CAREER: Catastrophic Rare Events: Theory of Heavy Tails and Applications

Northwestern University, Evanston IL

Investigators

Abstract

This Faculty Early Career Development Program (CAREER) grant will contribute to the advancement of national prosperity and welfare by developing mathematical tools that provide strategies to understand and mitigate risk associated with the "heavy-tail" phenomena. Heavy-tailed distributions provide useful mathematical models for seemingly disparate rare events, such as the global pandemic, the 2012 blackout in India, and the 2007 financial crisis. Beyond such isolated catastrophic events, heavy tails are pervasive in large-scale complex systems and modern algorithms. A particularly simple and well-known manifestation of heavy tails is the so-called “80-20 rule”, whose variations are repeatedly discovered in a wide variety of application areas. Under the presence of heavy tails, high-impact rare events are guaranteed to happen eventually, and may occur more frequently than decision-makers may account for. Accounting for (or even utilizing) the impact inflicted by such rare events will support the design and operation of reliable and resilient systems in many important scenarios, including environmental catastrophes, power system failures, financial crises. The accompanying educational plan aims to broaden STEM interest in underrepresented communities and train future leaders of academia, industry, and government by equipping them with fundamental skills in risk analysis. This research will develop a comprehensive theory of large deviations and metastability for heavy-tailed stochastic systems. The classical theory of large deviations and rare-event simulation has a long history but these approaches and the metastability framework often fall short when the underlying uncertainties are heavy-tailed. This project leverages and extends recent advances in extreme value theory, optimization, control, and stochastic simulation to fill the gap by building large deviations and metastability frameworks tailored for heavy-tailed systems. With the new framework, the project will also address open problems in artificial intelligence and actuarial science. This research will contribute to a rigorous theoretical foundation for designing reliable and accountable AI so that the technology can be applied to high-stake decision-making problems. Successful implementation of such a program will expand our understanding of how system failures and phase transitions arise in many stochastic systems, which, in turn, will provide provably efficient computational machinery for insurance risk management and accountable AI design. 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.