Abstract

Indonesia is located on the ring of fire and the meeting of 3 large tectonic plates, namely the Indo-Australian plate, Eurasian plate and the Pacific plate. Indonesia is often referred to as the Ring of Fire so that many natural disasters, especially earthquakes, volcanic eruptions, tsunamis and landslides. As a result of this natural disaster clearly gives a great loss in social and economic terms. The losses are spread in the infrastructure sector and public facilities such as public roads and offices, residential areas, then the agricultural sector such as damage to agricultural land, to the socio-cultural sector that has a direct impact on the welfare of the community around the area of natural disasters. From an economic perspective, the occurrence of natural disasters has a direct impact on the level of the economy in Indonesia. One way in financing disaster risk that can be done is by insurance services or insurance companies. Insurance companies are referred to as individual risk insurers who take out insurance. Therefore, this research aims to make a mathematical model to determine the amount of premiums that must be paid by the government. Determination of the aggregation claim model uses data on the number of claims taken from the number of events and the amount of claims taken from the amount of losses due to natural disasters in Indonesia. From the results of the study obtained optimal insurance premiums paid by the local government. Natural disaster insurance premiums are determined using the Black Scholes Method, where the value of the premiums is obtained from numerical simulation results.