Cone-constrained Monotone Mean-Variance Portfolio Selection Under Diffusion Models

TL;DR

This paper derives closed-form optimal strategies for monotone mean-variance portfolio problems with conic constraints under diffusion models, showing their equivalence to mean-variance solutions and highlighting the importance of orthogonality in the constraints.

Contribution

It extends the equivalence between MMV and MV preferences to constrained cases with conic convex sets, providing explicit solutions and analysis.

Findings

Optimal strategies are in closed form for both MMV and MV problems.

The solutions coincide, confirming the equivalence under conic constraints.

Orthogonality in the conic set is key to the equivalence result.

Abstract

We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies to both problems in closed form and find that they coincide, without and with the presence of the conic constraint. This result generalizes the equivalence between MMV and MV preferences from non-constrained cases to a specific constrained case. A comparison analysis reveals that the orthogonality property under the conic convex set is a key to ensuring the equivalence result.