Dynamically Optimal Portfolios for Monotone Mean-Variance Preferences

• 成果类型: Article; Early Access
• 署名作者: Cerny, Ales; Ruf, Johannes; Schweizer, Martin
• 署名单位: University of London; London School Economics & Political Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.1136
• 发表日期: 2026-04-20
• 关键词: monotone mean-variance efficiency; monotone Sharpe ratio; local utility; sigma-special processes; variance-optimal separating measure; Utility maximization; martingale measures; selection; models

摘要

Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz mean-variance (MV) utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price models with independent returns. The task is performed under minimal assumptions, weaker than the existence of an equivalent martingale measure and with no restrictions on the moments of asset returns. We interpret the maximal MMV utility in terms of the monotone Sharpe ratio (MSR) and show that the global squared MSR arises as the nominal yield from continuously compounding at the rate equal to the maximal local squared MSR. The paper gives simple necessary and sufficient conditions for MV efficient portfolios to be MMV efficient. Several illustrative examples contrasting the MV and MMV criteria are provided.