Mathematics, stock markets, floods and other risks

Mathematicians, bankers and analysts use ideas from extreme events like natural disasters: earthquakes, floods or avalanches. The mathematics section of EPFL, in cooperation with ETHZ, has put in place a training program on Quantitative Risk Management, intended for Risk Managers.


The modelling of rare events enables improvements in anticipative risk management, by helping to estimate the probabilities of the occurrences of these events, such as earthquakes and dramatic events like the one currently afflicting Japan, or stock-exchange crashes. These phenomena are not covered by classical probability distributions, exemplified by the well-known bell-curve, the classical Gaussian density. Only relatively recently introduced in some areas, this statistical research into extremes has been applied with success by Valérie Chavez, Anthony Davison, and other members of the EPFL Chair of Statistics.

Extreme Value Theory is used by scientists to estimate the characteristics of exceptional events, such as their frequency, their severity and their probability of arising at a given time. The resulting statistical methods may be regarded as risk prevention tools, with potential for use in many different domains.

Saturated markets

The accumulation of phenomenal financial losses over the last few decades has defined a new field of application for the statistics of extremes, where standard methods fail. The Basel Committee on Banking Supervision requires banks to have a minimum reserve capital proportional to their risks. The estimates of risks linked to credit and markets have also been reviewed. The challenges faced by these models is to take into account the interdependence of the risk factors, in order to correspond to reality.

Together with Anthony Davison and Paul Embrechts (ETHZ), Valérie Chavez tries to raise the awareness of Risk Managers and to introduce them to these methods through training, but there is still a lot of work to do. “The awareness of the use and power of the models linked to extremes is still too recent in many fields”, she explains.

In the environmental area, the application of these statistics is more firmly established, especially with regard to forecasts of risks of earthquakes or flooding. Under the supervision of Anthony Davison, various partnerships are in place. For example, with the Institute for Atmospheric and Climate Science at the ETH (IACETH) in the case of atmospheric ozone; with the Institute for Snow and Avalanche Research (SLF) in the case of snow and permafrost, and the Federal Office for the Environment (FOEN) for flooding. Anthony Davison is also a co-organiser of a week-long workshop on environmental risks and extreme events, to be held in Ascona in July 2011.

Links:
http://stat.epfl.ch/
http://stat.epfl.ch/ascona2011
http://www.math.ethz.ch/~valerie/QRM.pdf


Author: Nicolas Guérin
Source: EPFL