CONSTRAINED STOCHASTIC LQ CONTROL WITH REGIME SWITCHING AND APPLICATION TO PORTFOLIO SELECTION

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 optimal control problem with regime switching, random coefficients and cone control constraint. The randomness of the coefficients comes from two aspects: The Brownian motion and the Markov chain. Using Itô's lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ESREs). We prove the existence and uniqueness of the two ESREs using tools including multidimensional comparison theorem, truncation function technique, log transformation and the John-Nirenberg inequality. These results are then applied to study mean-variance portfolio selection problems with and without short-selling prohibition with random parameters depending on both the Brownian motion and the Markov chain. Finally, the efficient portfolios and efficient frontiers are presented in closed forms.

Original languageEnglish
Pages (from-to)426-460
Number of pages35
JournalAnnals of Applied Probability
Volume32
Issue number1
DOIs
Publication statusPublished - Feb 2022

Keywords

  • Constrained stochastic LQ control
  • existence
  • extended stochastic Riccati equation
  • mean-variance portfolio selection
  • regime switching
  • uniqueness

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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