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An Optimal Trading Rule Under a Switchable Mean-Reversion Model

Author

Listed:
  • Duy Nguyen

    (University of Georgia)

  • Jingzhi Tie

    (University of Georgia)

  • Qing Zhang

    (University of Georgia)

Abstract

This work provides an optimal trading rule that allows buying and selling an asset sequentially over time. The asset price follows a switchable mean-reversion model with a Markovian jump. Such a model can be applied to assets with a “staircase” price behavior and yet is simple enough to allow an analytic solution. The objective is to determine a sequence of trading times to maximize an overall return. The corresponding value functions are characterized by a set of quasi-variational inequalities. A closed-form solution is obtained under suitable conditions. The sequence of trading times can be given in terms of a set of threshold levels. Finally, numerical examples are given to demonstrate the results.

Suggested Citation

  • Duy Nguyen & Jingzhi Tie & Qing Zhang, 2014. "An Optimal Trading Rule Under a Switchable Mean-Reversion Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 145-163, April.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-012-0260-x
    DOI: 10.1007/s10957-012-0260-x
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    References listed on IDEAS

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    1. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    2. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
    3. L. P. Bos & A. F. Ware & B. S. Pavlov, 2002. "On a semi-spectral method for pricing an option on a mean-reverting asset," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 337-345.
    4. Arne Løkka & Mihail Zervos, 2011. "A Model For The Long-Term Optimal Capacity Level Of An Investment Project," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 187-196.
    5. Liam A. Gallagher & Mark P. Taylor, 2002. "Permanent and Temporary Components of Stock Prices: Evidence from Assessing Macroeconomic Shocks," Southern Economic Journal, John Wiley & Sons, vol. 69(2), pages 345-362, October.
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    Cited by:

    1. Valeriy Zakamulin & Javier Giner, 2024. "Optimal trend-following rules in two-state regime-switching models," Journal of Asset Management, Palgrave Macmillan, vol. 25(4), pages 327-348, July.
    2. Kiyoshi Suzuki, 2021. "Infinite-Horizon Optimal Switching Regions for a Pair-Trading Strategy with Quadratic Risk Aversion Considering Simultaneous Multiple Switchings: A Viscosity Solution Approach," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 336-360, February.
    3. Zakamulin, Valeriy & Giner, Javier, 2023. "Optimal trend-following with transaction costs," International Review of Financial Analysis, Elsevier, vol. 90(C).

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