Statistical modelling and measuring risks in banking and insurance

我正在进行的研究计划的目标是了解金融和保险市场固有的风险的潜在概率和统计结构，并开发新的数据分析模型和方法，为这些不稳定的行业提供改进的风险评估工具。本建议中的问题类别考虑了各种风险模型和方法的理论方面和实际应用。具体而言，在定量风险分析的背景下，我的研究计划将在以下两个方向进行：（1）混合损失数据的统计建模;（2）多变量风险的测量。关于第一个方向，保险和金融损失数据通常具有重尾性，高偏度和多模态。尽管众所周知的非高斯参数分布族（如Student's t、Pareto、Burr、Log-normal和Weibull）可以有效地用于对极值进行建模，但它们缺乏拟合多峰分布形状的灵活性。在许多研究领域中，使用多组分混合物一直是对复杂数据建模的最有效方法之一。沿着线与我最近的研究长度偏威布尔混合灵活建模的损失严重程度的数据，我的目标是研究基于混合的模型分析各种金融/保险损失数据。我还将致力于动态扩展的混合模型与一个mixture-based损失模型的一个mixture-based/Gother-type串行依赖结构和一些易于处理的多元扩展。这些研究的主要应用包括灾难性损失、财务回报、信贷和运营损失的建模。至于第二个方向，全系统或综合风险管理需要考虑风险措施，这些措施可以反映各实体之间的相互作用或相互依赖关系以及潜在的风险因素。为了不同的目的，文献中已经提出了一些常用的独立风险度量（如风险价值和预期短缺）的多变量扩展。在众多的风险度量中，具有条件期望形式的多变量风险度量最近受到了相当大的关注。与此相一致，我将研究基于条件期望的多变量风险度量的理论、实践和统计方面，并将其应用于风险聚合、风险分配和系统性市场风险评估。我将考虑各种类型的多变量风险模型，包括Copula族，以及市场和信用风险的因子模型。还将采用一些非参数或半参数方法对多变量风险度量进行统计估计。

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.