Threshold for Stop-Loss Reinsurance Modeling Using Expected Shortfall

Abstract

Insurance companies play a vital role in safeguarding individuals or groups from unforeseen risks. Reinsurance, particularly stop-loss reinsurance, is a key risk management strategy that provides insurers with protection against large claims. Setting an appropriate threshold in stop-loss reinsurance is crucial, as a low threshold increases reinsurance costs, while a high threshold heightens exposure to extreme losses. Traditional methods such as Value-at-Risk (VaR) are often used but have limitations in capturing heavy tail risks. Expected Shortfall (ES) offers a more robust alternative by accounting for both the probability and severity of losses beyond the threshold. This study explores the use of ES in determining stop-loss reinsurance thresholds. The proposed approach aims to improve risk management efficiency and strengthen the financial stability of insurers in the face of high uncertainty.