Unified Framework of Mean-Field Formulations for Optimal Multi-Period Mean-Variance Portfolio Selection
Accepted by IEEE Transactions on Automatic Control, Forthcoming
29 Pages Posted: 11 Apr 2014 Last revised: 19 Apr 2020
Date Written: February 21, 2014
Abstract
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.
Keywords: Stochastic optimal control, mean-field formulation, multi-period portfolio selection, multi-period mean-variance formulation, intertemporal restrictions, risk control over bankruptcy
JEL Classification: G11
Suggested Citation: Suggested Citation
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