Statistical modelling and measuring risks in banking and insurance

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The goals of my on-going research program are to understand the underlying probabilistic and statistical structures of risks inherent to financial and insurance markets, and to develop novel models and methods for data analysis to provide improved risk assessment tools for these volatile industries. The classes of problems included in this proposal consider both theoretical aspects and practical applications of various risk models and methods. Specifically, in the context of quantitative risk analysis, my research program will proceed in the following two directions: (1) statistical modelling of loss data with mixtures; and (2) measurement of multivariate risks. With regards to the first direction, insurance and financial loss data often feature heavy-tailedness, high skewness, and multimodality. Even though the well-known non-Gaussian parametric distribution families such as Student's t, Pareto, Burr, Log-normal, and Weibull can be effectively used to model extremes, they lack flexibility to fit multimodal distribution shapes. Across many research fields, the use of mixtures with multiple components has been one of the most effective ways to model complex data. Along the line with my recent research on length-biased Weibull mixtures for flexible modelling of loss severity data, I aim to study mixture-based models for analysis of various financial/insurance loss data. I will also work on dynamic extensions of mixture models with an ARCH/GARCH type serial dependence structure and some tractable multivariate extensions of mixture-based loss models. The primary applications of these studies include the modelling of catastrophic losses, financial returns, credit, and operational losses. As for the second direction, enterprise-wide or integrated risk management requires consideration of risk measures that can capture interaction or dependence among entities and underlying risk factors. For various purposes, several multivariate extensions of commonly used stand-alone risk measures such as Value-at-Risk and Expected Shortfall, have been proposed in literature. Amongst many, multivariate risk measures with a form of conditional expectation on some scenarios have recently received considerable attention. In line with this, I will study theoretical, practical, and statistical aspects of conditional expectation-based multivariate risk measures with applications to risk aggregation, risk allocation, and systemic market risk assessment. I will consider various classes of multivariate risk models, including copula families, and factor models for market and credit risks. Statistical estimation of multivariate risk measures using some non-parametric or semi-parametric methods will also be pursued.