Passive aggressive ensemble for online portfolio selection

Kailin XIE, Jianfei YIN, Hengyong YU, Hong FU, Ying CHU

Research output: Contribution to journalArticlespeer-review


Developing effective trend estimators is the main method to solve the online portfolio selection problem. Although the existing portfolio strategies have demonstrated good performance through the development of various trend estimators, it is still challenging to determine in advance which estimator will yield the maximum final cumulative wealth in online portfolio selection tasks. This paper studies an online ensemble approach for online portfolio selection by leveraging the strengths of multiple trend estimators. Specifically, a return-based loss function and a cross-entropy-based loss function are first designed to evaluate the adaptiveness of different trend estimators in a financial environment. On this basis, a passive aggressive ensemble model is proposed to weigh these trend estimators within a unit simplex according to their adaptiveness. Extensive experiments are conducted on benchmark datasets from various real-world stock markets to evaluate their performance. The results show that the proposed strategy achieves state-of-the-art performance, including efficiency and cumulative return. Copyright © 2024 by the authors.

Original languageEnglish
Article number956
Issue number7
Early online dateMar 2024
Publication statusPublished - Apr 2024


Xie, K., Yin, J., Yu, H., Fu, H., & Chu, Y. (2024). Passive aggressive ensemble for online portfolio selection. Mathematics, 12(7), Article 956.


  • Online portfolio selection
  • Online ensemble learning
  • Passive aggressive algorithm


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