基数约束投资组合优化的限时元启发式算法
Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation
AI总结：
本文提出通过限制计算时间来公平比较元启发式算法在基数约束投资组合优化中的表现，并在1秒、5秒和25秒时限下评估模拟退火、禁忌搜索和遗传算法，发现模拟退火在5秒内即可获得近最优解且优于其他算法。
摘要：
金融投资组合包含若干资产，这些资产在提供收益的同时伴随一定水平的风险。为了最大化收益或最小化风险，必须对投资组合进行优化——即找到资产最优数量的理想组合。可能的组合数量极其庞大。此外，为了使问题更具现实性，可以对投资组合中持有的资产数量以及可分配给单一资产的最大投资组合比例施加约束。该问题无法使用二次规划求解，这意味着无法计算出最优解。一类被称为元启发式的算法能够在实际可接受的计算时间内找到近最优解。这些算法已成功应用于带约束的投资组合优化。然而，在以往的研究中，元启发式的计算时间并未受到限制，这意味着结果在质量和计算时间上均存在差异，难以进行公平比较。本研究提出了一种不同的元启发式测试方法，将其计算时间限制在特定时长内，从而使结果仅在质量上存在差异。考虑到在某些使用场景中优先考虑解的质量，而在另一些场景中优先考虑速度，本研究测试了1秒、5秒和25秒的时间限制。三种元启发式算法——模拟退火、禁忌搜索和遗传算法——在五组具有不同资产数量的历史市场数据上进行了评估。尽管这些元启发式算法在1秒内无法找到有竞争力的解，但模拟退火在除一个数据集外的所有数据集上均于5秒内找到了近最优解。质量最低的解由遗传算法获得。
英文摘要：
A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm.
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。
