Estimation of Incurred but Not yet Reported Claims Based on Poisson Distributed Reporting Delay - Gerthofer, Michal; Sládek, Václav; Zimmermann, Pavel (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2017)
A claim frequency model, which estimates number of claims that incurred but are not reported (IBNR), is a key component of an insurer’s future liability prediction. Several possible modelling approaches were developed in the past. Chain ladder method is a particularly popular distribution free method, which models development of the cumulative liability through weighted averages of the past development factors. The assumption of this model is that developments of the cumulative claims for each occurrence year are independent. If a trend is identified in occurrence years, predictions are biased. A modification of this method can be applied to relax this assumption. For example, development factors, can be extrapolated to the future by a trend function. Other approaches may be based e.g. on variety of regression specifications. In this contribution, a new approach is presented, which is based on the assumption that number of discrete years until the claim is registered has Poisson distribution. The mean of this distribution is estimated by maximum likelihood method, taking in to account that observations are truncated. An empirical study is presented and our approach is compared with the traditional Chain ladder method as well as the above-mentioned modification
20-th AMSE. Applications of Mathematics and Statistics in Economics. International Scientific Conference: Szklarska Poręba, 30 August- 3 September 2017. Conference Proceedings Full Text Papers, s. 183-194
Keywords: frequency model; Chain ladder; modified Chain ladder; Poisson distribution