Analyzing and Managing Extreme Risks in Insurance and Finance

极端风险来自罕见事件带来的灾难性经济和社会后果；例如，2008年的金融危机直接导致了2008年至2012年的全球经济衰退，以及2016年的麦克默里堡野火，这是加拿大历史上损失最惨重的灾难。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。******对这些极端风险的罕见认识使得它们特别难以预测。极值理论（EVT）提供了一种有效的研究方法。在本文的研究中，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）保险以及极端风险措施的统计推断。同时，当现有技术不适用时，将发展分析和概率技术。******基于上述问题，本文拟研究的目标是：1)分析保险和金融中的重尾和依赖风险；2)完善量化风险管理技术，防范极端风险；3)开发基于分位数的相关极端风险测度的稳健推理方法。本研究将有助于多元风险建模与管理新理论的发展。所提出的方法将对有关极端风险的重要风险管理问题给出分析性答案。将开发定量风险管理技术，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，使统计推断对重要的风险量是可行的。这将提高对极端风险本质的理解，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。******该研究计划每年将在精算科学、应用概率或统计学的顶级期刊上发表2-3篇独立或联合论文。研究生和优秀的本科生将集中参与这个项目。这种培训将导致一些未来的学术研究人员和专业员工应用和进一步扩展这些研究领域。

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.