Work

Robust Mean–Variance Portfolio Optimization: Mean–Variance–Variance Criterion Versus Mean–Variance–Standard Deviation Criterion

Year: 2026

Type: article

Abstract: ABSTRACT We study a dynamic portfolio optimization problem under the mean–variance–variance (M‐V‐V) criterion proposed by Maccheroni et al. It is an analogue of the Arrow–Pratt approximation to the well‐known smooth ambiguity model. Under the standard Black–Scholes framework, we derive fully explicit equilibrium investment strategies in which a DM's level of ambiguity, risk aversion, and ambiguity aversion are transparently captured. We find that the time horizon appears inconsistently in the objective function of the M‐V‐V criterion, in turn causing the equilibrium strategies to be nonmonotonic with respect to risk aversion. In response, we introduce a new mean–variance–standard deviation (M‐V‐SD) criterion to address this issue. Equilibrium strategies under the M‐V‐SD criterion exhibit an appealing feature of limited stock market participation which provides a theoretical justification to this phenomenon.

Source: Mathematical Finance

DOI: 10.1111/mafi.70039

Authors: David Landriault, Bin Li, Yuanyuan Zhang

Institution: University of Waterloo

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,840

Funders: National Natural Science Foundation of China, Natural Sciences and Engineering Research Council of Canada