Catastrophe Insurance: Estimation of the Generalized Tail Distortion Risk Measure and Earthquake and Wildfire Insurance Risk Modeling

In this thesis, we focus on catastrophic events in the context of insurance and risk management. \n \nInsurance risk arising from catastrophes such as earthquakes is one of the components of the Minimum Capital Test for federally regulated property and casualty insurance companies. 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 financial losses. %damage and the resulting financial losses and insurance claims.%, at a chosen epicenter location. \n \nHomeowners' insurance in wildfire-prone areas can be a very risky business that some insurers may not be willing to undertake. We create an actuarial spatial model for the likelihood of wildfire occurrence over a fine grid map of North America. Several models are used, such as generalized linear models and tree-based machine learning algorithms. A detailed analysis and comparison of the models show a best fit using random forests. Sensitivity tests help in assessing the effect of future changes in the covariates of the model. A downscaling exercise is performed, focusing on some high-risk states and provinces. The model provides the foundation for actuaries to price, reserve, and manage the financial risk from severe wildfires. \n \nWe explore the first and second-order asymptotic expansions of the generalized tail distortion risk measure for extreme risks. We propose to use the first-order asymptotic expansion to provide an estimator for this risk measure. The asymptotic normality of the estimator at intermediate and extreme confidence levels are shown, separately. Additionally, we provide bias-corrected estimators, where we focus on the case where the tail index is estimated by the Hill estimator. We perform a simulation study to assess the performances of the proposed estimators proposed and we compare them with other estimators in the literature. Finally, we showcase out estimator on several real-life actuarial data sets.

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