Modelling of Large Fire Insurance Claims: An Extreme Value Theory Approach

Abstract

This research paper aims to develop a mathematical model that employs Extreme Value Theory (EVT) and Risk Measures to estimate and forecast significant fire insurance claims. The primary goal is to provide insurance companies with a more accurate understanding of the potential risks associated with substantial fire-related losses. The study incorporates a three-parameter Generalized Pareto Distribution (GPD) within the EVT framework to assess insurer risk concerning catastrophic fire events. The importance of evaluating fire-related financial losses for insurers is emphasized, especially given the impact of infrequent yet impactful extreme events on overall loss trends. By applying EVT techniques, including the GPD and Peaks Over Threshold (POT) method, to a historical dataset of fire insurance claims, the study effectively models the tail behavior of large losses. Parameters obtained from these models facilitate the calculation of probabilities for extreme loss occurrences, thereby enhancing risk management and pricing strategies for insurance firms. The results demonstrate the EVT approach's effectiveness in accurately modeling and estimating the risk associated with significant fire insurance claims. This research contributes to the insurance domain by presenting an enhanced mathematical and statistical framework for modeling substantial fire insurance claims. Such an approach enables insurers to better comprehend the potential financial implications of rare fire incidents, leading to more informed risk evaluation and resource allocation.

Keywords: Extreme Value Theory (EVT), Generalized Pareto Distribution (GPD), Fire Insurance Claims, Risk Management, Catastrophic Events.