Modeling Tail Risk of Employment Injury Claims using the Extreme Value Theory Framework

Abstract

This study investigates the implementation of Extreme Value Theory (EVT) in modeling tail risk associated with employment injury insurance claims, addressing the critical need for robust risk estimation in the presence of rare, high-severity losses. The dataset consists of 1,177 historical claims from BPJS Ketenagakerjaan Makassar recorded between 2016 and 2023. Preliminary diagnostic procedures, including hill plots and mean excess function analysis, reveal heavy-tailed behaviour with a tail index greater than one, implying the possibility of infinite variance—a characteristic often underestimated by traditional actuarial models. Due to the limited number of extreme exceedances, the block maxima framework was adopted, and a Generalized Extreme Value (GEV) distribution was fitted to weekly maxima using L-moment estimation to ensure parameter convergence. The resulting GEV parameters (location = 50.27, scale = 67.19, shape = 0.443) confirm a Fréchet-type distribution, consistent with a heavy-tailed risk profile. Comparative analysis shows that the GEV-based 99.5% VaR (1,484.09 million IDR) is more than three times higher than the empirical estimate (450.56 million IDR). Return level analysis further contextualized the estimates, indicating a one-year return level of 768.51 million IDR. These findings demonstrate that empirical methods substantially underestimate extreme loss potential, potentially threatening insurer solvency. Overall, this study provides a statistically rigorous framework for capital reserve and reinsurance optimization, offering a more conservative and theoretically justified approach to managing catastrophic occupational risks.