Application of the Collective Risk Model to the Number of Claims with a Negative Binomial Distribution and the Size of Claims with a Discrete Uniform Distribution

Abstract

An insurance claim is a form of request from the policy holder to obtain protection against financial losses due to a risk that occurs. Claims that occur every time there is a risk are called individual claims, while the total of individual claims during one insurance period is called aggregate claims. Claims are an important factor in optimizing insurance company expenses, where one of the calculations that insurance companies need to know based on claims is aggregate loss. Aggregate loss is the total loss in a period experienced by policy holders covered by an insurance company. This study aims to determine the average and variance of claims for the number of claims (frequency) with a Negative Binomial distribution and the amount of claims (severity) with a Discreate Uniform distribution in claim payments according to all types of guarantees and the nature of PT injuries. Jasa Raharja (Persero) Purwakarta Representative during the 2018-2020 period. This research uses a collective risk model and the help of Easyfit software to determine the best distribution for the number and size of claims. The results of the research show that from the recapitulation data of claim payments according to all types of coverage and nature of injury in PT. Jasa Raharja (Persero) Purwakarta Representative during the 2018-2020 period, with the number of claims having a Negative Binomial distribution and the amount of claims having a Discrete Uniform distribution, the average aggregate claim occurrence was IDR  with a variance of IDR  during the 2018-2020 insurance period.