Measuring the Risk of Extreme Events ∗ Kay Giesecke † Cornell University Thorsten Schmidt ‡ Universit¨atLeipzig Stefan Weber § Cornell University July 20, 2005 Abstract Event risk is described by the distribution of excessive financial losses due to broad, abrupt shocks. We consider the measurement of event risk in the context of the classical, axiomatic definition of risk measures initiated by Artzner, Delbaen, Eber & Heath (1999). The class of utility-based risk measures is shown to be particularly suited for the detection and quantification of event risk. We illustrate this using standard extreme value distributions. Key words: Distribution-invariant risk measures, utility-based shortfall risk, aver- age value at risk, value at risk, event risk, extreme events * We would like to thank the Isaac Newton Institute Cambridge for its hospitality and financial support. † School of Operations Research and Industrial Engineering, 237 Rhodes Hall, Cornell University, Ithaca, NY 14853, USA, Phone (607) 255 9140, Fax (607) 255 9129, email giesecke@orie.cornell.edu. ‡ Department of Mathematics, Universit¨at Leipzig, Augustusplatz 10/11, 04105 Leipzig, Germany, email Thorsten.Schmidt@math.uni-leipzig.de. § School of Operations Research and Industrial Engineering, 279 Rhodes Hall, Cornell University, Ithaca, NY 14853, USA, Phone (607) 254 4825, Fax (607) 255 9129, email sweber@orie.cornell.edu. 1