AI 中文总结
研究无再平衡时指数跟踪问题，提出更稳健的混合整数线性规划模型，开发基于元启发式算法和局部分支的启发式方法求解，该方法能收敛到最优解，生成的投资组合在样本内和样本外数据方面均优于商业求解器。
AI 中文摘要
在过去几年中，被动管理因其管理费和交易成本较低等优势而越来越受欢迎。指数跟踪致力于用较少的资产集重现指数的表现。本文提出了一种新颖的公式，它不仅比现有公式更稳健，而且在样本外数据上表现更好，能够长期跟踪指数而无显著偏差或无需再平衡。由于指数跟踪问题具有NP难性质，在多项式时间内求解具有挑战性。为此，还开发了一种基于元启发式算法和局部分支的新颖启发式方法来求解该模型。该启发式方法不仅具有遗传算法的探索能力，还具有局部搜索算法的特点。使用来自OR库的数据来验证所提出启发式方法与商业求解器相比的能力。结果表明，该启发式方法不仅能够收敛到非大规模问题规模的最优解，而且其生成的投资组合在样本内和样本外数据方面均优于商业求解器生成的投资组合。
英文摘要
Passive management has increasingly won popularity over the past few years because of its advantages, such as lower management fees and transaction costs. Index tracking endeavors to reproduce the performance of an index with smaller sets of assets. In this paper, a novel formulation is proposed that is not only more robust than the existing ones but also performs better on out-of-sample data and tracks indices over long periods without any considerable deviation or the need for rebalancing. Solving index tracking problems in a polynomial time is a challenging task due to their NP-hard nature. To address this issue, a novel heuristic based on metaheuristic algorithms and local branching is also developed to solve the proposed model. The heuristic enjoys not only the exploration capabilities of a genetic algorithm but the characteristics of local search algorithms as well. The data from the OR library is used to verify the capabilities of the proposed heuristic in comparison with commercial solvers. Results indicate that not only is the heuristic able to converge to optimal solutions for not-so-large problem sizes, but the portfolios it generates also outperform those yielded by commercial solvers in terms of both in-sample and out-of-sample data.
