Extreme Value Theory

In the summer semester 2002 this two-hour course is given jointly by Prof. Dr. Paul Embrechts and Prof. Dr. Alexander McNeil. Based on the textbook

P. Embrechts, C. Klüppelberg and T. Mikosch:
Modelling Extremal Events for Insurance and Finance,
Springer-Verlag, Berlin (1997)

both the theory and applications of extreme value theory (ETV) will be presented.

Topics treated on the more methodological side include:

• Basic limit theorems in EVT (comparing and contrasting sums and maxima of i.i.d. random variables),
• Point process methods,
• Theory of order statistics,
• Statistical theory of extremes: Maximum-likelihood estimators, Peaks over thresholds, Hill-type estimation,
• Multivariate extremes and extremes of processes.

Applications include:

• Analysing heavy-tailed data in insurance and finance,
• Risk Management (enhancing Value-at-Risk).

Instructions for Using EVIS at ETH

1. Log onto a Sun workstation
2. Download the file evis4.zip from http://www.math.ethz.ch/~mcneil/ftp/
3. Create a directory Slibrary in your home directory and unzip evis4.zip into this directory
4. Start S-PLUS with command: Splus -g
5. Make evis library available with command: assign(where = 0, "lib.loc", "/afs/ethz.ch/users/m/username/Slibrary") substituting for username as appropriate
6. Attach library with command: library(evis4)
7. Download the EVIS worksheet at http://www.math.ethz.ch/~mcneil/protected/worksheet_evis.html using the username and password you receive in lecture course

Some Extra Literature

• Brief notes on likelihood theory.