Volume 28, 2022
|Number of page(s)||24|
|Published online||17 January 2022|
Constrained stochastic LQ control on infinite time horizon with regime switching
Univ Rennes, CNRS, IRMAR-UMR 6625,
2 School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250100, China.
3 Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong.
** Corresponding author: email@example.com
Accepted: 24 December 2021
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.
Mathematics Subject Classification: 93E20 / 60H30 / 91G10
Key words: Stochastic LQ control / regime switching / infinite time horizon / extended stochastic Riccati equation / nonnegative solutions
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).
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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