THE IMPACT OF OUTLIER ON THE PREDICTION OF CLAIMS RESERVE AND ROBUST CHAIN-LADDER - SERU (NIM: 20814025) , FEBY
The chain-ladder method is often used to predict claims reserve in a long tail insurance business. The method is a distribution free method. In this thesis, the prediction of the claims reserve is carried out using a stochastic approach; that is using a Generalized Linear Model (GLM). The incremental claims data is assumed to follow a Poisson distribution with a natural logarithm link function. This model produced a prediction of the claims reserve which is the same as that produced by the chain-ladder method. However, the prediction based on a chain-ladder method is very sensitive to outliers. The existence of an outlier gives an underestimate or overestimate prediction of claims reserve compared with that when there is no outlier. The sensitivity of the chain-ladder estimator may be analyzed using the Inﬂuence Function (IF) based on a GLM approach. The chain-ladder method has an Inﬂuence Function (IF) value which goes to inﬁnity; this indicates that the chain-ladder estimator is not robust. Another way to predict the claims reserve is to substitute the chain-ladder estimator by a robust estimator and to re-weight the estimator to produce a robust chain-ladder estimator. For data with no outliers, there is no signiﬁcant diﬀerence between the prediction of the the claims reserve produced by the chain-ladder method and that produced by the robust chain-ladder method. However, when there is an outlier in the data, the robust chain-ladder method will produce a better prediction in that the prediction is close to the prediction when there is no outlier in the data.