Open-loop Solvability for Mean-field Stochastic Linear Quadratic Optimal Control Problems of Markov Regime-switching System

Kehan Si, Zhenda Xu, Ka Fai Cedric Yiu, Xun Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

This paper investigates the mean-field stochastic linear quadratic optimal control problem of Markov regime switching system (M-MF-SLQ, for short). The representation of the cost functional for the M-MF-SLQ is derived using the technique of operators. It is shown that the convexity of the cost functional is necessary for the finiteness of the M-MF-SLQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. We demonstrate with a few examples that our results can be employed for tackling some financial problems such as mean-variance portfolio selection problem.

Original languageEnglish
Pages (from-to)2415-2433
Number of pages19
JournalJournal of Industrial and Management Optimization
Volume18
Issue number4
DOIs
Publication statusPublished - 2022

Keywords

  • Linear quadratic optimal control
  • Markov regime switching
  • Mean-field
  • Open-loop solvability

ASJC Scopus subject areas

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics

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