Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a comprehensive overview of the various modeling approaches and strategies developed for index tracking, highlighting the strengths and limitations of each approach. We categorize the index tracking models into three broad frameworks: optimization-based models, statistical-based models and machine learning based data-driven approach. A comprehensive empirical study conducted on the S\&P 500 dataset demonstrates that the tracking error volatility model under the optimization-based framework delivers the most precise index tracking, the convex co-integration model, under the statistical-based framework achieves the strongest return-risk balance, and the deep neural network with fixed noise model within the data-driven framework provides a competitive performance with notably low turnover and high computational efficiency. By combining a critical review of the existing literature with comparative empirical analysis, this paper aims to provide insights into the evolving landscape of index tracking and its practical implications for investors and fund managers.

翻译：指数跟踪，亦称被动投资，因其以成本效益高且高效的方式复制特定市场指数表现的特点，在金融市场中获得了广泛关注。本综述论文全面概述了为指数跟踪开发的各种建模方法与策略，重点阐述了每种方法的优势与局限性。我们将指数跟踪模型归纳为三大框架：基于优化的模型、基于统计的模型以及基于机器学习的数据驱动方法。在标普500数据集上进行的一项全面实证研究表明：在基于优化的框架下，跟踪误差波动率模型能实现最精确的指数跟踪；在基于统计的框架下，凸协整模型可获得最佳的收益-风险平衡；而在数据驱动框架内，带固定噪声的深度神经网络模型展现出具有竞争力的性能，其换手率显著较低且计算效率高。通过结合对现有文献的批判性综述与比较实证分析，本文旨在深入剖析指数跟踪领域的发展态势，及其对投资者和基金管理者的实际意义。