Novel tools in quantitative risk management

This theses proposes novel methods to analyze risk and dependence across a joint probability distribution. It is well known in finance and insurance that risk and dependence are vastly different in the tails compared to the rest of the distribution. Tails characterize events such as market crisis and natural catastrophes, and contribute to a significant portion of overall risk and dependence. However, typical measures of risk and dependence capture the overall result and mask variations across the probability distribution. Random quantities are partitioned into infinitesimal layers capturing outcomes of various magnitude and likelihood. Risk and dependence are then measured across layers using established methods such as distortion and correlation. Layers are standard constructs representing (re)insurance coverage, capital consumption and shortfall, derivative payouts, and tranches of collateralised debt obligations. This thesis expresses layer endpoints using percentiles or more commonly known as Values-at-Risk (VARs), hence each layer occupies a relative position in the probability distribution. This thesis also extends distortion risk measurement by capturing upside risk in addition to downside risk. In financial and insurance markets with strong competition and limited availability of capital, an explicit view of upside risk is required to reflect opportunity costs. Developments in this thesis formalise existing, and reveal new, insights to risk and diversification.For example, the framework explains weak diversification in financial and insurance markets despite moderate correlations overall. The framework also deals with problems such as setting capital buffers, reinsurance purchase and assessing the credit quality of debt tranches. These insights arise from a deeper understanding of how risk and dependence varies across a probability distribution. Proposed methods apply consistent concepts such as VaRs, distortion and layers, and hence form a coherent analytical framework. These concepts are well established and hence the resulting framework integrates and expands current disparate approaches. The proposed framework is a complete tool to quantitative risk management, by first analysing risk and dependence when imperfectly dependent random quantities are aggregated, and then guiding strategies to optimally manage and reduce risk.