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.