THE DETERMINATION OF THE PREMIUM OF AN EXCESS OF LOSS REINSURANCE BUSINESS USING THE EXCESS-LOSS FUNCTION AND MONTE CARLO SIMULATION

• Main Author: Robertus Hartono, Yoshua
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/76325
• Institution: Institut Teknologi Bandung

Buying a reinsurance product is an effort by an insurance company to protect itself against the risk of large claims. An excess of loss reinsurance pays claims in excess of a certain retention up to a certain maximum limit specified in the reinsurance contract. In an excess of loss reinsurance, an insurance company may share or manage the risk coverage in layers. The formation of a layering system is due to the risk of paying large claims of which risk is shared by the insurance company and other reinsurance companies. Halliwell (2012) introduced the excess-loss function as a very powerful tool for determining reinsurance premiums at a loss layer. This final project aims to use the excess-loss function to determine analytically the reinsurance premiums, as well as using Monte Carlo simulations, if there are several layers. In this final project, the reinsurance premium for each layer is calculated using the expected value principle and the standard deviation principle. Loss is assumed to have a mixed exponential, lognormal, gamma, and inverse gaussian distributions. For the mixed exponential distribution, calculations are performed using the excess-loss function analytically; while for the lognormal, gamma, and inverse gaussian distributions, Monte Carlo simulations are used. From the resulting calculated premiums, for the corresponding loading factors, the premium in the first and second layers calculated using the expected value principle is greater than that calculated using the standard deviation principle; while for the third and fourth layers, the opposite applies. For all distributions, whether calculated analytically or simulated, the values of covariance and correlation between layers are positive which indicates a linear relationship between each layer. However, the correlation between layers decreases as the distance between layers increases