A Quantum Online Portfolio Optimization Algorithm

Portfolio optimization plays a central role in finance to obtain optimal portfolio allocationsthat aim to achieve certain investment goals. Over the years, many works have investigateddifferent variants of portfolio optimization. Portfolio optimization also provides a rich area tostudy 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 optimizationalgorithm by Helmbold et al., for which we in turn develop a quantum version. The quantumadvantage is achieved by using techniques such as quantum state preparation, inner productestimation and multi-sampling. Our quantum algorithm provides a quadratic speedup inthe time complexity, in terms of n, where n is the number of assets in the portfolio. Thetransaction cost of both of our classical and quantum algorithms is independent of n whichis especially useful for practical applications with a large number of assets.