ESTIMATING AGREGATE IBNR CLAIM RESERVES USING A MARKED POISSON-GAMMA DISTRIBUTION WITH A GENERALIZED LINEAR MODEL (GLM)
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 d...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/76239 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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