Modeling Financial Catastrophe and COVID-19 Super Spreader Events

自2008年以来，金融圈的一个主要问题是，两家大银行（“大到不能倒”）实际上可以同时倒闭。我们提供数学模型来检测这种情况何时发生。要做到这一点，我们需要创造新的理论，超越传统的信用风险模型。事实证明，这种数学模型可以很容易地修改，以模拟流行病传播中的某些问题（例如当前的COVID-19大流行）。特别是，想象一群人参加一个超级传播者活动。假设有很多人会感染这种疾病，其中一部分人需要住院治疗，那么，从健康控制和医院容量控制的角度来看，人们可能想知道两个或两个以上的人同时感染这种疾病的概率。重要的是要注意，在同一事件中接触该疾病的两个人将在不同时间感染该疾病（如果有的话），并且疾病在其体内的进展将取决于大量因素，其中许多因素是未知的，或无法量化；因此需要随机建模。该项目将为参与研究的研究生提供培训机会和支持。在信用风险理论中，违约时间通常通过Cox结构建模，对于两个不同的公司，标准假设是停止时间是有条件独立的，给出可观察事件的潜在过滤。然而，由于在Cox结构中使用了独立的指数随机变量，这种模型不允许同时默认。我们建议用多元指数代替独立指数，例如使用Marshall和Olkin在1967年提出的形式。然后，我们将使用鞅正交性来代替条件独立性，以对默认时间的不同属性进行所需的计算。这个扩展在模拟灾难性信贷事件时尤其有用，例如两家银行同时违约，这两家银行都“太大而不能倒”。我们建议研究的另一类问题是在个体层面上对COVID-19（或其他流行病）的发展进行建模。一个关键的例子是，如果两个人参加“超级传播者”活动，同时接触疾病发展的时间是多少？也许令人惊讶的是，这可以与上面讨论的信用风险问题进行近乎完美的类比。例如，这些模型可用于特定地区的医院准备工作。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

A major problem in financial circles, since 2008, is that two big banks ("too big to fail") actually can fail at the same time. We provide mathematical models to detect when this could happen. To do this we need to create new theory, beyond the traditional models for credit risk. It turns out that such mathematical models can easily be modified to model certain issues in the propagation of epidemics (such as the current COVID-19 pandemic). In particular, imagine that a group of people attend a super spreader event. Assuming more than a few will contract the disease, with a subset needing hospitalization, then - from the standpoint of health control and hospital capacity control - one might want to know the probability of two or more people getting the disease at once. It is important to note that two people exposed to the disease at the same event will contract the disease at different times (if at all), and the progress of the disease within their bodies will depend on a large number of factors, many of which are unknown, or impossible to quantify; hence the need for random modeling. The project will provide training opportunities and support for graduate students to be involved in the research.In Credit Risk Theory, default times are typically modeled via a Cox construction, and for two different companies a standard assumption is that the stopping times are conditionally independent, give the underlying filtration of observable events. Such models do not allow, however, for simultaneous defaults, due to the use of independent exponential random variables used in the Cox constructions. We propose to replace the independent exponentials with multivariate exponentials, using (for example) the form proposed in 1967 by Marshall and Olkin. We will then use martingale orthogonality in place of conditional independence to make the desired calculations of different properties of the default times. This extension should be especially useful when modeling catastrophic credit events, such as the simultaneous default of two banks, both of them being "too big to fail." The other class of problems we propose to study is the modeling of the development of COVID-19 (or other epidemics) on an individual level. A key example is that if two people attend a "super spreader" event, what are the times after simultaneous exposure to the development of disease? Perhaps surprisingly this can be modeled in a near perfect analogy with the credit risk issues discussed above. Such models could be useful for, for example, hospital preparedness in a given locality.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.