Value at Risk (VaR) is a tool widely used in financial applications to assess portfolio risk. The historical stock return data used in calculating VaR may be sensitive to rare news events that occur during the sampled period and cause trend disruptions. Therefore, in this paper, we measure the effects of various news events on stock prices. Subsequently, we identify irregular events using a Poi...

The more tests we perform on a set of data, the more likely we are to reject the null hypothesis when it is true (i.e., a “Type I” error). This is a consequence of the logic of hypothesis testing: We reject the null hypothesis if we witness a rare event. But the larger the number of tests, the easier it is to find rare events and therefore the easier it is to make the mistake of thinking that t...

Extreme events are defined as extreme high (or low) values of whatever statistics of the output of the system we are interested in. These values play an important role because they may correspond to abnormal or dangerous operating conditions. Classical statistical inference techniques provide a good description of central behaviour, but not of extreme events. This was our motivation for resorti...

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role of " large deviations " is best understood through an example. Suppose that X random variables, for instance, normally distributed with mean zero and variance 1. Then, E e θ(X 1 +···+X n) = E[e θX ...

We use the theory of large deviations to study the pricing of investment-grade tranches of synthetic CDO’s. In this paper, we consider a simplified model which will allow us to introduce some of the concepts and calculations.

The type species of the monotypic beetle genus Rioneta Johnson, 1975, previously known from three specimens, is rediscovered in the Uluguru Mountains, Tanzania. A second sympatric species, R. inexpectata sp.n., is described. The relatively rare event of apparently obligate aptery in Ptiliidae is reported. The genus Rioneta, as well as Leptinla Johnson, 1985, are removed from the non-monophyleti...

Filicide (the killing of a child by a parent) followed by the offender’s suicide is a tragic but, fortunately, rare event. The contexts and circumstances surrounding filicide-suicide may provide insight into parental psychology. We tested several hypotheses about filicidesuicide using a database that includes incident-level information on 11,018 homicides committed in Chicago during the years 1...

Extreme Value theory is part and parcel of any study of order statistics in one-dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum “interpoint distance,” in multi-dimensions. We show that for the spherically symmetric families of densities, these statistics have a Gumbel type limit, generalizing several existing result...

Special Issue A Comparison of Shewhart Individuals Control Charts Based on Normal, Non-parametric, and Extreme-value Theory‡ M. B. (Thijs) Vermaat1, Roxana A. Ion2, Ronald J. M. M. Does1,3,∗,† and Chris A. J. Klaassen1,3 1Institute for Business and Industrial Statistics of the University of Amsterdam, IBIS UvA BV, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands 2Eurandom, PO Box 51...