Constrained stochastic LQ control on infinite time horizon with regime switching

Ying Hu; Xiaomin Shi; Zuo Quan Xu

doi:10.1051/cocv/2021110

Constrained stochastic LQ control on infinite time horizon with regime switching

Ying Hu, Xiaomin Shi, Zuo Quan Xu

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

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 language	English
Article number	5
Pages (from-to)	1-24
Number of pages	24
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	28
DOIs	https://doi.org/10.1051/cocv/2021110
Publication status	E-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

More information

10.1051/cocv/2021110

http://hdl.handle.net/10397/93915

Cite this

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title = "Constrained stochastic LQ control on infinite time horizon with regime switching",

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.",

keywords = "Extended stochastic Riccati equation, Infinite time horizon, Nonnegative solutions, Regime switching, Stochastic LQ control",

author = "Ying Hu and Xiaomin Shi and Xu, {Zuo Quan}",

note = "Funding Information: ∗Partially supported by Lebesgue Center of Mathematics “Investissements d{\textquoteright}avenir”program-ANR-11-LABX-0020-01, ANR CAESARS (No. 15-CE05-0024) and ANR MFG (No. 16-CE40-0015-01). ∗∗∗Partially supported by NSFC (No. 11801315, 71871129), NSF of Shandong Province (No. ZR2018QA001, ZR2020MA032), and the Colleges and Universities Youth Innovation Technology Program of Shandong Province (No. 2019KJI011). ∗∗∗∗Partially supported by NSFC (No. 11971409), Hong Kong GRF (No. 15204216 and No. 15202817), The PolyU-SDU Joint Research Center on Financial Mathematics and the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, The Hong Kong Polytechnic University. Publisher Copyright: {\textcopyright} The authors. Published by EDP Sciences, SMAI 2022.",

year = "2022",

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doi = "10.1051/cocv/2021110",

language = "English",

volume = "28",

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journal = "ESAIM - Control, Optimisation and Calculus of Variations",

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T1 - Constrained stochastic LQ control on infinite time horizon with regime switching

AU - Hu, Ying

AU - Shi, Xiaomin

AU - Xu, Zuo Quan

N1 - Funding Information: ∗Partially supported by Lebesgue Center of Mathematics “Investissements d’avenir”program-ANR-11-LABX-0020-01, ANR CAESARS (No. 15-CE05-0024) and ANR MFG (No. 16-CE40-0015-01). ∗∗∗Partially supported by NSFC (No. 11801315, 71871129), NSF of Shandong Province (No. ZR2018QA001, ZR2020MA032), and the Colleges and Universities Youth Innovation Technology Program of Shandong Province (No. 2019KJI011). ∗∗∗∗Partially supported by NSFC (No. 11971409), Hong Kong GRF (No. 15204216 and No. 15202817), The PolyU-SDU Joint Research Center on Financial Mathematics and the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, The Hong Kong Polytechnic University. Publisher Copyright: © The authors. Published by EDP Sciences, SMAI 2022.

PY - 2022/1/17

Y1 - 2022/1/17

N2 - 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.

AB - 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.

KW - Extended stochastic Riccati equation

KW - Infinite time horizon

KW - Nonnegative solutions

KW - Regime switching

KW - Stochastic LQ control

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M3 - Journal article

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VL - 28

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EP - 24

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

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Constrained stochastic LQ control on infinite time horizon with regime switching

Abstract

Keywords

ASJC Scopus subject areas

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Stochastic LQ control with regime switching and random coefficients

機制轉換模型下帶約束的線性二次控制問題及金融應用

Cite this

Constrained stochastic LQ control on infinite time horizon with regime switching

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Activities

Stochastic LQ control with regime switching and random coefficients

機制轉換模型下帶約束的線性二次控制問題及金融應用

Cite this