The passive management approach offers conservative investors a way to reduce risk concerning the market. This investment strategy aims at replicating a specific index, such as the NASDAQ Composite or the FTSE100 index. The problem is that buying all the index's assets incurs high rebalancing costs, and this harms future returns. The index tracking problem concerns building a portfolio that follows a specific benchmark with fewer transaction costs. Since a subset of assets is required to solve the index problem this class of problems is NP-hard, and in the past years, researchers have been studying solution approaches to obtain tracking portfolios more practically. This work brings an analysis, spanning the last decade, of the advances in mathematical approaches for index tracking. The systematic literature review covered important issues, such as the most relevant research areas, solution methods, and model structures. Special attention was given to the exploration and analysis of metaheuristics applied to the index tracking problem.

翻译：被动管理方法为保守型投资者提供了降低市场风险的途径。该投资策略旨在复制特定指数（如纳斯达克综合指数或富时100指数）。然而，购买指数中所有资产会带来高昂的再平衡成本，进而损害未来收益。指数追踪问题涉及构建一个以较低交易成本跟随特定基准的投资组合。由于解决指数问题需要选取资产子集，此类问题属于NP难问题。近年来，研究者一直致力于探索更实用的追踪投资组合求解方法。本文对过去十年间指数追踪数学方法的进展进行了分析。这一系统性文献综述涵盖了重要议题，例如最具相关性的研究领域、求解方法及模型结构。其中特别关注并分析了元启发式算法在指数追踪问题中的应用。