Multi-Period Mean-Variance Portfolio Optimization with High-Order Coupled Asset Dynamics

Jianping He, Qing Guo Wang, Peng Cheng, Jiming Chen, Youxian Sun

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


This paper is concerned with a multi-period portfolio management problem over a finite horizon. The objective is to seek the optimal investment policy series which maximizes the weighted sum of a linear combination of the expected return and the variance of portfolio over all the investment periods. This formulation enables the investor to adjust weights for any period and have full freedom and control over their best tradeoff between return and risk over each period. We show that such a problem is a convex quadratic programming problem in terms of the decision variables, regardless of price dynamic nature (either linear or nonlinear cases). By solving the stationary equation directly, an optimal solution is developed for its original problem without using embedding method. The solution is simplified for a general linear price model with high-order and coupled asset dynamics and shown to be implementable with historical price data. Simulation is carried out on USA and China stock markets with real data, which demonstrates feasibility and better performance of the proposed solution than the special case considered in the literature. In particular, the proposed solution with suitable nonzero weights on intermediate time periods offers higher return at the same risk level, compared with one involving the terminal wealth only in the objective function.

Original languageEnglish
Article number6955839
Pages (from-to)1320-1335
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number5
Publication statusPublished - 1 May 2015
Externally publishedYes


  • Coupled asset dynamics
  • Portfolio optimiation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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