INTEGER-VALUED AUTOREGRESSIVE(1) POISSON PROCESS APPLICATION FOR MODELLING INCURRED BUT NOT REPORTED CLAIM COUNTS: YULLER-WALKER METHOD AND ITERATIVE WEIGHTED CONDITIONAL LEAST SQUARES ESTIMATION METHOD

• Main Author: Sugiono, Daniel
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/42424
• Institution: Institut Teknologi Bandung

An insurance company need to determine its claims reserve. The Chain-Ladder and the Bornhuetter-Ferguson methods are often used to estimate the outstanding claims liability. However, both methods do not assume any distributions to the underlying data. In this final project, a time-series model, namely an Integer-Valued Autoregressive(1) Poisson or the Poisson INAR(1) model is used to analyze the unclosed claims frequency or the Incurred But Not Reported (IBNR) claims. The Poisson INAR(1) model consists of three parameters: the probability of the unclosed claims; the total expected number of claims which occur and have been reported but not yet been settled; and the proportion of the reported number of claims but not yet been settled. In this final project, those three parameters are estimated using two estimation methods: the Yuller-Walker and the Iterative Weighted Conditional Least Squares Estimation methods. The way to compare the two methods is by observing some run-off triangles generated by the model. After comparing the two methods, it is found that the Iterative Weighted Conditional Least Squares Estimation method is better in predicting the unclosed claim frequencies. The prediction error of the resulting predictions of the unclosed claims frequencies is in the range that make sense. But, because the parameter estimation error is ignored, the prediction error is less than it should be.