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On solving robust log-optimal portfolio: A supporting hyperplane approximation approach

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  • Hsieh, Chung-Han

Abstract

A log-optimal portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor’s wealth, which typically assumes prior knowledge of the true return distribution. However, in practice, return distributions are often ambiguous; i.e., the true distribution is unknown, making this problem challenging to solve. This paper proposes a supporting hyperplane approximation approach, reformulating a class of distributional robust log-optimal portfolio problems with polyhedron ambiguity sets into tractable robust linear programs. An efficient algorithm is presented to determine the optimal number of hyperplanes. Additionally, to adapt to the constantly changing market, we propose an online trading algorithm using a sliding window approach to solve a sequence of robust linear programs, offering significant computational advantages. The effectiveness of the proposed approach is supported by empirical studies using historical stock price data.

Suggested Citation

  • Hsieh, Chung-Han, 2024. "On solving robust log-optimal portfolio: A supporting hyperplane approximation approach," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1129-1139.
    • Handle: RePEc:eee:ejores:v:313:y:2024:i:3:p:1129-1139
    DOI: 10.1016/j.ejor.2023.09.040
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    References listed on IDEAS

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