February 24, 25, 26, 2010

The Distinguished Lecture Series is a series of three lectures. The first lecture is intended for a general audience. This year the lectures will be given by:

William F. Shadwick Managing Director Omega Analysis Limited

Dr. Shadwick has graciously made availble to us the slides of his lectures:

• Lecture 1: The Right Answers to The Wrong Questions
• Lecture 2: Risk (Mis)management and the Financial Crisis
• Lecture 3: The Geometry of Probability Distributions

And the short movie played during the third lecture:

• Omega movie

A poster advertising the event created by John Rader.

February 2010 is the 50th anniversary of Eugene Wigner's On the Unreasonable Effectiveness of Mathematics in the Natural Sciences. In that paper, Wigner speculated that the benefits that mathematics had provided to physics might in future spread to 'wide branches of learning'. In this talk I will survey the history of attempts to apply mathematics in economics and finance. This is a story of missed opportunities in which the right answers to the wrong questions have had a large impact. While this lecture is about mathematics, it is for a general audience and assumes no specialist knowledge of mathematics or finance.

Extreme Value Theory is a branch of statistics which is over 80 years old. Expected Shortfall is the statistical term for the average loss beyond a given threshold. Using Extreme Value Theory to estimate Expected Shortfall is a common risk management practice in the insurance industry. In the Finance Industry risk 'management' has relied instead on normal distributions and Value at Risk. The failure to predict the losses that rocked markets in 2007, 2008 and 2009 was not a failure of markets or an example of the futility of attempting to predict market behavior with statistics. In this talk, I'll provide a brief introduction to the statistics of extremes and show that, if the correct tools had been used, the recent financial crisis (in common with earlier crashes) would have been seen to be all too probable. A cursory knowledge of probability and statistics is the only prerequisite for this material.

In studying probability distributions, a natural specialisation is to consider distributions which have a finite mean. A recently discovered method of describing the probability distributions with this property leads naturally to an affine equivalence problem. The affine geometry of probability distributions reveals remarkable structure including a natural measure of dispersion about the mean, improvements on the Markov and Chebychev inequalities, a new affine invariant and a new central limit theorem. The talk is intended to be accessible to graduate students in Mathematics.

The Speaker:

William F. Shadwick is Managing Director of Omega Analysis Limited, a London based company that specializes in statistical analysis of financial market data.

During his previous career in mathematics, his results ranged from extending work of Elie Cartan to collaborations with NASA on aircraft flight control. He was responsible for establishing the Fields Institute for Research in Mathematical Sciences and was a professor of Mathematics at the University of Waterloo and a professor of Mathematics and Computer and Electrical Engineering at the University of Toronto. He was a member of the Institute for Advanced Study, Princeton, the Mathematical Sciences Research Institute, Berkeley, the Mathematical Sciences Institute, Cornell, the NASA Ames Research Center, the Center for Nonlinear Studies, Los Alamos and the Instituto de Matemćtica Pura e Aplicada (IMPA), Rio de Janeiro. He was elected as a Fellow of the Fields Institute in 2003.

He has continued to be involved in academic research since entering the Finance industry in 1998, as a member of the Steering Committee of the Financial Markets Group at the London School of Economics from 1998 to 2002 and as a founding member of the Steering Committee for the UK Quantitative Finance Network. He has published key contributions to finance theory and practice and has made invited presentations of his work in quantitative finance to leading industry groups and academic centers. Jointly with Ana Cascon, he has pioneered a fundamentally new approach to the study of probability and statistics which continues to generate powerful new tools for performance measurement, risk management and trading strategies. In 2007 Cascon and Shadwick were the recipients of the Journalism Award of the Investment Management Consultant’s Association for their published research on risk and performance measurement.

Location:

For the location of the relevant buildings (Keller Hall, Campus Center, Bilger Hall) consult the campus map.

The Sponsors:

The lectures are sponsored by the National Science Foundation, and the Department of Mathematics and the College of Natural Sciences of the University of Hawaii, Manoa.