Pricing catastrophe reinsurance risk premium using Peaks over Threshold (POT) model

An incident that cost more lives than a certain threshold is called a catastrophic event. In the world of insurance, the incidence of catastrophe causes many policies to make a claim together, so it can cause big losses for insurance companies. The risk of catastrophic events can be minimized by purchasing a catastrophic reinsurance contract. The reinsurance company then calculates the amount of risk premium for catastrophic reinsurance to be paid by the insurance company. The model used to calculate the risk premium is the peaks over threshold (POT) model. The POT model is generally used to model extreme events. In this model, the number of catastrophic events is modeled using the Poisson distribution. Then, the number of casualties is modeled using the discrete generalized Pareto distribution (DGPD). To estimate the parameters of the model, the maximum likelihood method is used and the data on the number of fatalities resulting from a particular event in Indonesia is collected and compiled. Furthermore, the number of claims is modeled with the Beta-Binomial distribution and the size of claims resulting from a catastrophic event is modeled by Exponential distribution. Numerical simulations are then performed to obtain the total size of claims resulting from all catastrophic events within 1 year of catastrophic reinsurance contracts. Ultimately the risk premium can be calculated using the standard deviation premium principle by utilizing the expected value and the variance of the total amount of the claim.