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Title: | Open-loop solvability for mean-field stochastic linear quadratic optimal control problems of Markov regime-switching system | Authors: | Si, K Xu, Z Yiu, KFC Li, X |
Issue Date: | Jul-2022 | Source: | Journal of industrial and management optimization, July 2022, v. 18, no. 4, p. 2415-2433 | Abstract: | This paper investigates the mean-field stochastic linear quadratic optimal control problem of Markov regime switching system (M-MF-SLQ, for short). The representation of the cost functional for the M-MF-SLQ is derived using the technique of operators. It is shown that the convexity of the cost functional is necessary for the finiteness of the M-MF-SLQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. We demonstrate with a few examples that our results can be employed for tackling some financial problems such as mean-variance portfolio selection problem. | Keywords: | Linear quadratic optimal control Markov regime switching Mean-field Open-loop solvability |
Publisher: | American Institute of Mathematical Sciences | Journal: | Journal of industrial and management optimization | ISSN: | 1553-166X | EISSN: | 1547-5816 | DOI: | 10.3934/jimo.2021074 | Rights: | This is an Open Access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). The following publication Kehan Si, Zhenda Xu, Ka Fai Cedric Yiu, Xun Li. Open-loop solvability for mean-field stochastic linear quadratic optimal control problems of Markov regime-switching system. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2415-2433 is available at https://doi.org/10.3934/jimo.2021074. |
Appears in Collections: | Journal/Magazine Article |
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