A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control

Atul Deshpande, B. Ross Barmish

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The starting point of this paper is the so-called Robust Positive Expectation (RPE) Theorem, a result which appears in literature in the context of Simultaneous Long-Short stock trading. This theorem states that using a combination of two specially-constructed linear feedback trading controllers, one long and one short, the expected value of the resulting gain-loss function is guaranteed to be robustly positive with respect to a large class of stochastic processes for the stock price. The main result of this paper is a generalization of this theorem. Whereas previous work applies to a single stock, in this paper, we consider a pair of stocks. To this end, we make two assumptions on their expected returns. The first assumption involves price correlation between the two stocks and the second involves a bounded non-zero momentum condition. With known uncertainty bounds on the parameters associated with these assumptions, our new version of the RPE Theorem provides necessary and sufficient conditions on the positive feedback parameter K of the controller under which robust positive expectation is assured. We also demonstrate that our result generalizes the one existing for the single-stock case. Finally, it is noted that our results also can be interpreted in the context of pairs trading.

Original languageEnglish (US)
Title of host publication2018 European Control Conference, ECC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages7
ISBN (Electronic)9783952426982
StatePublished - Nov 27 2018
Externally publishedYes
Event16th European Control Conference, ECC 2018 - Limassol, Cyprus
Duration: Jun 12 2018Jun 15 2018

Publication series

Name2018 European Control Conference, ECC 2018


Conference16th European Control Conference, ECC 2018

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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