Time-consistency in the mean-variance problem: A new perspective

TL;DR

This paper presents a novel approach to solving discrete-time mean-variance portfolio optimization problems by transforming them into a deterministic model, enabling recursive solutions that ensure time consistency.

Contribution

The authors introduce a new model transforming the mean-variance problem into a deterministic framework, allowing for recursive, time-consistent solutions using Bellman equations.

Findings

Successfully transforms the mean-variance problem into a deterministic model

Enables recursive, time-consistent solutions via Bellman optimality

Provides explicit solutions for a more general framework

Abstract

We investigate discrete-time mean-variance portfolio selection problems viewed as a Markov decision process. We transform the problems into a new model with deterministic transition function for which the Bellman optimality equation holds. In this way, we can solve the problem recursively and obtain a time-consistent solution, that is an optimal solution that meets the Bellman optimality principle. We apply our technique for solving explicitly a more general framework.