ESTIMATING AGREGATE IBNR CLAIM RESERVES USING A MARKED POISSON-GAMMA DISTRIBUTION WITH A GENERALIZED LINEAR MODEL (GLM) - Maulana Meidiawan, Nibras
Estimating claim reserve forecasts is crucial for insurance companies. These predictions determine the magnitude of liabilities the company holds. Typically, this estimation is performed by calculating the aggregate claim amount in previous years. The distribution of this aggregate claim can be derived from the frequency distribution of claims and severity of claims or assumed to follow a certain conjugate distribution. The frequency distribution of claims can be assumed to follow a marked Poisson distribution, with the marked part being the size of claim delays and claim events, while the severity of claims is assumed to follow a Gamma distribution, resulting in a marked Poisson-Gamma distribution for the claims. The Conjugate distribution for aggregate claims can be assumed to follow a Tweedie family distribution, which is a sub-family of the Exponential distribution, and the identification of the distribution within the Tweedie family is based on the parameter p. Estimating claim reserve prediction can be done using two different models: the Chain Ladder (CL) model, which does not require distribution assumptions, and the Generalized Linear Model (GLM), which does require distribution assumptions. Both models provide estimated for the lower triangle in the run-off triangle, which represents the expected claim development over time. The case study used in this research involves worker compensation data from 1989-1997 at an company named West Bend Mut Ins Grp in the US. The results obtained indicate the CL method yields smaller standard error compared to GLM, but it has higher coefficient of variance (CV). Another result obtained the GLM Poisson-gamma is the best model among GLM Over-Dispersed Poisson, Marked Poisson-gamma, and gamma.