MULTIVARIATE EXTREMAL EVENTS AND MARKET STRESS SCENARIOS

Paul Embrechts
(joint work with A.A. Balkema)

Abstract

A new, more geometrically oriented theory for multivariate extremes will be presented. This theory is motivated by the need to model the limit conditional distribution of high-dimensional random vectors, given that the vector takes values in a remote hyperplane. The latter corresponds to a so-called market stress scenario. The theory yields a natural generalixation of the Generalised Pareto Laws in the one- dimensional case. We will discuss both the conditional limit laws as well as their domains of attraction. Applications to financial risk management will be indicated.