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

When a dynamic optimization problem is not decomposable by a stage-wise backward recursion, it is nonseparable in the sense of dynamic programming. The classical dynamic programming-based optimal stochastic control methods would fail in such nonseparable situations as the principle of optimality no longer applies. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posed a great challenge to our research community until recently. Different from the existing literature that invokes embedding schemes and auxiliary parametric formulations to solve the dynamic mean-variance portfolio selection formulation, 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.