Abstract
Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.
Highlights
Extreme events are events that rarely occur, but can cause very large losses
The extreme distribution is the distribution of a random variable which is only limited to values that have a small probability of occurrence
Reinsurance companies must determine the amount of claims so that the probability of it occuring is not too great. This extreme distribution will greatly help reinsurance companies in determining the amount of claims it bears because the occurrence of claims is included in extreme events with a small probability of occurrence
Summary
Extreme events are events that rarely occur, but can cause very large losses. This incident can occur in various fields such as health, finance, agriculture and others. One tool that can be used to explain the risk of these events is the extreme distribution. Reinsurance companies must determine the amount of claims so that the probability of it occuring is not too great. This extreme distribution will greatly help reinsurance companies in determining the amount of claims it bears because the occurrence of claims is included in extreme events with a small probability of occurrence
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