Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
IEEE Journal of Selected Topics in Signal Processing, Forthcoming, 2016
12 Pages Posted: 24 Aug 2015 Last revised: 26 Jun 2017
Date Written: August 22, 2015
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
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