论文标题
量子在线投资组合优化算法
A Quantum Online Portfolio Optimization Algorithm
论文作者
论文摘要
投资组合优化在金融中起着核心作用，以获得旨在实现某些投资目标的最佳投资组合分配。多年来，许多作品研究了投资组合优化的不同变体。投资组合优化还提供了一个丰富的领域，可以研究量子计算机的应用以获得比古典计算机的优势。在这项工作中，我们提供了Helmbold等人的现有古典在线投资组合优化算法的采样版本，我们又为此开发了量子版本。量子优势是通过使用量子态制备，内部产品估计和多样采样等技术来实现的。我们的量子算法在时间复杂性上提供了二次加速，而$ n $，其中$ n $是投资组合中的资产数量。我们的经典和量子算法的交易成本与$ n $无关，这对于拥有大量资产的实际应用特别有用。
Portfolio optimization plays a central role in finance to obtain optimal portfolio allocations that aim to achieve certain investment goals. Over the years, many works have investigated different variants of portfolio optimization. Portfolio optimization also provides a rich area to study the application of quantum computers to obtain advantages over classical computers. In this work, we give a sampling version of an existing classical online portfolio optimization algorithm by Helmbold et al., for which we in turn develop a quantum version. The quantum advantage is achieved by using techniques such as quantum state preparation, inner product estimation and multi-sampling. Our quantum algorithm provides a quadratic speedup in the time complexity, in terms of $n$, where $n$ is the number of assets in the portfolio. The transaction cost of both of our classical and quantum algorithms is independent of $n$ which is especially useful for practical applications with a large number of assets.
