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.
翻译:在本文中,我们处理动态组合优化问题,即确定资产投资组合在一段时间内的最佳交易轨迹,同时考虑到交易成本和其他可能的制约因素。这个问题对于量化融资至关重要。在详细介绍这一问题之后,我们在不同硬件平台上实施了若干量子和量子驱动算法,利用8年来每天52个资产的价格提供的真实数据,解决其离散的配置问题,并详细比较获得的夏普比率、利润和计算时间。特别是,我们采用古典解答器(Gekko,详尽无遗)、D-瓦韦混合量子肛门,两种基于静态量子交换法的不同方法。在IBM-Q上(其中一个是全新的,适应问题),我们首次在不同硬件平台上采用量子和量子驱动的算法,利用Tensor网络的8年价格实际数据解决其离散配置问题。为了将数据纳入每个具体的硬件平台,我们还考虑根据资产组合进行预处理。我们从比较中得出的结论是,D-Wielve和Tensor混合量子网的两种不同方法,最终可以将12号数学模型的计算方法用于处理最大可能的系统。我们的研究。