Analysis of Aggregated Claim Numbers with Geometric Distribution and Claim Sizes with Weibull Distribution Using Convolution Method

Abstract

An insurance claim is a form of claim from the insured party to the insurer, in this case the insurance company, which is submitted when a disaster or event that causes loss occurs. This claim is based on an agreement contract in the form of an insurance policy that has been agreed upon by both parties. Claims that arise every time a risk occurs are known as individual claims, while the total of individual claims that occur during a certain insurance period is called an aggregate claim. Aggregate loss refers to the total loss that must be borne by the insurance company due to claims filed by policyholders in a certain period. This study aims to estimate the total aggregate claim (aggregate loss) by modeling the number of claims using the Geometric distribution and the size of the claim using the Weibull distribution. The research was conducted using simulated data from PT Insurance XYZ. The method used in this research is the convolution method, which allows the calculation of the distribution of total aggregated claims based on the pairwise multiplication of the probability density function. To support the analysis, Easyfit and R Studio software were used in data processing and simulation. The results showed that the estimated total aggregate claim (aggregate loss) for a 12-month period on the simulated data was IDR2,809,454,000 using the Geometric distribution for the number of claims and the Weibull distribution for the size of the claim. In addition, the variance value obtained from the simulation results is 5.051215e-06. These findings provide an important overview of the estimation of potential losses that must be borne by insurance companies and can be used as a reference in risk management and the establishment of a more optimal financial strategy.