Predicting the Claims-Development-Result in the Chain-Ladder Method for Correlated Run-Off Portfolios

In the present paper we analyse how the estimators from Merz u. Wüthrich (2007) could be generalised to the case of N correlated run-off triangles. The simultaneous view on N correlated subportfolios is motivated by the fact, that in practice a run-off portfolio often has to be divided in subportfolios, so that the homogeneity assumption of the claims reserving method on each subportfolio is satisfied. We derive an explicit formula for the process-variance, the estimation-error and the prediction error made by the forecast for the claims development result with the Chain-Ladder method. We illustrate the results by an example