Constrained stochastic LQ control on infinite time horizon with regime switching

Ying Hu, Xiaomin Shi, Zuo Quan Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.

Original languageEnglish
Article number5
Pages (from-to)1-24
Number of pages24
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume28
DOIs
Publication statusE-pub ahead of print - 17 Jan 2022

Keywords

  • Extended stochastic Riccati equation
  • Infinite time horizon
  • Nonnegative solutions
  • Regime switching
  • Stochastic LQ control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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