The University of Hawai`i Mathematics Department’s 2010 Distinguished Lecture series

Managing Director, Omega Analysis Limited, London, UK

GENERAL AUDIENCE LECTURE
The Right Answers to The Wrong Questions
A Brief History of Mathematics in Finance

Abstract: 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.

Risk (Mis)management and the Financial Crisis
The Impact of the All Too Probable

Abstract: 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.

The Geometry of Probability Distributions
A New Source of Statistics

Abstract: In studying probability distributions, a natural specialization 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.

Three lectures on mathematical finance