Mean-Variance Optimization in Ambiguous Financial Markets with Learning

2026-06-09

AI Summary

This study addresses dynamic mean-variance portfolio optimization in a continuous-time multi-asset Black-Scholes market where investors face uncertainty about asset return drifts and exhibit ambiguity aversion. By adopting the variance decomposition criterion of Maccheroni et al., the framework explicitly distinguishes between market risk and model ambiguity. Integrating Bayesian learning, stochastic control, and mean-variance optimization, the authors develop a tractable dynamic decision-making framework that accommodates parameter uncertainty. Within a class of adaptive learning strategies, they derive the optimal investment policy in closed form. Numerical experiments demonstrate that ambiguity aversion substantially reduces allocations to risky assets, underscoring the critical influence of model uncertainty on investor behavior.

Abstract

We consider a continuous time investment problem in a multi-asset Black-Scholes market with the following features: The assets' drifts are not known and constitute a source of model ambiguity. However, there is a prior distribution (knowledge) on the possible drifts. Our investor is ambiguity averse and wants to maximize a mean-variance criterion for the terminal wealth where ambiguity aversion is incorporated in a smooth way. We consider here the criterion introduced in Maccheroni et al. 2013 where the variance is decomposed and each part is weighted differently to account for different levels of market risk and model ambiguity aversion. We use a novel approach to find the optimal dynamic investment strategy within the class of all adapted strategies which allow for learning. We also present a number of numerical results which help to understand how the model parameters affect the optimal investment strategy. In general it turns out that ambiguity averse investors invest less in the risky assets.

Problem

• mean-variance optimization
• model ambiguity
• ambiguity aversion
• drift uncertainty
• continuous-time portfolio selection

Innovation

• model ambiguity
• mean-variance optimization
• learning in finance
• ambiguity aversion
• dynamic investment strategy