FLOOD REINSURANCE PREMIUM PRICING BASED ON THE STANDARD DEVIATION PRINCIPLE WITH POT-BASED THRESHOLDS FOR MORTALITY AND PROPERTY DAMAGE RISKS - Vanessa Anggriawan; Ferry Jaya Permana; Benny Yong (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2026)
Disasters that occur in Indonesia lead to financial loss. One approach to mitigating the financial impact is through the utilization of natural disaster insurance. Although natural disasters occur with a relatively small frequency, the associated losses are substantial. Insurance companies need to carefully consider the characteristics of natural disaster data, as these events can lead to significant claims and potentially result in the bankruptcy of insurance companies. Insurance companies can reduce the risk of bankruptcy by transferring some risk to reinsurance companies. In this paper, the disaster reinsurance premium is determined by considering both the mortality and economic risks using the peaks over threshold (POT) model under the standard deviation principle. The Poisson, generalized Pareto, and lognormal distributions are used to determine the premium, with parameters estimated using the maximum likelihood method. A simulation analysis is conducted using synthetic data generated with RStudio software, which includes the frequency of floods per year over 20 years, as well as the number of deaths and the number of houses damaged in each flood event. The threshold is determined using the percentage method, where 10% of the data is considered extreme values. The POT model is applied to various retention cases. The simulation results show that the risk of the number of damaged houses has a greater impact on the premium amount that the insurance company must pay to the reinsurance company than the risk of the number of deaths. Additionally, cases with retention values below the threshold result in the highest reinsurance premiums, while cases with retention values above the threshold result in the lowest reinsurance premiums. This paper also shows that the reinsurance premium changes almost linearly with the increase in the extreme value percentage. This study is among the first to apply the peaks over threshold model in combination with multiple distributions for reinsurance premium estimation in the Indonesian context. The findings provide new insights into the sensitivity of reinsurance premiums to damage thresholds and retention levels, offering a practical tool for insurers in disaster-prone regions.