Explicit Solution for Constrained Scale-State Stochastic Linear-Quadratic Control with Multiplicative Noise

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

6 Scopus Citations
View graph of relations


  • Weiping Wu
  • Jianjun Gao
  • Duan Li
  • Yun Shi

Related Research Unit(s)


Original languageEnglish
Pages (from-to)1999-2012
Journal / PublicationIEEE Transactions on Automatic Control
Issue number5
Online published30 Apr 2018
Publication statusPublished - May 2019


We study in this paper a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piece-wise affine function of the state and can be computed off-line efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.

Research Area(s)

  • Constrained linear quadratic control, dynamic mean-variance portfolio selection, Mathematical model, Optimal control, Optimization, Portfolios, Riccati equations, stochastic control, Stochastic processes, Stochastic systems