Models and Methods for Multivariate Risk Assessment

多元风险评估的模型和方法

• 批准号: RGPIN-2019-05462
• 负责人: Nolde, Natalia
• 金额: $ 1.82万
• 依托单位: University of British Columbia
• 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=765719
• 关键词: Models; Methods; Multivariate; Risk; Assessment

Risk assessment lies at the core of risk management and risk mitigation in areas such as finance, insurance, hydrology, geoscience and engineering. The key ingredients in risk assessment are a probabilistic model describing the stochastic behaviour of the underlying system, an estimation procedure linking the data at hand to the model and a functional used as a measure of risk. The overarching goal of the proposal is to contribute to a more realistic and accurate modelling of risk in a variety of multivariate settings via development of flexible modelling frameworks and effective estimation methods that are specifically designed to deal with extreme values of the underlying processes and data sparsity in the risk regions of interest. Risk is intrinsically linked to extreme and hence rare events. The approaches we investigate involve a parametric modelling component in order to gain estimation efficiency in the face of data sparsity. However, reliance is made upon asymptotic approximations in the spirit of extreme value theory in order to develop methods that work in the tail regions of considered physical processes. As data in the real world exhibit different stochastic properties, a variety of settings need to be explored in order to accurately capture important data characteristics. The proposal covers three themes based on probabilistic settings considered for the data. The financial crisis of 2007-2009 highlighted the importance of systemic financial risk and its potential to destabilize the global economy. One popular measure of systemic risk is CoVaR. A methodology is proposed to estimate CoVaR semi-parametrically within the classical framework of multivariate extreme value theory. This framework covers heavy-tailed financial data, which exhibit what is known as tail dependence. While this setting is typical for many financial time series, several empirical studies indicated situations where asymptotic independence may be a more appropriate assumption. More revealing in this context are models with light tails, of which the multivariate Gaussian distribution is a standard example. Estimation of multivariate risk measures in the setting of light-tailed distributions with the property of asymptotic independence presents particular technical challenges both in terms of probabilistic approximations and inference, which will be explored as part of the research program. Finally, the third theme is devoted to the idea of bridging between the two paradigms of asymptotic dependence and independence by considering construction of models using a shape set, whose geometry is related to extremal properties of the underlying distribution and hence has the potential to capture the two situations in a unifying way.

风险评估是金融、保险、水文、地球科学和工程等领域风险管理和减轻风险的核心。风险评估的关键要素是描述基础系统随机行为的概率模型、将手头数据与模型联系起来的估计程序以及用作风险度量的函数。该提案的总体目标是，通过制定灵活的建模框架和有效的估计方法，促进在各种多变量环境中建立更加现实和准确的风险建模，这些框架和方法专门设计用于处理相关风险区域的基本过程的极端值和数据稀疏性。风险与极端事件有着内在的联系，因此也是罕见的事件。我们调查的方法涉及参数建模组件，以获得估计效率，面对数据稀疏。然而，依赖于渐近近似的极值理论的精神，以开发的方法，在考虑的物理过程的尾部区域的工作。由于真实的世界中的数据表现出不同的随机属性，因此需要探索各种设置以准确地捕获重要的数据特征。该提案涵盖了三个主题的基础上考虑的数据的概率设置。2007-2009年的金融危机凸显了系统性金融风险的重要性及其破坏全球经济稳定的潜力。一个流行的系统性风险度量是CoVaR。在经典的多元极值理论框架下，提出了一种半参数估计CoVaR的方法。这个框架涵盖了厚尾金融数据，表现出所谓的尾部依赖。虽然这种设置是典型的许多金融时间序列，一些实证研究表明，渐近独立的情况下，可能是一个更合适的假设。在这种情况下，更有启发性的是具有轻尾的模型，其中多变量高斯分布是一个标准的例子。在具有渐近独立性的轻尾分布的情况下，多变量风险度量的估计在概率近似和推断方面都提出了特殊的技术挑战，这将作为研究计划的一部分进行探索。最后，第三个主题是致力于两个范例之间的桥梁的想法，考虑建设的模型使用的形状集，其几何形状是相关的极值属性的基础分布，因此有可能捕捉到这两种情况下，在一个统一的方式。