Analyzing and Managing Extreme Risks in Insurance and Finance

极端风险来自伴随灾难性经济和社会后果的罕见事件；例如，直接导致2008年全球经济衰退的2008年金融危机，以及2016年麦克默里堡野火，这是加拿大历史上代价最高的灾难。这些在统计数据中产生异常值的人为或自然灾害，都对金融市场和(再)保险业产生了重大影响。由于这些灾难性的后果，一个运作良好的风险管理系统至关重要。 这些极端风险的稀缺性使得它们尤其难以预测。极值理论(EVT)为研究它们提供了一种有效的方法。在拟议的研究中，EVT将成为研究各种风险管理问题的重要工具箱，如投资组合多样化、巨灾风险的(再)保险以及极端风险度量的统计推断。同时，当现有技术不适用时，将开发分析和概率技术。 基于上述问题，建议的研究目标是：1)分析保险和金融领域的重尾和相依风险；2)改进量化风险管理技术，以防范极端风险；3)开发基于分位数的相依极端风险度量的稳健推理方法。这项研究将有助于多元风险建模和管理的新理论的发展。建议的方法将对有关极端风险的重要风险管理问题给出分析答案。将开发量化风险管理技术，以在实践中改进CAT债券的设计和估值，从而减轻极端风险，例如加拿大的野火风险。将开发稳健的估计方法，以便对重要的风险量进行统计推断是可行的。这将提高对极端风险性质的理解，从而帮助保险公司在实践中更好地预测、评估和管理这些风险。 这一研究计划每年将发表2-3篇独著或联合论文，发表在精算学、应用概率或统计学的顶级期刊上。研究生和优秀的本科生将集中参与这个项目。这一培训将使一些未来的学术研究人员和专业员工进一步应用和扩展这些研究领域。

Extreme risks come from rare events accompanied by disastrous economic and social consequences; for example, the 2008 financial crisis, which directly led to the 2008 2012 global recession, and the 2016 Fort McMurray wildfire, which is the costliest disaster in Canadian history. These man-made or natural catastrophes, which produce outliers in statistical data, all substantially affect the financial markets and (re)insurance industry. Due to these disastrous consequences, a well-functioning risk management system is of crucial importance. The rareness of these extreme risks makes them especially hard to predict. Extreme Value Theory (EVT) provides an efficient way to study them. In the proposed research, EVT will be an important toolbox to investigate various risk management questions, such as the portfolio diversification, the (re)insurance of catastrophic risks, and the statistical inference of measures for extreme risks. In the meantime, analytical and probabilistic techniques will be developed when existing techniques are not applicable. Based on the aforementioned questions, the objectives of the proposed research are: 1) to analyze the heavy-tailed and dependent risks in insurance and finance; 2) to improve quantitative risk management techniques to protect from extreme risks; 3) to develop robust inference methods for quantile-based measures of dependent extreme risks. This research will contribute to the development of new theories in multivariate risk modeling and management. The proposed methods will give analytical answers to important risk management questions concerning extreme risks. Quantitative risk management techniques will be developed to improve the design and valuation of CAT bonds in practice, and, therefore to mitigate extreme risks, for example wildfire risks in Canada. Robust estimation methods will be developed such that statistical inferences are feasible for important risk quantities. This will improve the understanding of the nature of extreme risks, and therefore help insurers to better predict, evaluate and manage these risks in practice. This research program will produce 2-3 sole-authored or joint papers per year to be published in top tier journals in actuarial science, applied probability or statistics. Graduate students and exceptional undergraduate students will be intensively involved in this program. This training will lead to a number of future academic researchers and professional employees applying and extending these areas of research even further.