Modeling Aggregate Losses for Third Party Liability Insurance Using the Panjer Recursive Method
DOI:
https://doi.org/10.36456/jstat.vol18.no2.a10886Keywords:
Aggregate Loss Modeling, Panjer Rekursif, Poisson Distribution, Pareto Type II Distribution, Insurance Risk, Third Party Liability InsuranceAbstract
The increasing number of passenger vehicles in densely populated areas such as Jakarta, West Java, and Banten has increased the risk of financial losses due to accidents, theft, and vehicle damage. This study aims to model the aggregate loss distribution in Third Party Liability (TPL) insurance using the Panjer recursive method. The data used are real observations from PT. XYZ for passenger vehicles insured between IDR 125 million and IDR 200 million in the 2018 underwriting year. Claim frequency is modeled using a Poisson distribution, while claim severity follows a Pareto Type II distribution. Model parameters are estimated using the Maximum Likelihood Estimation (MLE) method, and goodness-of-fit is evaluated using the Chi-square and Kolmogorov–Smirnov tests. The results show that the aggregate loss distribution can be effectively constructed using the Panjer recursive method. A dominant discrete probability mass occurs at zero aggregate loss with a probability of 0.992664, while the continuous component covers positive losses up to IDR 23,400,000. This result indicates that TPL claims in the observed portfolio are extremely sparse, which has important implications for premium pricing and risk management in motor vehicle insurance.
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