PREMIUM OPTIMIZATION FOR EXCESS OF LOSS REINSURANCE USING THE EXTREME VALUE THEORY MODEL

• Main Author: Fajri Rajmi (NIM: 20817011), Nuzulia
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/29855
• Institution: Institut Teknologi Bandung

An insurance or ceding company need to manage the insurance risk by sharing it with a reinsurance company. The characteristics of the claims severity and claims frequency of an insurance business are dependent on its nature. For some insurance businesses, significant number of claims with extreme large claims may occur. In this thesis, claims severity data is analyzed using an Extreme Value Theory (EVT) model with the Peak Over Threshold (POT) approach. An Excess of Loss (non-proportional treaty) reinsurance with four layers is applied to the data. The determination of the gross premium is dependent on the number of the reinsurance layers and the amount of the own retention. Having fitted the EVT model with POT approach to the data, an optimal retention levels are determined using an optimization technique with the objective function of minimizing the claims variation. The constraints used are: the level of own retention determined by the regulators; the limits of the reinsurance layers; and the targeted profit. Additional to those constraints, the fact that the variance of the ceding company’s claims data will be reduced due to reinsurance schemes is also used as a constraint. The methodology discussed in this thesis is applied to an earthquake insurance data.