Equilibrium Solutions of Multi-Period Mean-Variance Portfolio Selection

TL;DR

This paper tests a general theory for time-inconsistent stochastic control problems and advances the solvability of multi-period mean-variance portfolio selection by removing a common assumption and establishing new existence conditions.

Contribution

It extends previous theory to multi-period mean-variance problems, removing a key assumption and providing clear conditions for equilibrium solution existence.

Findings

Removed the nondegenerate assumption in portfolio selection.

Established neat conditions for equilibrium solution existence.

Validated the theory through application to portfolio problems.

Abstract

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.