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An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company

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.