Deviance Voronoi Residuals for Space-Time Point Process Models: An Application to Earthquake Insurance Risk

TL;DR

This paper introduces deviance Voronoi residuals for evaluating space-time point process models in earthquake insurance risk, providing new tools for model assessment, simulation, and capital requirement calculations.

Contribution

It extends Voronoi residuals to deviance residuals for better model fit assessment and develops a simulation approach using earthquake hazard maps for insurance risk analysis.

Findings

Deviance Voronoi residuals effectively identify model inadequacies in specific locations.

A simulation-based method estimates earthquake damages and insurance claims.

A new formula for country-wide minimum capital test based on provincial correlations.

Abstract

Insurance risk arising from catastrophes such as earthquakes a component of the Minimum Capital Test for federally regulated property and casualty insurance companies. Analyzing earthquake insurance risk requires well-fitted spatio-temporal point process models. Given the spatial heterogeneity of earthquakes, the ability to assess whether the fits are adequate in certain locations is crucial in obtaining usable models. Accordingly, we extend the use of Voronoi residuals to calculate deviance Voronoi residuals. We also create a simulation-based approach, in which losses and insurance claim payments are calculated by relying on earthquake hazard maps of Canada. As an alternative to the current guidelines of OSFI, a formula to calculate the country-wide minimum capital test is proposed based on the correlation between the provinces. Finally, an interactive web application is provided which allows the user to simulate earthquake damage and the resulting financial losses and insurance claims, at a chosen epicenter location.