Projection for Claims Triangles by Affine Age-to-Age Development

By Thomas Muller

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Actuaries have always had the impression that the chain-ladder reserving method applied to real data has some kind of “upward” bias. This bias will be explained by the newly reported claims (true IBNR) and taken into account with an additive part in the age-to-age development. The multiplicative part in the development is understood to be restricted to the changes in the already reported claims (IBNER, “incurred but not enough reserved”). Based on regression theory the reserve as well as error formulae are generalized from the purely multiplicative chain-ladder model to our considerably more stable “affine” models.

Keywords: Claims reserving, chain-ladder method, IBNR and IBNER, linear regression, standard error, weighted least squares estimators, chain-ladder bias


Muller, Thomas, "Projection for Claims Triangles by Affine Age-to-Age Development," Variance 10:1, 2016, pp. 121-144.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.