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Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

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  • Gili Rosenberg
  • Poya Haghnegahdar
  • Phil Goddard
  • Peter Carr
  • Kesheng Wu
  • Marcos L'opez de Prado

Abstract

We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.

Suggested Citation

  • Gili Rosenberg & Poya Haghnegahdar & Phil Goddard & Peter Carr & Kesheng Wu & Marcos L'opez de Prado, 2015. "Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer," Papers 1508.06182, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1508.06182
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    References listed on IDEAS

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    1. 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.
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    3. Corazza, Marco & Favaretto, Daniela, 2007. "On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1947-1960, February.
    4. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    5. Galluccio, Stefano & Bouchaud, Jean-Philippe & Potters, Marc, 1998. "Rational decisions, random matrices and spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 259(3), pages 449-456.
    6. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    7. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    8. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
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    Citations

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    Cited by:

    1. Adam Bouland & Wim van Dam & Hamed Joorati & Iordanis Kerenidis & Anupam Prakash, 2020. "Prospects and challenges of quantum finance," Papers 2011.06492, arXiv.org.
    2. Kyle Steinhauer & Takahisa Fukadai & Sho Yoshida, 2020. "Solving the Optimal Trading Trajectory Problem Using Simulated Bifurcation," Papers 2009.08412, arXiv.org.
    3. Samuel Fern'andez-Lorenzo & Diego Porras & Juan Jos'e Garc'ia-Ripoll, 2020. "Hybrid quantum-classical optimization for financial index tracking," Papers 2008.12050, arXiv.org, revised Oct 2021.
    4. Davide Venturelli & Alexei Kondratyev, 2018. "Reverse Quantum Annealing Approach to Portfolio Optimization Problems," Papers 1810.08584, arXiv.org, revised Oct 2018.
    5. Xiaoyuan Liu & Hayato Ushijima-Mwesigwa & Avradip Mandal & Sarvagya Upadhyay & Ilya Safro & Arnab Roy, 2022. "Leveraging special-purpose hardware for local search heuristics," Computational Optimization and Applications, Springer, vol. 82(1), pages 1-29, May.
    6. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    7. Martin Vesely, 2023. "Finding the Optimal Currency Composition of Foreign Exchange Reserves with a Quantum Computer," Papers 2303.01909, arXiv.org.
    8. Samuel Mugel & Enrique Lizaso & Roman Orus, 2020. "Use Cases of Quantum Optimization for Finance," Papers 2010.01312, arXiv.org.

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