Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

IEEE Journal of Selected Topics in Signal Processing, Forthcoming, 2016

NYU Tandon Research Paper No. 2649376

12 Pages Posted: 24 Aug 2015 Last revised: 26 Jun 2017

See all articles by Gili Rosenberg

Gili Rosenberg

1QBit

Poya Haghnegahdar

1QBit

Phil Goddard

1QBit

Peter Carr

New York University Finance and Risk Engineering

Kesheng Wu

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab)

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; AQR Capital Management, LLC

Date Written: August 22, 2015

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.

Keywords: Qubit, quantum computer, optimal trading trajectory, portfolio optimization, quantum annealing

JEL Classification: G0, G1, G2, G15, G24, E44

Suggested Citation

Rosenberg, Gili and Haghnegahdar, Poya and Goddard, Phil and Carr, Peter P. and Wu, Kesheng and López de Prado, Marcos, Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer (August 22, 2015). IEEE Journal of Selected Topics in Signal Processing, Forthcoming, 2016; NYU Tandon Research Paper No. 2649376. Available at SSRN: https://ssrn.com/abstract=2649376 or http://dx.doi.org/10.2139/ssrn.2649376

Gili Rosenberg

1QBit ( email )

Suite 900, 609 W Hastings Street
Vancouver, BC V6B 4W4
Canada

Poya Haghnegahdar

1QBit ( email )

Suite 900, 609 W Hastings Street
Vancouver, BC V6B 4W4
Canada

Phil Goddard

1QBit ( email )

Suite 900, 609 W Hastings Street
Vancouver, BC V6B 4W4
Canada

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Kesheng Wu

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab) ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

Marcos López de Prado (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

HOME PAGE: http://www.orie.cornell.edu

AQR Capital Management, LLC

One Greenwich Plaza
Greenwich, CT 06830
United States

HOME PAGE: http://www.aqr.com

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