Determining Fire Insurance Premium in Indonesia based on Severity and Frequency Claim Distributions

This research utilizes a fitted distribution for calculating fire insurance premiums in Indonesia. This research aims to study, analyze, and estimate the premium of some coverage on fire insurance data in Indonesia. Here, we study data on fire insurance in Indonesia from the period of 2006 to 2016. Property that can be insured based on the type of building used is called occupation. This is regulated in the 2017 Otoritas Jasa Keuangan (OJK) Circular Letter. Furthermore, one type of occupation is selected namely occupation number 2937 and as a result, we analyze 530 claims in total with three types of coverage; (i) building, (ii) stock and content, and (iii) building, stock, and content including severity of the claim. For the number of claims, we assume the data following the Poisson distribution. In contrast, for the severity of claim, two of the three candidate distributions are heavy-tailed distributions i.e. Weibull, Lognormal, and the latter is light-tailed distribution Gumbel. At first, it is assumed that the severity is Weibull distribution, considering that fire is a rare occurrence and can be considered as a Non-Homogeneous Poisson process. To obtain the best-fit distribution from these distributions, the traditional method Kolmogorov-Smirnov is applied for each distribution. We also estimate each parameter for a best-fit distribution. Those parameters are used to estimate the premium for each coverage above. According to the probability density function's graph, the most fitted distribution for (i) and (ii) is Gumbel while the most fitted distribution for (iii) is Lognormal. The Indonesia's fire insurance data fits the heavy-tail distributions.