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Generalization of Affine Feedback Stock Trading Results to Include Stop-Loss Orders

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  • Chung-Han Hsieh

Abstract

The takeoff point of this paper is to generalize the existing stock trading results for a class of affine feedback controller to include consideration of a stop-loss order. Using the geometric Brownian motion as the underlying stock price model, our main result is to provide a closed-form expression for the cumulative distribution function for the trading profit or loss. In addition, we show that the affine feedback controller with stop-loss order indeed generalizes the result without stop order in the sense of distribution function. Some simulations and illustrative examples are also provided as supporting evidence of the theory. Moreover, we provide some technical results aimed at addressing the issues about survivability, cash-financing considerations, long-only property, and lower bound of the expected gain or loss.

Suggested Citation

  • Chung-Han Hsieh, 2020. "Generalization of Affine Feedback Stock Trading Results to Include Stop-Loss Orders," Papers 2004.12848, arXiv.org.
    • Handle: RePEc:arx:papers:2004.12848
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    References listed on IDEAS

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    1. Handa, Puneet & Schwartz, Robert A, 1996. "Limit Order Trading," Journal of Finance, American Finance Association, vol. 51(5), pages 1835-1861, December.
    2. Edward O. Thorp, 2011. "The Kelly Criterion in Blackjack Sports Betting, and the Stock Market," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 54, pages 789-832, World Scientific Publishing Co. Pte. Ltd..
    3. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2019. "The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Hold," Papers 1907.08771, arXiv.org.
    4. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2019. "On Positive Solutions of a Delay Equation Arising When Trading in Financial Markets," Papers 1901.02480, arXiv.org, revised Oct 2019.
    5. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.
    6. Albanese, Claudio & Campolieti, Giuseppe, 2005. "Advanced Derivatives Pricing and Risk Management," Elsevier Monographs, Elsevier, edition 1, number 9780120476824.
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