Unification of Stochastic Reserving Models

In their daily reserving tasks, general insurance actuaries often use a mix of chain-ladder, Bornhuetter-Ferguson and Cape-Cod methods to estimate the ultimate reserve amounts. These methods are usually applied on cumulative triangles and a payment or incurred pattern is derived from the application of the chain-ladder method on these cumulative triangles. This pattern is then used in the Bornhuetter-Ferguson or Cape-Cod method. In contradiction to this practice, T. Mack in its 2008 article “The Prediction Error of Bornhuetter/Ferguson” demonstrated that the stochastic model underlying this method should be based on incremental triangles. In addition, in 2015, A. Saluz used a stochastic model for the Cape-Cod method based also on incremental triangles. Actually, it is natural to use incremental triangles for any stochastic reserving model due to the independence property between each cell of such a triangle. Such independence property does not exist on cumulative triangles. As a result, following on the works of Mack and Saluz, this article will therefore redevelop the chain-ladder model on incremental triangles. As a consequence, based on incremental individual claims analysis, it will be possible to unify the stochastic models of chain-ladder, Bornhuetter-Ferguson and Cape-Cod into a single model for the estimation of ultimate value, volatility and skewness of the reserving distribution.