Oberwolfach-Seminar: Dependence and Tail Modelling with Applications to Finance, Insurance, Teletraffic and Climate

Date:

November 19th - November 25th, 2006

Organizers:

Richard Davis, Fort Collins

Holger Drees, Hamburg

Thomas Mikosch, Copenhagen

Programme:

The analysis of data exhibiting heavy tails often depends on the notion of regular variation (power law behavior of tails) of random variables and random vectors. In the course we show that multivariate regular variation arises in some common linear and non-linear time series models. Therefore it is a very natural concept in this context that also fits nicely into the theory of multivariate extremes. Moreover, the relationship between regular variation and the convergence of certain point processes can be used to derive the large sample behavior of statistics describing the dependence between the observations. Finally, an extension of regular variation to stochastic processes and its applications to large deviations for random walks and Levy processes with heavy tails are discussed.

Prerequisites:

Familiarity with stochastic processes and measure theory.

Literature:

• Davis, R., and Mikosch, T. (2001) Point process convergence of stochastic volatility processes with application to sample autocorrelations. J. Appl. Probab. Special Volume 38A, 93--104.
• Draisma, G, Drees, H., Ferreira, A. and de Haan, L. (2004). Bivariate tail estimation: dependence in asymptotic independence. Bernoulli 10, 251-280.
• Drees, H. (2003). Extreme Quantile Estimation for Dependent Data with Applications to Finance. Bernoulli 9, 617-657.
• Hult, H., and Lindskog, P. (2005) Extremal behavior of regularly varying stochastic processes. Stochastic Process. Appl. 115, 249--274.
• Hult, H., Lindskog, P., Mikosch, T., and Samorodnitsky, G. (2005) Functional large deviations for multivariate regularly varying random walks. Ann. Appl. Probab., 15 (4) to appear.
• Mikosch, T., Resnick, S., Rootzen, H., and Stegeman, A. (2002) Is network traffic approximated by stable Levy motion or fractional Brownian motion? Ann. Appl. Probab. 12, 23--68.

Deadline for applications:

October 1, 2006

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.