Equilibrium Solutions of Multi-Period Mean-Variance Portfolio Selection

This is a companion paper of [Mixed equilibrium solution of time-inconsistent stochastic LQ problem, arXiv:1802.03032], where general theory has been established to characterize the open-loop equilibrium control, feedback equilibrium strategy and mixed equilibrium solution for a time-inconsistent stochastic linear-quadratic problem. This note is, on the one hand to test the developed theory of that paper, and on the other hand to push the solvability of multi-period mean-variance portfolio selection. A nondegenerate assumption has been removed in this note, which is popular in existing literature about multi-period mean-variance portfolio selection; and neat conditions have been obtained to characterize the existence of equilibrium solutions.