Optimal Investment Strategy for α-Robust Utility Maximization Problem

Zhou Yang (), Danping Li (), Yan Zeng () and Guanting Liu ()
Additional contact information
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

Mathematics of Operations Research, 2025, vol. 50, issue 1, 606-632

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.

Keywords: Primary: 91G10; Secondary: 93E20; α-robust utility maximization; dynamic inconsistency; precommitted strategy; open-loop equilibrium strategy; closed-loop equilibrium strategy (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2023.0076 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:1:p:606-632

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().