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：被动管理策略为保守型投资者提供了一种降低市场风险的方法。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，买入指数所有资产会产生高昂的再平衡成本，从而损害未来收益。指数跟踪问题涉及构建一个能以较低交易成本追踪特定基准的投资组合。由于求解此类问题需要选取资产子集，其属于NP难问题。近年来，研究者们一直在探索更具实用性的跟踪组合求解方法。本文对过去十年间指数跟踪数学方法的进展进行了分析。该系统性文献综述覆盖了关键议题，包括最相关的研究领域、求解方法及模型结构，并特别关注了应用于指数跟踪问题的元启发式算法的探索与分析。