Copula approach for simulated damages caused by landfalling US hurricanes

Abstract

Hurricanes are destructive forces of nature that have the ability to cause vast devastation both economically and socially. Estimating the potential damage caused by hurricanes aids local, state and federal governments as well as insurance and reinsurance companies to plan for future hurricanes. Direct damages caused by hurricanes are difficult to estimate. There are multiple factors that could contribute to the damages caused by a hurricane. Wind is typically considered the most important factor to account for when estimating potential damage. Aside from the complex physical processes, the difficultly in estimating hurricane damages is further compounded by limited data and a changing climate. Fitting models with limited data presents a series of challenges. These challenges include outliers that could form a large proportion of the data, overfitting, missing data and it becomes difficult to leave out a portion of the data for external validation. This study found a significant positive correlation using the Kendall rank correlation coefficient between hurricane damages, measured by the area of total destruction and the maximum landfalling wind speed (τ = 0.451). A copula-based approach was used to model their dependency. Both bivariate Archimedean and elliptical copulae families were assessed as potential models. A bivariate Frank copula with Weibull marginals was found to be the most appropriate fitting model based on a visual inspection of the contour plots of the fitted copulae. Simulation from the fitted copula was qualitatively similar to observation. This study demonstrated a potential method to overcome the limitation of small data facing models to estimate hurricane damages.