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Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature

Abstract

Since the pioneering work of Harry Markowitz, mean–variance portfolio selection model has been widely used in both theoretical and empirical studies, which maximizes the investment return under certain risk level or minimizes the investment risk under certain return level. In this paper, we review several variations or generalizations that substantially improve the performance of Markowitz’s mean–variance model, including dynamic portfolio optimization, portfolio optimization with practical factors, robust portfolio optimization and fuzzy portfolio optimization. The review provides a useful reference to handle portfolio selection problems for both researchers and practitioners. Some summaries about the current studies and future research directions are presented at the end of this paper.

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Funding was provided by National Natural Science Foundation of China (Grant No. 71371027).

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Zhang, Y., Li, X. & Guo, S. Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature. Fuzzy Optim Decis Making 17, 125–158 (2018). https://doi.org/10.1007/s10700-017-9266-z

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Keywords

  • Portfolio selection
  • Mean–variance model
  • Dynamic optimization
  • Fuzzy optimization
  • Robust optimization