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arXiv 2007.00017quant-phcs.CEq-fin.ST
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使用量子处理器和量子启发张量网络的真实数据集的动态投资组合优化

Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks

Samuel Mugel, Carlos Kuchkovsky, Escolastico Sanchez, Samuel Fernandez-Lorenzo, Jorge Luis-Hita, Enrique Lizaso, Roman Orus

备注：
13 pages, 5 figures, 5 tables, revised version, to appear in Physical Review Research
发表信息：
Phys. Rev. Research 4, 013006 (2022)
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摘要：

在本文中，我们解决了动态投资组合优化问题，即，在一段时间内确定资产投资组合的最佳交易轨迹，同时考虑交易成本和其他可能的约束。这个问题是定量金融的核心。在详细介绍了该问题之后，我们在不同的硬件平台上实现了一些量子和量子启发的算法，使用52种资产8年来每日价格的真实数据来求解其离散公式，并对所获得的夏普比率，利润和计算时间进行了详细的比较。特别是，我们在IBM-Q上实现了经典求解器（Gekko，穷举），D-Wave混合量子退火，两种基于变分量子本征求解器的不同方法（其中一种是全新的，针对问题量身定制），并且在此背景下首次实现了基于张量网络的量子优化器。为了使数据适合每个特定的硬件平台，我们还考虑进行基于资产聚类的预处理。从我们的比较中，我们得出结论，D-Wave混合网络和张量网络能够处理最大的系统，其中我们计算了高达1272个完全连接的量子位用于演示目的。最后，我们还讨论了如何在数学上实现其他可能的现实生活中的约束，以及一些想法，以进一步提高所研究的方法的性能。

英文摘要：

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. This problem is central to quantitative finance. After a detailed introduction to the problem, we implement a number of quantum and quantum-inspired algorithms on different hardware platforms to solve its discrete formulation using real data from daily prices over 8 years of 52 assets, and do a detailed comparison of the obtained Sharpe ratios, profits and computing times. In particular, we implement classical solvers (Gekko, exhaustive), D-Wave Hybrid quantum annealing, two different approaches based on Variational Quantum Eigensolvers on IBM-Q (one of them brand-new and tailored to the problem), and for the first time in this context also a quantum-inspired optimizer based on Tensor Networks. In order to fit the data into each specific hardware platform, we also consider doing a preprocessing based on clustering of assets. From our comparison, we conclude that D-Wave Hybrid and Tensor Networks are able to handle the largest systems, where we do calculations up to 1272 fully-connected qubits for demonstrative purposes. Finally, we also discuss how to mathematically implement other possible real-life constraints, as well as several ideas to further improve the performance of the studied methods.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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