Sensitivity, uncertainty and robustness of risk models in insurance

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Insurance companies are exposed to a unique landscape of risks including financial and insurance risks. Insurance contracts have extremely long maturities, resulting in long-dated risks, and are typically grouped into extremely heterogeneous portfolios. Understanding the risks embedded in the aggregation of such heterogeneous portfolios is highly non-trivial, particularly due to challenges in estimating and specifying interdependence. Numerical and computational advances, notably in machine learning techniques, accelerated the use of quantitative, highly sophisticated statistical models throughout the insurance industry. Typically in financial and insurance risk management, far-reaching decisions are grounded on low dimensional summaries of model outputs. Thus, understanding output variability resulting from uncertainty in model components is critical for making well-informed decisions. Risk managers and regulation alike call for quantification of model stability, robustness, and sensitivity. One of this research proposal's vision is to develop new and original sensitivity und uncertainty analysis tools for models used in financial and insurance risk management. Thus, addressing the immense demand from risk managers, policy makers, and model (end-)users for reliable tools to understand and gain insight into their models' uncertainties and limitations. Misspecification in model components are ubiquitous and arise from parameter estimation, from missing data, and from inaccurate collection of data. Analyzing the propagation of misspecification, that is the cascading of stresses from one single model component through an entire model to the model's output, provides invaluable information about the model's structure. Specifically, dependences between model components are the critical drivers of propagation of stresses and form the core of this proposal's second research stream. Understanding the cascading effects of stresses have applications in financial risk management, such as systemic risk and stress testing. As performing stress tests is a regulatory requirement for banking institutions and insurance companies alike, and that systemic stability of the financial system is of paramount concern to policy makers, this research proposal has high potential for industrial applications and practical and regulatory relevance.