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

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  • Atul Deshpande
  • B. Ross Barmish

Abstract

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.

Suggested Citation

  • Atul Deshpande & B. Ross Barmish, 2018. "A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control," Papers 1803.04591, arXiv.org.
  • Handle: RePEc:arx:papers:1803.04591
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    File URL: http://arxiv.org/pdf/1803.04591
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    References listed on IDEAS

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    1. Atul Deshpande & B. Ross Barmish, 2016. "A General Framework for Pairs Trading with a Control-Theoretic Point of View," Papers 1608.03636, arXiv.org.
    2. Dokuchaev, Nikolai G. & Savkin, Andrey V., 2002. "A bounded risk strategy for a market with non-observable parameters," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 243-254, April.
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    Cited by:

    1. Xin-Yu Wang & Chung-Han Hsieh, 2023. "On Robustness of Double Linear Policy with Time-Varying Weights," Papers 2303.10806, arXiv.org.
    2. Chung-Han Hsieh, 2022. "On Robust Optimal Linear Feedback Stock Trading," Papers 2202.02300, arXiv.org.
    3. Michael Heinrich Baumann, 2022. "Beating the market? A mathematical puzzle for market efficiency," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 279-325, June.
    4. Chung-Han Hsieh, 2022. "On Robustness of Double Linear Trading with Transaction Costs," Papers 2209.12383, arXiv.org.
    5. Atul Deshpande & John A Gubner & B. Ross Barmish, 2020. "On Simultaneous Long-Short Stock Trading Controllers with Cross-Coupling," Papers 2011.09109, arXiv.org.

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