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http://hdl.handle.net/10397/93915
Title: | Constrained stochastic LQ control on infinite time horizon with regime switching | Authors: | Hu, Y Shi, X Xu, ZQ |
Issue Date: | 2022 | Source: | ESAIM. Control, optimisation and calculus of variations, 2022, v. 28, 5 | 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: | Stochastic LQ control Regime switching Infinite time horizon Extended stochastic Riccati equation Nonnegative solutions. |
Publisher: | EDP Sciences | Journal: | ESAIM. Control, optimisation and calculus of variations | ISSN: | 1292-8119 | EISSN: | 1262-3377 | DOI: | 10.1051/cocv/2021110 | Rights: | © 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. The following publication Hu, Y., Shi, X., & Xu, Z. Q. (2022). Constrained stochastic LQ control on infinite time horizon with regime switching. ESAIM: Control, Optimisation and Calculus of Variations, 28, 5 is available at https://doi.org/10.1051/cocv/2021110 |
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