NDLI: On stock trading using a PI controller in an idealized market: The robust positive expectation property

Content Provider	IEEE Xplore Digital Library
Author	Malekpour, S. Primbs, J.A. Barmish, B.R.
Copyright Year	2013
Description	Author affiliation: Dept. of Syst. Eng., Univ. of Texas, Dallas, TX, USA (Primbs, J.A.) \|\| Dept. of Electr. & Comput. Eng., Univ. of Wisconsin, Madison, WI, USA (Malekpour, S.) \|\| Dept. Of Electr. & Comput. Eng., Univ. of Wisconsin, Madison, WI, USA (Barmish, B.R.)
Abstract	In a number of recent papers, a new line of research has been unfolding which is aimed at using classical linear feedback control in a model-free stock trading context. The salient feature of this approach is that no model for stock price dynamics is used to determine the dollar amount invested I(t). Instead, the investment level is performance driven and generated in a model-free manner via an adaptive feedback on the cumulative gains and losses g(t). One of the main results obtained to date is paraphrased as follows: Under idealized market conditions with stock prices governed by a non-trivial Geometric Brownian Motion (GBM), a combination of two static linear feedbacks, one long and one short, leads to a positive expected value for the trading gain g(t) for all t > 0. Since this holds independently of the parameters underlying the GBM process, it is called the “robust positive expectation” property. Working in this same GBM setting, the main objective in this paper is to generalize this result from static to dynamic feedback. To this end, we consider a Proportional-Integral (PI) controller for the investment function I(t). Subsequently, we reduce the stochastic trading equations for the expectation of g(t) to a classical second order system and use the closed- form solution to prove that the robust positive expectation property still holds. We also consider a number of other issues such as the analysis of the variance of g(t) and the monotonic dependence of g(t) on the feedback gains. Finally, we provide simulations showing how the PI controller performs in a real market with prices obtained from historical data.
Sponsorship	IEEE Control Syst. Soc.
Starting Page	1210
Ending Page	1216
File Size	1327400
Page Count	7
File Format	PDF
ISBN	9781467357142
ISSN	07431546
e-ISBN	9781467357173
DOI	10.1109/CDC.2013.6760047
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-12-10
Publisher Place	Italy
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Ear Equations Mathematical model
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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