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Equations and Shape of the Optimal Band Strategy

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  • Joachim de Lataillade
  • Ayman Chaouki

Abstract

We consider the problem of the optimal trading strategy in the presence of a price predictor, linear trading costs and a quadratic risk control. The solution is known to be a band system, a policy that induces a no-trading zone in the positions space. Using a path-integral method introduced in a previous work, we give equations for the upper and lower edges of this band, and solve them explicitly in the case of an Ornstein-Uhlenbeck predictor. We then explore the shape of this solution and derive its asymptotic behavior for large values of the predictor, without requiring trading costs to be small.

Suggested Citation

  • Joachim de Lataillade & Ayman Chaouki, 2020. "Equations and Shape of the Optimal Band Strategy," Papers 2003.04646, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:2003.04646
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    References listed on IDEAS

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    1. Richard Martin & Torsten Schoneborn, 2011. "Mean Reversion Pays, but Costs," Papers 1103.4934, arXiv.org.
    2. Ayman Chaouki & Stephen Hardiman & Christian Schmidt & Emmanuel S'eri'e & Joachim de Lataillade, 2020. "Deep Deterministic Portfolio Optimization," Papers 2003.06497, arXiv.org, revised Apr 2020.
    3. Nicolae Gârleanu & Lasse Heje Pedersen, 2013. "Dynamic Trading with Predictable Returns and Transaction Costs," Journal of Finance, American Finance Association, vol. 68(6), pages 2309-2340, December.
    4. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    5. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    6. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    7. Richard J. Martin, 2012. "Optimal multifactor trading under proportional transaction costs," Papers 1204.6488, arXiv.org.
    8. Joachim de Lataillade & Cyril Deremble & Marc Potters & Jean-Philippe Bouchaud, 2012. "Optimal Trading with Linear Costs," Papers 1203.5957, arXiv.org.
    9. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    10. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    11. Ren LIU & Johannes MUHLE-KARBE & Marko WEBER, 2014. "Rebalancing with Linear and Quadratic Costs," Swiss Finance Institute Research Paper Series 14-16, Swiss Finance Institute.
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