Annual Report 2008.pdf - SAMSI

mrl@stat.unc.edu
“When EVT May be Inappropriate for Risk Assessment – Some Issues and Cases”
To many of us it seems natural to attempt to formulate almost any assessment of risk or system
failure probability within the context of Extreme Value Theory, using as elaborate a framework
(e.g. multivariate) as seems necessary to induce a reasonable “fit”. Arising from occasional
embarrassing personal experiences, we have in the past urged caution in such knee-jerking
application. Here we plan to briefly revisit a few of the situations in which ill-considered use of
the asymptotic theory can seem attractive but be inappropriate, drawn from environmental
regulation, and problems of integrity and stability of ocean structures and vessels in storms.
Alternative approaches will be indicated for capsize risk of vessels in following seas. (This topic
involves joint work with Igor Rychlik and Armelle Guillou)
Thomas Mikosch
University of Copenhagen
mikosch@math.ku.dk
“Regularly Varying Functions”
Regular variation plays an important role in extreme value theory, summation theory, and time
series analysis. We start by looking at some functions of regularly varying vectors (linear
combinations and products with regularly varying components). Then we consider solutions to
stochastic differential equations driven by an alpha-stable Levy motion and show that its finitedimensional
distributions are regularly varying (joint work with Serge Cohen). Then we switch
to the notion of infinite-dimensional regular variation and its connections with large deviations
for processes with heavy-tailed marginal distributions (joint work with Henrik Hult, Filip
Lindskog and Gennady Samorodnitsky).
Pilar Munoz
Technical University of Catalonia
pilar.munyoz@upc.edu
“Price, Volatility and Risk in the Electricity Markets”
During the last 15 years, the liberalization and deregulation of the electricity markets in
developed countries have triggered important changes on the management of electricity
companies as well as on their largest customers, due to the price volatilities and the changing
market conditions.
One of the restrictions of the Electricity Markets is that instantaneous supply and demand must
be balanced, in general every hour, and that the market clearing price is gotten from matching the
cumulative demand and supply curves.
As a traded commodity, electricity is becoming well-known for its volatility being orders of
magnitude higher than it is generally observed in other financial markets; yet effective price risk
management is a crucial component of business performance in this sector, being price volatility