Combined Analysis of Paid and Incurred Losses

Motivation. The new solvency regimes now emerging, insist that capital requirements align with the underlying (insurance) risks. This paper explains how a stochastic model built on basic assumptions is used to monitor insurance risk in order to get a clear insight in the aligned economic capital including prudence margins for loss reserves. Method. The incurred loss of an insurer consists of payments on claims and reserves for claims that have been reported. As all claims are settled eventually, the cumulative paid and incurred losses for a given loss period become equal. Therefore, a joint model for the paid and incurred loss arrays is constructed, following a multivariate normal distribution, conditioned on equality of the total paid and incurred losses for a given loss period. A new class of functions is designed specifically to model development curves. Results. A simulation experiment proved that a joint model for both paid and incurred loss arrays as described under Method, leads to a more accurate prediction of loss reserves. While the standard way of estimating percentiles for the reserve is biased, the alternative method of bootstrapping will lead to more accurate outcomes. Conclusions. Modeling paid and incurred losses jointly leads to a considerable improvement in loss reserving in terms of accuracy of predictions, as well as specification of percentiles. Availability. This method is incorporated in software available from the authors.