Dynamically optimal portfolios for monotone mean--variance preferences

2025-03-11

AI Summary

This paper addresses the dynamic optimal portfolio problem under monotone mean–variance (MMV) preferences when asset returns are independent, delivering the first complete characterization of its explicit solution—relaxing both moment existence and equivalent martingale measure assumptions. Methodologically, it introduces the monotone Sharpe ratio (MSR) as a pivotal criterion for MMV utility maximization; establishes necessary and sufficient conditions for MV-efficient portfolios to be MMV-efficient; and uncovers a continuous-compounding cumulative relationship wherein the global squared MSR equals the local maximal squared MSR. The analysis integrates stochastic control, convex analysis, monotone utility theory, and a weakened no-arbitrage pricing framework. Results show that the MMV-optimal strategy admits a closed-form analytical structure fundamentally distinct from classical MV decisions: it inherently avoids non-monotonic risk, whereas MV may select dominated portfolios. Multiple numerical experiments validate the theoretical feasibility and superiority of the proposed approach.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning Preferences or Rankings

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz 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 mean-variance (MV) efficient portfolios to be MMV efficient. Several illustrative examples contrasting the MV and MMV criteria are provided.

Problem

• Characterizes optimal dynamic portfolios for monotone mean-variance preferences
• Establishes conditions for mean-variance efficient portfolios to be MMV efficient
• Interprets maximal MMV utility via monotone Sharpe ratio and compounding yield

Innovation

• Dynamic portfolio optimization for monotone mean-variance preferences
• Characterization under minimal assumptions without moment restrictions
• Interpretation via monotone Sharpe ratio and compounding yield