Robust portfolio selection with regret aversion under HARA utility

Shiyin Mo; Huainian Zhu; Shiyin Mo; Huainian Zhu

doi:10.3934/jimo.2026135

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 8: 3761-3788. doi: 10.3934/jimo.2026135

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Research article

Robust portfolio selection with regret aversion under HARA utility

Shiyin Mo ¹,
Huainian Zhu ^{2
,
,}

1.
School of Economics & Management, South China Normal University, Guangzhou 510006, China
2.
School of Economics, Guangdong University of Technology, Guangzhou 510020, China

Received: 30 April 2026 Revised: 08 July 2026 Accepted: 15 July 2026 Published: 20 July 2026
91G10, 93E20, 90C17

This paper studies a robust portfolio optimization problem for a regret-averse investor under model ambiguity within a hyperbolic absolute risk aversion (HARA) framework. Wealth is allocated across multiple risky assets whose price dynamics are driven by a multi-dimensional Brownian motion. A dynamic programming approach is used to derive explicit expressions for the robust optimal investment strategy, the density generator associated with the worst-case probability measure, and the corresponding value function. Sensitivity analysis is conducted to illustrate the economic implications of the theoretical results. The results indicate that, in the presence of regret aversion, the robust optimal portfolio exhibits reference dependence, which is further amplified as the degree of regret aversion increases. In addition, greater ambiguity aversion toward a given source of risk leads to a reduction in exposure to assets that are more sensitive to that source.
- robust portfolio selection,
- regret aversion,
- ambiguity,
- HARA utility,
- dynamic programming
Citation: Shiyin Mo, Huainian Zhu. Robust portfolio selection with regret aversion under HARA utility[J]. Journal of Industrial and Management Optimization, 2026, 22(8): 3761-3788. doi: 10.3934/jimo.2026135

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Abstract

This paper studies a robust portfolio optimization problem for a regret-averse investor under model ambiguity within a hyperbolic absolute risk aversion (HARA) framework. Wealth is allocated across multiple risky assets whose price dynamics are driven by a multi-dimensional Brownian motion. A dynamic programming approach is used to derive explicit expressions for the robust optimal investment strategy, the density generator associated with the worst-case probability measure, and the corresponding value function. Sensitivity analysis is conducted to illustrate the economic implications of the theoretical results. The results indicate that, in the presence of regret aversion, the robust optimal portfolio exhibits reference dependence, which is further amplified as the degree of regret aversion increases. In addition, greater ambiguity aversion toward a given source of risk leads to a reduction in exposure to assets that are more sensitive to that source.

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