In my research group, we’re diving into some fascinating challenges within the risk and extremes. We’re developing scalable algorithms for generating extreme events, leveraging novel deep neural network architectures that are informed by extreme value theory (EVT). These are crucial for understanding and predicting rare, high-impact occurrences, whether in climate modeling, finance, or natural disasters.

By pushing the boundaries of EVT, we’re able to create new, more efficient ways to model and simulate these extreme events on a large scale. For example, some of the algorithms that we have produced are among the first asymptotically optimal algorithms for the simulation of max-stable processes—a key area in the study of extremes. Max-stable processes are fundamental to capturing the behavior of extremes across space and time, and our algorithms are designed to handle this complexity efficiently.

Another exciting area is our work on large deviations analysis of stochastic networks. By understanding the probabilities of rare events in these networks, we’ve developed rare event simulation algorithms that are also asymptotically optimal, ensuring that we can accurately and efficiently model rare but critical events in complex systems.

Our work in this space has strong synergies with some of the other topics we’ve been working on. For example, we’re developing distributionally robust extreme value theory estimators, which combine ideas from distributionally robust optimization with EVT to create more resilient models that can perform well even when there’s uncertainty about the underlying distributions.

This blend of stochastic analysis, risk modeling, and cutting-edge algorithm design is helping us tackle some of the most challenging and impactful problems in the study of risk and extremes. It’s an exciting time, and we’re making significant progress in both theory and applications.