Long range dependence, heavy tails and rare events.


MaPhySto Centre for Mathematical Physics and Stochastics Funded by The Danish National Research Foundation	CAF Centre for Analytical Finance Funded by The Danish Social Science Foundation	DYNSTOCH Statistical Methods for Dynamical Stochastic Models EU Research Training

Advanced Concentrated Course on

Long Range Dependence, Heavy Tails and Rare Events

with Applications to Finance and Telecommunications

Main Lectures by

Gennady Samorodnitsky (Cornell University)

Further Lectures by:

Søren Asmussen (Lund), Patrik Albin (Chalmers), Dima Korshunov (Heriot Watt), Ilkka Norros (VTT Helsinki), Murad Taqqu (Boston), Stan Zachary (Heriot Watt) Bert Zwart (INRIA)

Monday, May 6, 2002 - Friday, May 10, 2002

University of Copenhagen

The Advanced Concentrated Course will be given at the Institute of Mathematical Sciences, University of Copenhagen. There will be 5 hours of lectures per day. The course is organized by Søren Asmussen (University of Lund), Thomas Mikosch (University of Copenhagen) and Michael Sørensen (University of Copenhagen)

Description of Gennady Samorodnitsky's course

The notion of long range dependence has traditionally been defined through a slow decay of correlations. This approach may be completely inappropriate in the case of a stochastic process with heavy tails. Yet long memory has been reported to be found in various fields where heavy tails are a standard feature of the commonly used stochastic models. Financial and communications networks data are among those often believed to exhibit long memory. Furthermore, even if the tails are not ``too heavy'', correlations may carry only very limited information, as anyone familiar with GARCH modeling knows.

Rare events are, by definition, those events that do not occur very often. The theory of large deviations studies how rare events occur; the acquired wisdom in that theory is that ``rare events occur in the most likely way''. This means that most of the ways a rare event can occur are so unlikely in comparison to the event itself that they are not even worth mentioning. Only very special ways a rare event can happen are most likely to cause the event; and the study of how rare events happen turns out to be useful when talking about long range dependence.

Starting with classical ideas on heavy tails, long range dependence and large deviations, we will try to show how these ideas can be combined into a fruitful point of view on the length of memory in a stochastic system. Areas of applications discussed will include finance and risk, communication networks and climate related issues.

The following distinguished researchers have agreed to give supplementary lectures on topics related to finance, telecommunications, risk and extremes: Patrik Albin (Chalmers University Gothenburg), Søren Asmussen (University of Lund), Dima Korshunov (Heriot Watt) Ilkka Norros (VTT Helsinki), Murad Taqqu (Boston University), Stan Zachary (Heriot Watt) Bert Zwart (INRIA).

The Advanced Concentrated Course aims at the graduate student in probability theory, statistics, finance, telecommunications and the researcher who wants to get an overview of methods and techniques on modeling heavy tails, long range dependence and rare events given by some of the leading specialists.

Registration and Accommodation

There will be a registration fee of 500 DKK, and the participants are expected to have their expenses covered by their home institutions or from other sources.

Please register via the registration form at your earliest convenience before May 1, 2002.

If you wish that we book accommodation for you please indicate this on the registration form.

The Course starts on Monday, 6 May, 10 a.m. and finishes on Friday, 10 May, 12 a.m.

List of Participants

Tentative Programme and Recent Information

Since the course will be given during the teaching period, the lectures will be given in different buildings on campus. Precise information about the programme and the location of the lecture halls will be provided at the registration.

Lunches are provided in Krogh's Kokken on campus Monday-Wednesday. Notice that Thursday is an official holiday in Denmark and the canteens will be closed. Lunches on Thursday and Friday will be provided in the Mathematics Institute at the HC Ørsteds Institute. Prices of lunches are included in the registration fee.

Those participants who have not paid the registration fee are kindly asked to pay at the registration.

We intend to have an informal conference dinner on Wednesday which is not included in the registration fee. Those who want to joint the dinner are kindly asked to indicate their interest at the registration.

Those participants who will not stay until the end of the course and do not need lunch on Friday are kindly asked to indicate this at the registration.

One lecture lasts about 50 minutes, and we intend to have breaks of 10 minutes between the lectures.

Copies of Gennady Samorodnitsky's transparencies and other material will be handed out to the participants at the registration.

09.30-10.00 Registration in the Lobby of the HC Ørsteds Institute (see below for information how to get there)

Two applications of phase-type distributions to telecommunications and insurance (abstract),

Subexponential distributions revisited: local behaviour of convolutions (abstract),

Extremes of random walks with heavy-tailed increments, with applications to queueing models (abstract),

More Information

We have a page with information on how to get to the HC Ørsteds Institute, where the Course will be given.

Do not hesitate to contact the MaPhySto secretariat (maphysto@maphysto.dk), the secretaries of the Laboratory of Actuarial Mathematics (Actuarial@act.ku.dk) or the local organizers Thomas Mikosch (mikosch@math.ku.dk) and Michael Sørensen (michael@stat.ku.dk) for more information.

This document was last modified November 22, 2001. Questions or comments to the contents of this document should be directed to Actuarial@act.ku.dk.