems to be completely unknown in the field of claims reserving, although its execution is nearly as simple as that of the chain ladder method.

Keywords

Cross-classified data(automobile & property) ratemakingIBNR claimsGamma modelmaximum likelihood method.
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 21 , Issue 1 , April 1991 , pp. 93 - 109
Copyright
Copyright © International Actuarial Association 1991

References

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