Projection for Claims Triangles by Affine Age-to-Age Development
By Thomas Muller
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