State-space models for predicting IBNR reserve in row-wise ordered runoff triangles: calendar year IBNR reserves & tail effects

The issue of modeling and forecasting IBNR (incurred but not reported) actuarial reserve under Kalman filter techniques and extensions, using data arranged in a runoff triangle, is a frequent theme in the literature. One quite recent approach is to order the runoff triangle under a row-wise fashion and use linear state-space models for the resulting data set. To allow new possibilities for short-term IBNR reserves as well as to mitigate insolvency risk, in this paper we extend such a state-space method by: (i) a calendar year IBNR reserve prediction; and (ii) a tail effect for the row-wise ordered triangle. The extension is implemented with a real runoff triangle and compared with some traditional IBNR predictors. Empirical results indicate that the approach of this paper outperforms the competing methods in terms of out-of-sample comparisons and gives more conservative IBNR reserves than the original state-space method.