The age of regular variation: tales on tails
Symposium on the occasion of Guus Balkema's 65th birthday
| 11.00-11.30 | Coffee and welcome | |
| 11.30-11.35 | Opening | |
| 11.35-12.20 | Paul Embrechts | Ruin, operational risk and how fast stochastic processes mix |
| 12.20-14.00 | Lunch break | |
| 14.00-14.45 | Claudia Kluppelberg | Limit laws for exponential families - theoretical results and applications |
| 14.45-15.30 | Sidney Resnick | Limits of On/Off Hierarchical Product Models for Data Transmission |
| 15.30-16.00 | Tea | |
| 16.00-16.45 | Laurens de Haan | Approximations for the tail (empirical) distribution function |
| 16.45-17.00 | Closing | Closing by Tom Koornwinder (director of the Korteweg-de Vries Institute for Mathematics) |
| 17.00 | Reception |
Programme and abstracts are also available as a ps and a pdf file
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Paul Embrechts: Ruin, operational risk and how fast stochastic processes
mix Due to the new guidelines on banking supervision, operational risk has become a focus of attention for risk managers. This talk is based on joint work with Gennady Samorodnitsky; see here for a copy of the paper. A robustness type of result for heavy-tailed ruin esti- mates in a risk process under a broad class of time change models will be presented. These results will be motivated by questions concerning the quan- titative modelling of Operational Risk. |
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Laurens de Haan: Approximations for the
tail (empirical) distribution function Extreme value conditions have been with us for a long time. Somewhat more recently second order extreme value conditions have been studied and used. The former and the latter can be expressed both in terms of the distribution function and in terms of the quantile function. Recently (1998) Holger Drees derived sharp uniform inequalities connected with the limit relations for the quantile function and showed that these lead to a useful approximation for the tail empirical quantile function. I want to present analogous inequalities connected with the limit relation for the distribution function and show that these lead to a useful approximation for the tail empirical distribution. I shall mention two probabilistic applications but shall not mention any statistical application... (joint work with Holger Drees and Deyuan Li) |
| Claudia Klüppelberg:
Limit laws for exponential families - theoretical results and applications See the ps or the pdf file of the programme for the abstract |
| Sidney Resnick:
Limits of On/Off Hierarchical Product Models for Data Transmission A hierarchical product model seeks to model network traffic as a product of independent on/off processes. Previous studies have assumed a Markovian structure for component processes amounting to assuming that exponential distributions govern on and off periods but this is not in good agreement with traffic measurements. However, if the number of factor processes grows and input rates are stabilized by allowing the on period distribution to change suitably, a limiting on/off process can be obtained which has exponentially distributed on periods and whose off periods are equal in distribution to the busy period of an M/G/ºº queue. We give a fairly complete study of the possible limits of the product process as the number of factors grow and offer various characterizations of the approximating processes. We also study the dependence structure of the approximations. (joint work with Gennady Samorodnitsky) |