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Solving the Optimal Trading Trajectory Problem Using Simulated Bifurcation

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  • Kyle Steinhauer
  • Takahisa Fukadai
  • Sho Yoshida

Abstract

We use an optimization procedure based on simulated bifurcation (SB) to solve the integer portfolio and trading trajectory problem with an unprecedented computational speed. The underlying algorithm is based on a classical description of quantum adiabatic evolutions of a network of non-linearly interacting oscillators. This formulation has already proven to beat state of the art computation times for other NP-hard problems and is expected to show similar performance for certain portfolio optimization problems. Inspired by such we apply the SB approach to the portfolio integer optimization problem with quantity constraints and trading activities. We show first numerical results for portfolios of up to 1000 assets, which already confirm the power of the SB algorithm for its novel use-case as a portfolio and trading trajectory optimizer.

Suggested Citation

  • Kyle Steinhauer & Takahisa Fukadai & Sho Yoshida, 2020. "Solving the Optimal Trading Trajectory Problem Using Simulated Bifurcation," Papers 2009.08412, arXiv.org.
    • Handle: RePEc:arx:papers:2009.08412
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    References listed on IDEAS

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    1. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    2. 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.
    3. 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.
    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. Jeffrey Cohen & Alex Khan & Clark Alexander, 2020. "Portfolio Optimization of 40 Stocks Using the DWave Quantum Annealer," Papers 2007.01430, arXiv.org.
    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. 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.
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    Cited by:

    1. Thomas Bouquet & Mehdi Hmyene & Franc{c}ois Porcher & Lorenzo Pugliese & Jad Zeroual, 2021. "Approximating Optimal Asset Allocations using Simulated Bifurcation," Papers 2108.03092, arXiv.org, revised Dec 2021.

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