Old and New on some IBNR Methods

Three maincategories of IBNR methods are considered: the standard IBNR methods (chain-ladder, Cape Cod, Bornhuetter-Ferguson), the IBNR loss ratio methods (loss ratios instead of link ratios) and the stochastic IBNR methods (calculation of standard deviation and percentiles). The main IBNR loss ratio methods include the individual and collective loss ratio methods as well as a credibility mixture of them, the so-called credibility loss ratio method. The latter includes variants by Benktander, Neuhaus and an optimal version by the author. We observe that the standard IBNR methods can be reinterpreted in the context of the IBNR loss ratio methods and extended to optimal credible standard IBNR methods. Among the stochastic IBNR methods we focus on stochastic chain-ladder models (including the multivariate setting), distribution based reserving models and multi-state reserving models. In particular, we propose a new and simple stochastic IBNR model based on the log-Laplace distribution. Numerical examples demonstrate that it is comparable in accuracy to the standard and loss ratio IBNR methods. As a new feature,the expected dynamic development of IBNR methods is studied in detail. It uses newly defined case reserve development factors. Numerical examples illustrate and compare the divers IBNR methods.