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Assessing Individual Unexplained Variation in Non-Life Insurance

Published online by Cambridge University Press:  09 August 2013

Ola Hössjer ,
Bengt Eriksson ,
Kajsa Järnmalm  and
Esbjörn Ohlsson
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Abstract

We consider variation of observed claim frequencies in non-life insurance, modeled by Poisson regression with overdispersion. In order to quantify how much variation between insurance policies that is captured by the rating factors, one may use the coefficient of determination, R2, the estimated proportion of total variation explained by the model. We introduce a novel coefficient of individual determination (CID), which excludes noise variance and is defined as the estimated fraction of total individual variation explained by the model. We argue that CID is a more relevant measure of explained variation than R2 for data with Poisson variation. We also generalize previously used estimates and tests of overdispersion and introduce new coefficients of individual explained and unexplained variance.

Application to a Swedish three year motor TPL data set reveals that only 0.5% of the total variation and 11% of the total individual variation is explained by a model with seven rating factors, including interaction between sex and age. Even though the amount of overdispersion is small (4.4% of the noise variance) it is still highly significant. The coefficient of variation of explained and unexplained individual variation is 29% and 81% respectively.

Keywords

Claim frequency variationcoefficient of determinationcoefficient of individual determinationunexplained individual variationoverdispersionPoisson regressionrating factors
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 249 - 273
Copyright
Copyright © International Actuarial Association 2009

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