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In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints.
1904
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1904
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1905
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Harry Markowitz, “Portfolio selection,” The Journal of Finance 7
1952
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M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics 144
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E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, “Quantum computation by adiabatic evolution,” (2000) , quant-ph/0001106
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Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5
2014
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Román Orús, “A practical introduction to tensor networks: Matrix product states and projected entangled pair states,” Annals of Physics 349
2014
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M. López de Prado, “Generalized optimal trading trajectories: A financial quantum computing application,” (2015), 10.2139/ssrn.2575184 , http://dx.doi.org/10.2139/ssrn.2575184
2015
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2018
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Logan D.R. Beal, Daniel C. Hill, R. Abraham Martin, and John D. Hedengren, “GEKKO optimization suite,” Processes 6
2018
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John Preskill, “Quantum Computing in the NISQ era and beyond,” Quantum 2
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Román Orús, “Tensor networks for complex quantum systems,” Nature Reviews Physics 1
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G. Rosenberg, “Finding optimal arbitrage opportunities using a quantum annealer,” (2016)
2016
Cited alongside, same era.
Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng Wu, and Marcos López De Prado, “Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer,” IEEE Journal of Selected Topics in Signal Processing 10
2016
Cited alongside, same era.
A. Milne, M. Rounds, and P. Goddard, “Optimal feature selection in credit scoring and classification using a quantum annealer,” (2017)
2017
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Román Orús, Samuel Mugel, and Enrique Lizaso, “Quantum computing for finance: Overview and prospects,” Reviews in Physics 4
Cited in the paper.
Román Orús, Samuel Mugel, and Enrique Lizaso, “Forecasting financial crashes with quantum computing,” Phys. Rev. A 99
Cited in the paper.
An obvious but non-trivial remark: imposing ∑ n = 1 N ω ¯ n , t ≤ K \sum\displaylimits_{n=1}^{N}\overline{\omega}_{n,t}\leq K instead, may actually produce portfolios with higher returns. Notice also that K K is the investment, and not the value of the investment, e.g. K = 3 K=3 apples, not the value (e.g. in dollars) of those 3 3 apples
Cited in the paper.
A different splitting amounts to a rescaling of the optimal Lagrange multiplier ρ \rho , without changing the actual solution
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See, e.g., https://en.wikipedia.org/wiki/Rate _ \_ of _ \_ return
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2019
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Maria Schuld, Alex Bocharov, Krysta M. Svore, and Nathan Wiebe, “Circuit-centric quantum classifiers,” Phys. Rev. A 101
2020
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Catherine McGeoch and Pau Farré, “The d-wave advantage system: An overview,” D-Wave Whitepaper (2020)
2020
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