Sensitivity, uncertainty and robustness of risk models in insurance

保险公司面临着独特的风险环境，包括财务风险和保险风险。保险合同的到期日非常长，从而导致长期风险，并且通常被归类为极其异质的投资组合。理解嵌入在这些异质组合的聚合中的风险是非常重要的，特别是由于评估和指定相互依赖的挑战。数值和计算技术的进步，特别是机器学习技术的进步，加速了在整个保险行业中定量、高度复杂的统计模型的使用。通常在金融和保险风险管理中，影响深远的决策是基于模型输出的低维摘要。因此，理解由模型组件的不确定性导致的输出可变性对于做出明智的决策至关重要。风险管理者和监管机构都要求对模型的稳定性、稳健性和敏感性进行量化。本研究计划的愿景之一是开发新的和原创的敏感性和不确定性分析工具，用于金融和保险风险管理模型。因此，解决了来自风险管理者、政策制定者和模型（最终）用户的巨大需求，他们需要可靠的工具来理解和洞察他们的模型的不确定性和局限性。模型组件中的错误规范是普遍存在的，并且是由参数估计、缺失的数据和不准确的数据收集引起的。分析错误规范的传播，即从单个模型组件通过整个模型到模型输出的压力级联，提供了关于模型结构的宝贵信息。具体来说，模型组件之间的依赖关系是应力传播的关键驱动因素，并形成了本提案第二个研究流的核心。理解压力的级联效应在金融风险管理中有应用，如系统风险和压力测试。由于进行压力测试是银行机构和保险公司的监管要求，并且金融体系的系统稳定性是政策制定者最关心的问题，因此本研究建议具有很高的工业应用潜力以及实际和监管相关性。

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.