On New Classes of Control Problems Motivated by Stock Trading

February 21, 2014, Webb 1100

Bob Barmish

University of Wisconsin-Madison, Electrical & Computer Engineering


In this seminar, I will describe some new problems in control theory which are motivated by my last few years of research in the area of stock trading. To this end, I will begin by formulating a “robust positivity” problem which involves keeping a scalar state variable x(t) positive via the use of a feedback control u(x). Robustness considerations enter the picture because the simple nonlinear state equation x˙ = u(x)v(x, t) under consideration includes the disturbance term v(x, t) which can be rather arbitrary. This problem will be used as a vehicle to introduce the notion of “twin control systems” and how they can be used in solution of the positivity problem. In addition, it will serve as a launching point into a discussion of ongoing stock trading research. Beginning from the perspective that stock price models should be distrusted, the controllers under consideration will be model free. That is, no generating mechanism for the stock price is assumed and no parameter identification is involved. The stock-trading controller which we consider is performance driven and based on adaptive adjustment of the investment level I(t) using the trend in the cumulative gains or losses g(t). Such an approach to trading is often described by the words technical analysis. In contrast to the finance literature, where conclusions about technical analysis are drawn based on statistical evidence from the past, the control-theoretic point of view leads to robust certification theorems describing various aspects of performance.

Speaker's Bio

B. Ross Barmish received the Bachelor’s degree in Electrical Engineering from McGill University in 1971. In 1972 and 1975 respectively, he received the M.S. and Ph.D. degrees, both in Electrical Engineering, from Cornell University. From 1975 to 1978, he served as Assistant Professor of Engineering and Applied Science at Yale University. From 1978 to 1984, he was as an Associate Professor of Electrical Engineering at the University of Rochester and in 1984, he joined the University of Wisconsin, Madison, where he is currently Professor of Electrical and Computer Engineering. From 2001 to 2003, he was with the Department of Electrical Engineering and Computer Science at Case Western Reserve University, where he served as Department Chair while holding the endowed Nord Professorship.
Over the years, he has been involved in a number of IEEE Control Systems Society activities such as associate editorships, conference chairmanships, the Board of Governors and prize paper committees. He has also served as a consultant for a number of companies and is the author of the textbook New Tools for Robustness of Linear Systems, Macmillan, 1994. While his earlier work concentrated on robustness of dynamical systems, his current research concentrates on building a bridge between feedback control theory and trading in complex financial markets.

Professor Barmish is a Fellow of both the IEEE and IFAC for his contributions to the theory of robustness of dynamical systems. He received the Best Paper Award for Journal Publication in Automatica, covering a three-year period, on two consecutive occasions from the International Federation of Automatic Control.
He has also given a number of plenary lectures at major conferences. In December 2012, Professor Barmish was named by the IEEE Control SystemsSociety as the winner of the 2013 Bode Prize. In conjunction with this field award, he provided a keynote plenary at the 2013 IEEE Conference on Decision and Control, held in Florence, Italy.

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