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.
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DOI : 10.1051/cocv/2021110
Keywords: Stochastic LQ control, regime switching, infinite time horizon, extended stochastic Riccati equation, nonnegative solutions
@article{COCV_2022__28_1_A5_0,
author = {Hu, Ying and Shi, Xiaomin and Xu, Zuo Quan},
title = {Constrained stochastic {LQ} control on infinite time horizon with regime switching},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2021110},
mrnumber = {4364335},
zbl = {1482.93703},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021110/}
}
TY - JOUR AU - Hu, Ying AU - Shi, Xiaomin AU - Xu, Zuo Quan TI - Constrained stochastic LQ control on infinite time horizon with regime switching JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021110/ DO - 10.1051/cocv/2021110 LA - en ID - COCV_2022__28_1_A5_0 ER -
%0 Journal Article %A Hu, Ying %A Shi, Xiaomin %A Xu, Zuo Quan %T Constrained stochastic LQ control on infinite time horizon with regime switching %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021110/ %R 10.1051/cocv/2021110 %G en %F COCV_2022__28_1_A5_0
Hu, Ying; Shi, Xiaomin; Xu, Zuo Quan. Constrained stochastic LQ control on infinite time horizon with regime switching. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 5. doi: 10.1051/cocv/2021110
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