Reimagining Risk Beyond Normality: Managing Catastrophic Events and Higher-Order Moments

This paper proposes a new framework that enhances traditional risk assessment by incorporating higher-order statistical moments—specifically skewness and kurtosis—through the Cornish-Fisher expansion. Standard risk models, which rely primarily on mean and variance, often underestimate the financial buffers required to hedge against extreme, low-probability shocks. To address this limitation, this study applies the Cornish-Fisher expansion to develop a more comprehensive framework that quantifies the economic impact of extreme events, with direct implications for financial institutions and policymakers. Utilizing a two-period intertemporal consumption model, this study employs Monte Carlo simulations to assess how catastrophic shocks—such as the COVID-19 pandemic—affect key economic indicators. The results demonstrate that negative skewness amplifies downside risk, necessitating stronger precautionary savings and financial reserves. Furthermore, the persistent underinvestment in global preparedness—particularly in pandemic risk management—can be attributed to conventional risk models that fail to capture the full severity of extreme events. The perspective presented in this paper not only enhances theoretical models but also has critical implications for practical applications, particularly in risk management and policy design, where extreme outcomes must be carefully accounted for.