CMX Lunch Seminar
William F. Shadwick is Managing Director of Omega Analysis Limited. During his previous career in mathematics he was responsible for establishing the Fields Institute for Research in Mathematical Sciences and worked in many prestigious institutions, including the Institute for Advanced Study, Princeton, the Mathematical Sciences Research Institute, Berkeley, IMPA, Brazil and the NASA Ames Research Center. 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. Cascon and Shadwick were the recipients of the 2007 Journalism Award and the 2010 Edward D. Baker III Journal Award of the Investment Management Consultant’s Association for their published research on risk and performance measurement. In 2010, Shadwick was the University of Hawaii Mathematics Department’s Distinguished Lecturer. In October 2016, Omega Analysis came second, Highly Commended for ‘Best Economic Research’ in Investment Week’s inaugural Research Awards. In 2017, Omega Analysis was shortlisted in 2 categories, Best Research Report and Best Research Service in the Investment Week Research Awards. In 2018 Omega Analysis’ proprietary statistical tools won Investment Week’s Research Award for ‘Best use of technology’ and the company was an Equitywire finalist for Best U.S.Equity Research. Both Ana Cascon and William Shadwick are currently on a extended visit to IMPA, the national mathematics research institute in Brazil. Omega Analysis' risk technology is a truly revolutionary advance, not an incremental one. Based on new discoveries in fundamental mathematics and statistics, it provides unprecedented accuracy in measuring risk–and therefore unprecedented opportunities for controlling it.
We show that the Gompertz Function provides a generically excellent fit to viral and bacterial epidemics and endemic data. There is a ‘good' Gompertz Function fit for each time t, starting very early in any outbreak. Successive fits provide excellent forecasts for extended periods.
Examples include Influenza in 2017-18 and Covid-19 in the Spring of 2020 and the ‘second waves'.
The Gompertz Function's features have consequences for herd immunity and for the transition from epidemic to endemic diseaseâ€"which we argue is what we are now seeing in the so-called second waves.
We conjecture that the accuracy of the Gompertz Function fits is not a coincidence but reflects the human immune response to viral and bacterial infections that has evolved over millions of years. Based on the Gumbel distribution, which is one of the exceptional distributions for the geometry induced by the action of the ‘location-scale' group, it has a natural Hamiltonian structure an the energy is a key observable of the epidemic dynamics.
Finally, we illustrate the use of Extreme Value Theory to predict potential surges in the early phase of outbreaks where the Gompertz Function's predictive power is lowest.
The talk is based on joint work with Ana Cascon.