Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection

TL;DR

This paper introduces a unified mean-field framework that effectively addresses the nonseparable multi-period mean-variance portfolio optimization problem, providing analytical solutions and improving modeling efficiency.

Contribution

It presents a novel mean-field approach that directly tackles nonseparability in dynamic mean-variance portfolio problems, surpassing existing methods.

Findings

Analytical solutions for multi-period mean-variance problems

Enhanced modeling efficiency and accuracy

Effective handling of nonseparable dynamic optimization

Abstract

The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a great challenge to our research community until recently. A few solution methods, including the embedding scheme, have been developed in the last decade to solve the dynamic mean-variance portfolio selection formulation successfully. We propose in this paper a novel mean-field framework that offers a more efficient modeling tool and a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the multi-period mean-variance-type portfolio selection problems.