Time-Consistency in the Mean–Variance Problem: A New Perspective

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