An Enhanced Internal Model for Pandemic Risk, Hybrid LN-E-GPD Distribution and Combined Algorithmic

The COVID-19 pandemic highlighted major challenges in accurately assessing pandemic mortality risk for insurers such as AXA, which have significant international exposure. Under the Solvency II directive, a standard mortality shock of 0.15% is applied in calculating the Solvency Capital Requirement (SCR), but this uniform approach does not account for variations in age structure, gender distribution, and other factors. Consequently, insurers require sophisticated internal models that can adapt to these diverse factors. This study aims to develop an internal pandemic model tailored to insurers’ demographic and geographic profiles, making three key contributions. First, it builds on Swiss Re’s pandemic model by integrating epidemiological modelling with statistical methods to capture pandemic dynamics. Second, the model’s parameters are calibrated using extensive research, accounting for age, gender, and regional factors affecting lethality, while adjusting quarantine effects based on COVID-19 data. Finally, it introduces an innovative optimisation approach that combines genetic algorithms with the Levenberg–Marquardt method to streamline the CAT pandemic model and improve parameter fitting in multidimensional contexts. The model’s reliability is demonstrated through comparisons with the standard SCR formula and historical pandemic data, confirming its robustness in assessing mortality risk under extreme scenarios.