Multi-Year Non-Life Insurance Risk for Correlated Loss Portfolios Under Chain Ladder Model Assumptions

In this paper we extend the definition of multi-year claims development results and quantification of multi-year non-life insurance risk to the bivariate chain ladder model as introduced by Braun in 2004. In this model, we assume two correlated loss portfolios each of which is underlying the classical chain ladder model. In accordance with standard literature, multi-year risk is defined through the variation of the multi-year claims development result and quantified in terms of the corresponding mean squared error of prediction. Following previous research on the univariate chain ladder model, for the first time we derive closed analytical expressions for the prediction error of the aggregate multi-year claims development result via first-order Taylor approximation. We reproduce well-known results for the ultimo view from literature. The goodness of our approximation is confirmed by a simulation study. Furthermore, a case study demonstrates the applicability of our analytical formulae.