Application of Peak Over Threshold Approach to Model Extreme Motor Insurance Claims: A Case Study

Abstract

Prior to the economic recession in Sri Lanka, the motor insurance business grew significantly due to the excessive importation of vehicles. More vehicles on the road and reckless driving increase the risk of extreme claims, which creates a negative impact on the industry. In order to mitigate this issue, researchers attempted to model extreme claims and thereby to provide information for better management of business. The objective of this study is to identify the best fit model for tail of the claim distribution based on data obtained from a pioneer insurer in Sri Lanka from July to December of 2021. The Peak Over Threshold approach of the Extreme Value Theory was applied to model the extreme claims. The claims at 20 percentiles between 79% and 98% were considered as tentative thresholds and the excessive amounts over each of these thresholds were modeled separately as Generalized Pareto Distributions (GPDs) using four different parameter estimation methods. Then the Mean Squared Error (MSE) at each threshold for each parameter estimation method was examined to compare their performances. The threshold and the parameter estimation method with the minimum MSE were selected as their optimum values while identifying the GPD fitted as the best model. The Bootstrap goodness of fit measured the validity of modelling. The extent of claims varied from Rs. 2167.00 to 193,065.00 during the study period with a positive skewness of 2.45 and leptokurtic, which confirmed the existence of a heavy tailed distribution for claims. The best fitted model was the GPD with the shape and scale of 1.02 and 92.09 respectively, which was attained at the optimal threshold of 91st percentile using the Biased Probability Weighted Moment method. The information on the tail helps review existing strategies for the better management of risk due to such extreme claims in future.