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Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling

Published online by Cambridge University Press:  29 August 2014

Gordon K. Smyth  and
Bent Jørgensen
Gordon K. Smyth*
Affiliation:
Walter and Eliza Hall Institute of Medical Research, Melbourne, Australia
Bent Jørgensen
Affiliation:
Department of Statistics and Demograph, University of Southern Denmark
*
1Dr G.K. Smyth, Bioinformatics, Walter and Eliza Hall Institute of Medical Research, Post Office, Royal Melbourne Hospital, Parkville, VIC 3050, Australia
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Abstract

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We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, μ say. They observed that the dependence of the likelihood function on μ is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

Keywords

Car insuranceClaims dataCompound Poisson modelExposureGeneralized linear modelsDispersion modellingDouble generalized linear modelsPower variance functionREMLRisk theoryTarification
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 32 , Issue 1 , May 2002 , pp. 143 - 157
Copyright
Copyright © International Actuarial Association 2002

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