Exploring and exploiting new representations for multivariate extremes

探索和利用多元极值的新表示

• 批准号: EP/X010449/1
• 负责人: Jennifer Wadsworth
• 金额: $ 56.21万
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX010449%2F1
• 关键词: Exploring; exploiting; new; representations; multivariate

In all aspects of life, there is a need to proportionally mitigate against the risk posed by rare but potentially catastrophic events. For example, we protect ourselves from flooding through the construction of defences: in doing so, we balance risk and cost by building these high enough such that the probability of them being breached over their lifetime is small, but not so high that money is wasted on eliminating infinitesimal risks. Usually, we will be trying to protect against extreme events that are larger than we have ever observed, meaning that direct estimation of the probability of breach from existing data is impossible. Extreme value theory is the mathematically-justified approach for tackling this problem: we can learn from extremes we have seen to estimate probabilities of events not yet witnessed.Events that cause the most impact are often multivariate or spatial in nature. For example, damage to a structure may occur during a period of high winds, but that damage could be far more costly when accompanied by high rainfall. Equally, a large loss in a single element of a financial portfolio is less disastrous than multiple losses across the board. In order to understand the risks posed by such phenomena, we need tools for modelling the dependence between processes at extreme levels. To date there are a variety of methods available, each based on different underlying assumptions, and the extent to which these represent good statistical models rests strongly on the unknown underlying dependence. In this work we will exploit novel representations and recently-uncovered links between these methods to unify these disparate methodologies and provide a single, reliable strategy for modelling multivariate extremes.

在生活的各个方面，都需要相应地减轻罕见但潜在灾难性事件带来的风险。例如，我们通过建设防御设施来保护自己免受洪水的侵害：在这样做时，我们通过将防御设施建设得足够高来平衡风险和成本，这样它们在其使用寿命内被破坏的可能性很小，但又不会太高以致浪费金钱。消除无穷小的风险。通常，我们会尽力防范比我们观察到的更大的极端事件，这意味着不可能根据现有数据直接估计违规概率。极值理论是解决这个问题的数学合理方法：我们可以从我们所看到的极端情况中学习，以估计尚未目睹的事件的概率。造成最大影响的事件本质上通常是多变量或空间的。例如，在大风期间可能会发生对结构的损坏，但当伴随着高降雨量时，这种损坏的代价可能要高得多。同样，金融投资组合中单个要素的巨额损失比全面的多重损失的灾难性要小。为了了解此类现象带来的风险，我们需要工具来对极端级别的流程之间的依赖关系进行建模。迄今为止，有多种可用的方法，每种方法都基于不同的基本假设，并且这些方法代表良好统计模型的程度很大程度上取决于未知的基本依赖性。在这项工作中，我们将利用这些方法之间的新颖表示和最近发现的联系来统一这些不同的方法，并为多元极端建模提供单一、可靠的策略。