Catastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four-digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate.

In this paper, we suggest the bare minimum initial capital a firm providing insurance must hold to avoid going bankrupt. A case-separated investment discrete-time surplus process in motor insurance claims serves as the study's model. The 50th, 60th, 70th, and 80th percentiles are used as the dividing line between a claim's standard claim and large claim situations. We also discover a link between an insurance company's initial capital and the likelihood of ruin. The least squares regression method is utilized to calculate the minimum initial capital, and the simulation approach would be used to determine the ruin probability. The results indicate that the least initial capital is better provided by the 70th percentile than the 50th, 60th, and 80th percentiles, respectively.

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