Modeling risk in complex systems

复杂系统中的风险建模

• 批准号: RGPIN-2022-03614
• 负责人: Neslehova, Johanna
• 金额: $ 2.7万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759075
• 关键词: Modeling; risk; complex; systems

The increasing digitalization, urbanization, and interconnectedness of human economies come with growing vulnerability to natural and man-made catastrophes. Risk management and disaster preparedness are thus of paramount importance for society and sustainable development. In continuation of my previous NSERC Discovery Grant, the long-term vision of the proposed research program is to provide tractable and flexible models for risk management. My long-term goals are to develop statistical models and inference techniques to unravel complex dependence patterns in large collections of risk factors and to quantify causal effects on, and of, extremes. The quantification of complex and possibly extreme risks requires techniques beyond traditional approaches rooted in normality, correlation, and regression. The first short term objective is to advance my ongoing work on copula models, which can capture relationships that can't be adequately accounted for by traditional distributions. Using rank-based techniques, I will develop methodology for copula models for mixed data and devise tests of independence for arbitrary distributions in high dimensions. My recent results on the empirical multilinear copula process will also be used to validate generalized linear models. I further aim to find dependence patterns in large collection of variables through learning algorithms and functional data analysis techniques. The second short term goal will focus on statistical analysis of extremes. I will investigate the limiting behavior of, and develop inference for, maxima of dependent risks such as insurance claims in a common portfolio which may be dependent due to common external factors. I will further study flexible max-id models for maxima in the medium regime for which the standard extreme-value theory does not apply. Machine learning will be used to study 0-1 patterns that arise in the context of extreme phenomena, such as floods or heatwaves. To help understand the causes of natural hazards and improve their forecasts, the third short-term goal is to study quantile treatment effects for high quantiles and structure learning algorithms for extremes. The proposed research program will significantly impact the way researchers assess risk in complex systems. The methodology for multivariate data and rare events that will be developed will allow to capture much more versatile dependence patterns and data structures than those accounted for by traditional statistical models. The research will make advances in extreme-value analysis, dependence modeling, and causal inference which are of interest to a wide statistical audience. The proposed methods will further lead to improved practices in insurance, risk management, and natural hazard forecasting. The results will be disseminated broadly through journal articles and talks in Canada and abroad; software will be made available to end-users through the R Project for Statistical Computing.

人类经济的数字化、城市化和互联程度不断提高，同时也越来越容易受到自然和人为灾难的影响。因此，风险管理和备灾对于社会和可持续发展至关重要。延续我之前的 NSERC 发现资助计划，拟议研究计划的长期愿景是为风险管理提供易于处理且灵活的模型。我的长期目标是开发统计模型和推理技术，以揭示大量风险因素中复杂的依赖模式，并量化极端情况的因果影响。 复杂且可能极端的风险的量化需要超越基于正态性、相关性和回归的传统方法的技术。第一个短期目标是推进我正在进行的 copula 模型工作，该模型可以捕获传统分布无法充分解释的关系。使用基于排名的技术，我将开发混合数据的 copula 模型方法，并设计高维度任意分布的独立性测试。我最近关于经验多线性联结过程的结果也将用于验证广义线性模型。我的进一步目标是通过学习算法和功能数据分析技术来找到大量变量中的依赖模式。第二个短期目标将侧重于极端情况的统计分析。我将研究相关风险最大值的限制行为，并对其进行推断，例如公共投资组合中的保险索赔，这些风险可能由于常见的外部因素而相关。我将进一步研究标准极值理论不适用的中等状态下最大值的灵活 max-id 模型。机器学习将用于研究洪水或热浪等极端现象中出现的 0-1 模式。为了帮助了解自然灾害的原因并改进其预测，第三个短期目标是研究高分位数的分位数处理效果和极端情况的结构学习算法。拟议的研究计划将极大地影响研究人员评估复杂系统风险的方式。将开发的多变量数据和罕见事件的方法将允许捕获比传统统计模型所解释的更通用的依赖模式和数据结构。该研究将在极值分析、依赖性建模和因果推理方面取得进展，这些都是广大统计受众感兴趣的。所提出的方法将进一步改进保险、风险管理和自然灾害预测方面的实践。研究结果将通过加拿大和国外的期刊文章和讲座广泛传播；软件将通过 R 统计计算项目提供给最终用户。