On stock trading using a controller with delay: The Robust Positive Expectation Property

Abstract

This paper is part of a new line of research involving the use of a model-free controller to trade stock. The main result is a discrete-time version of the so-called Robust Positive Expectation Theorem which includes delay in the controller. To date, no results in the literature are available for this delay case. Motivated by robustness considerations and consistent with existing work, neither modelling nor identification of the stock price dynamics is involved. The time-varying investment level is generated using a “hard-wired” feedback controller which processes cumulative gains and losses. While this paper addresses discrete time, it is noted that the results also apply to high-frequency trading since the discretization interval Δt is allowed to be arbitrarily small.

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