Constrained stochastic LQ control with regime switching and application to portfolio selection - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Annals of Applied Probability Année : 2022

Constrained stochastic LQ control with regime switching and application to portfolio selection

Ying Hu
  • Fonction : Auteur
  • PersonId : 829971
  • IdHAL : ying-hu
Xiaomin Shi
  • Fonction : Auteur
Zuo Quan Xu
  • Fonction : Auteur

Résumé

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 (ES-REs). 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.
Fichier principal
Vignette du fichier
2004.11832.pdf (346.69 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04366941 , version 1 (29-12-2023)

Identifiants

Citer

Ying Hu, Xiaomin Shi, Zuo Quan Xu. Constrained stochastic LQ control with regime switching and application to portfolio selection. The Annals of Applied Probability, 2022, 32 (1), ⟨10.1214/21-AAP1684⟩. ⟨hal-04366941⟩
6 Consultations
3 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More