AN ESTIMATION OF THE OUTSTANDING CLAIMS LIABILITY USING THE LEVELED CHAIN LADDER MODEL WITH GIBBS SAMPLING

• Main Author: Valentino Kosasih, Leonardo
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/65450
• Institution: Institut Teknologi Bandung

A long tail general insurance business is an insurance business in which the period from the occurrence of an incident that results in an occurrence of a claim until the claim is paid off will take more than one year. This duration is due to the time lags between the occurrence of the incident and the claim is reported; between the claim is reported and the claim is processed; and between the claim is processed and it is fully paid. A long tail insurance business’ claims data is often recorded in a runoff triangle format. Estimating the outstanding claims liability for a long tail insurance business is not simple. The Chain Ladder (CL) method is often used to estimate the outstanding claims liability because it is simple and easy to be applied and could be used without using a parametric approach. However, probably because of its simplicity, the assumptions on which the CL method is based are often not met by many long tail insurance business claims data. The Leveled Chain Ladder (LCL) model is developed using the Bayesian approach and is expected to overcome one of the weaknesses of the CL method which tends to estimate the standard error of the ultimate claims to be lower than it should be. In this final project, two sets of long tail general insurance business data are used: the first, is a runoff triangle data from Schedule P of the National Association of Insurance Commissioners (NAIC) Annual Statement; and the second, is a runoff triangle data from an insurance business that is not from the Schedule P of the National Association of Insurance Commissioners (NAIC) Annual Statement. For the first data, it is found that the estimated total outstanding claims liabilities determined by the CL method and the LCL model are not much different; whereas the estimated standard error of the outstanding claims liability obtained by the LCL model is greater than that obtained by the CL method. For the second data, it is found that the estimated total outstanding claims liability obtained by the LCL model is much greater than that obtained by the CL method; whereas the estimated standard error of the outstanding claims liability determined by the LCL model is much smaller than that determined by the CL method. These may be due to the assumptions of the prior distributions for some parameters which are not met by the second data which is not from the Schedule P of the National Association of Insurance Commissioners (NAIC) Annual Statement.