Modeling and predicting IBNR reserve: extended chain ladder and heteroscedastic regression analysis

Abstract

This work deals with two methodologies for predicting incurred but not reported (IBNR) actuarial reserves. The first is the traditional chain ladder, which is extended for dealing with the calendar year IBNR reserve. The second is based on heteroscedastic regression models suitable to deal with the tail effect of the runoff triangle – and to forecast calendar year IBNR reserves as well. Theoretical results regarding closed expressions for IBNR predictors and mean squared errors are established – for the case of the second methodology, a Monte Carlo study is designed and implemented for accessing finite sample performances of feasible mean squared error formulae. Finally, the methods are implemented with two real data sets. The main conclusions: (i) considering tail effects does not imply theoretical and/or computational problems; and (ii) both methodologies are interesting to design softwares for IBNR reserve prediction.