Factor Copula Approaches for Assessing Spatially Dependent High-Dimensional Risks

In this article, we propose an innovative approach for modeling spatial dependence among losses from various geographical locations. The proposed model converts the challenging task of modeling complex spatial dependence structures into a relatively easier task of estimating a continuous function, of which the arguments can be the coordinates of the locations. The approach is based on factor copula models, which can capture various linear and nonlinear dependence. We use radial basis functions as the kernel smoother for estimating the key function that models all the spatial dependence structures. A case study on a thunderstorm wind loss dataset demonstrates the analysis and the usefulness of the proposed approach. Extensions to spatiotemporal models and to models for discrete data are briefly introduced, with an example given for modeling loss frequency with excess zeros.