Modeling Financial Catastrophe and COVID-19 Super Spreader Events

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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.