Group discussion on Future of EVT
Holger Rootzén – Chalmers University of Technology
& Ross Leadbetter (University of North Carolina – Chapel Hill)

• Subject
  Which future research to deal with extremes?
• Material
  Ross Leadbetter “Extremes under dependence – Personal perspectives”
• Summary of the group discussion:
  It is naïve to believe that one can predict the future of a field with any confidence, but it still may be
  useful to think about what developments may occur, and what are the present trends.

  The following trends which may lead into the future were discussed:

  • Big data and machine learning are at the center of current interest for much of statistics and also pose challenges for extreme value statistics, in general and in finance in particular. Conversely, extreme value methods are clearly relevant to and likely to become even more useful for high-dimensional statistics in general: what one can see in big and high-dimensional datasets are its striking (i.e. extreme) features.
  • Extreme values of random fields are important in climate science, biology and other fields. Development of theory, statistical methods, and application to real problems has started, but this is just a beginning.
  • Bayesian methods are becoming increasingly used in statistics, often for computational reasons. This may happen also to extreme values statistics in finance, but there it entails the extra risk that users tailor priors to produce the outcomes they which to achieve, say lower capital requirements.
  • Other developments which were brought up included nonstationary extremes; random volatility modelling; communication and thinking about risk; asymptotic independence and regime shifts; post crises risk estimation; Robust methods, outlier detection; and topological extremes
  • Miguel de Carvallo contributed a thought-provoking short essay which may be downloaded here.
  • Sergei Novak contributed the following point: “I’d like to see our voice heard and our expertise used. EVT has evolved considerably over the past few decades. Rather accurate methods of estimating measures of risk are now available, including methods of estimating from non- parametric classes of distributions. Meantime central banks are probably not aware of those developments, and banks’ internal methods are probably out of date. Otherwise, how can one explain that no bank expected any problem on the eve of the recent banking crisis, and no central bank could foresee any trouble with any commercial bank? Professor Dacarogna in his talk told us that he wanted the governments to force banks buying insurance against a future bailout. Can we, as a group of experts in EVT, influence central banks in a similar way? If we succeed, that could make a real contribution to improving health of the economy.”

Fellow IMS, Member ISI, co-editor Scandinavian Journal of Statistics, associate editor Annals of Statistics, former editor Extremes and Bernoulli, elected member of the Royal Swedish Academy of Science and of Kungliga Fysiografiska Sällskapet, leader of the Wallenberg project “Big Data and Big Systems – bridging local and global”, senior researcher the Foundation for Strategic Research project Material Structures Seen Through Microscopes and Statistics. Research: In finance, on risk management, credit risk and discrete hedging. General, on martingales and extreme value theory with applications to medicine, wind storm modeling, metal fatigue, pit corrosion analysis, internet traffic, and traffic safety. Has published about 80 papers in international journals, one book which continues to be a highly cited classic, one edited book, and one textbook. To know more…

Ross Leadbetter, University of North Carolina, Chapel Hill
Ross Leadbetter is Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill.
His research involves stochastic process theory and applications, point processes, and particularly extreme value and risk theory for stationary sequences and processes.