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Title: Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system
Authors: Zhang, X
Li, X 
Xiong, J
Issue Date: 2021
Source: ESAIM. Control, optimisation and calculus of variations, 2021, v. 27, 69
Abstract: This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markovian regime switching system is derived by the technique of Itô's formula with jumps. For the stochastic LQ optimal control problem of Markovian regime switching system, we establish the equivalence between the open-loop (closed-loop, resp.) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint. (i.e., the existence of a regular solution to Riccati equations). Also, we analyze the interrelationship between the strongly regular solvability of Riccati equations and the uniform convexity of the cost functional. Finally, we present an example which is open-loop solvable but not closed-loop solvable.
Keywords: Closed-loop solvability
Linear quadratic optimal control
Markovian regime switching
Open-loop solvability
Riccati equations
Publisher: EDP Sciences
Journal: ESAIM. Control, optimisation and calculus of variations 
ISSN: 1292-8119
EISSN: 1262-3377
DOI: 10.1051/cocv/2021066
Rights: © The authors. Published by EDP Sciences, SMAI 2021
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 Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system Xin Zhang, Xun Li and Jie Xiong ESAIM: COCV, 27 (2021) 69 is available at https://doi.org/10.1051/cocv/2021066
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