ESTIMATING PROBABLE MAXIMUM LOSS USING THE PEAKS OVER THRESHOLD APPROACH FOR PRIVATE AUTOMOBILE INSURANCE IN MIDWESTERN US

• Main Author: Wulandari, Annisa
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/42456
• Institution: Institut Teknologi Bandung

Traffic accidents are uncertain events which may result in deaths or financial losses. One way to minimize the financial losses is to buy a vehicle insurance. This type of insurance is useful to spread the risks of financial losses between policyholders and insurance companies. This Final Project discusses a statistical modeling for large claims data based on the extreme value theory with the Peaks Over Threshold (POT) approach on private automobile insurance claims data in Midwestern United States. The excess values of a threshold are modeled using a Generalized Pareto Distribution (GPD) or a G(; ) distribution probability model. The threshold selection is based on three methods: the plot of the mean excess function; the stability plot of the distribution parameters; and the Gerstengarbe and Werner plot. Cram´er-von Mises and Anderson Darling tests are carried out to check on the appropriateness of fitting a GPD to the data. For the given data, for a threshold of u = 2696; 3, the Maximum Likelihood Estimation (MLE) method gives the estimates of the parameters ^ = 2348; 6790 and ^ = 0; 2282. Furthermore, the resulting GPD model are used to determine the Probable Maximum Loss (PML) of the claims data. At the significance levels of = 1%; 5%; and 10%, the corresponding PML obtained are: $142; 288:9; $95; 732:46; and $80; 080:02, respectively. The PML could be used by an insurance company to determine the maximum risk it is willing to cover.