Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

• Published in: IEEE journal of selected topics in signal processing Vol. 10; no. 6; pp. 1053 - 1060
• Main Authors: Rosenberg, Gili, Haghnegahdar, Poya, Goddard, Phil, Carr, Peter, Kesheng Wu, Lopez de Prado, Marcos
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Annealing; Computer programs; Covariance matrices; Inversions; Markets; Mathematical models; MATHEMATICS AND COMPUTING; Optimal trading trajectory; Optimization; Portfolio management; portfolio optimization; Portfolios; quantum annealing; Signal processing; Software; Special issues and sections; Trajectory
• ISSN: 1932-4553; 1941-0484
• DOI: 10.1109/JSTSP.2016.2574703

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.