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Paper prepared for the Actuarial Studies in Non-Life Insurance Colloquium held on June 19-22 2007 in Orlando, USA. Two distribution dependent IBNR claims reserving models with gamma distributed paid claims are considered. The first model assumes independent development periods and allocates the coefficient of variation of the total ultimate claims of a line of business with multiple underwriting periods to the coefficient of variation of the total ultimate claims of a single underwriting period inverse proportionally to the squared-root premium volumes. The second model extension is based on a simple Fréchet like multivariate distribution, which models the whole range of dependence between independence and comonotone dependence. The chosen model uses only one additional dependence parameter, which is chosen such that it yields the most conservative model for IBNR claims reserving with respect to the concordance order for the bivariate margins of this model. The use of the introduced models is compared with the results obtained through application of a recent optimal credible loss ratio IBNR reserving method.
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