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Optimal Investment Strategy for α-Robust Utility Maximization Problem

Author

Listed:
  • Zhou Yang

    (School of Mathematical Sciences, South China Normal University, Guangzhou 516031, China)

  • Danping Li

    (School of Statistics, Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, East China Normal University, Shanghai 200062, China)

  • Yan Zeng

    (Lingnan College, Sun Yat-sen University, Guangzhou 510275, China)

  • Guanting Liu

    (School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia)

Abstract

In reality, investors are uncertain about the dynamics of risky asset returns. Therefore, investors prefer to make robust investment decisions. In this paper, we propose an α-robust utility maximization problem under uncertain parameters. The investor is allowed to invest in a financial market consisting of a risk-free asset and a risky asset. The uncertainty about the expected return rate is parameterized by a nonempty set. Different from most existing literature on robust utility maximization problems where investors are generally assumed to be extremely ambiguity averse because they tend to consider only expected utility in the worst-case scenario, we pay attention to the investors who are not only ambiguity averse but also ambiguity seeking. Under power utility, we provide the implicit function representations for the precommitted strategy, equilibrium strategy of the open-loop type, and equilibrium strategy of the closed-loop type. Some properties about the optimal trading strategies, the best-case and worst-case parameters under three different kinds of strategies, are provided.

Suggested Citation

  • Zhou Yang & Danping Li & Yan Zeng & Guanting Liu, 2025. "Optimal Investment Strategy for α-Robust Utility Maximization Problem," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 606-632, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:606-632
    DOI: 10.1287/moor.2023.0076
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