Extremes and Risks in Higher Dimensions

Description & Aim

Extreme value theory (EVT) is the branch of probability and statistics dealing with the modeling and the study of extreme and rare events, that is events whose magnitude and occurrence over time is not usual, but rather seen as “extremely different from the average”.

Within EVT, a recent field of research is the one related to multivariate extremes, or extremes in higher dimensions. When dealing with an earthquake, for example, we may not only be interested in the magnitude of the event, but also in its geographical extension, and the tsunami it may cause, when occurring close to the sea. A bank with an enormous portfolio of clients is not only interested in the possible losses coming from that particular counterparty, but also in the aggregated loss generating from the entire portfolio, and in the dependence structure among the different components of the portfolio. And again, when studying tornados, a researcher is often interested not only in the speed of winds, but also in the height of the waves it may generate.

To deal with multivariate extremes (and the related risk), many tools have been and are continuously proposed, from the more or less direct generalization of univariate techniques to new measures of extremal dependence, from copulas to urn-based shock models, from novel results in large deviations to multivariate Gaussian processes. From an applied point of view, multivariate extremes are becoming tremendously important in fields like finance and risk management, where the modeling of dependence, especially for extremal losses (or profits), is of pivotal importance.

In this workshop, thanks to the help of our invited speakers and the 10 contributed papers we will carefully select, we will cover the most important topics related to extremes and risks in higher dimensions. We will focus on the latest findings, and discuss about future trends, with the main aim of fostering new fruitful collaborations. A section with professionals from the financial sector will enrich the discussion from the applied side.