| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 69 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2021066 | |
| Published online | 02 July 2021 | |
Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system*
1
School of Mathematics, Southeast University,
Nanjing,
Jiangsu Province
211189, PR China.
2
Department of Applied Mathematics, The Hong Kong Polytechnic University,
Hong Kong, PR China.
3
Department of Mathematics, Southern University of Science and Technology,
Shenzhen,
Guangdong
518055, PR China.
** Corresponding author: xiongj@sustech.edu.cn
Received:
22
March
2020
Accepted:
12
June
2021
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.
Mathematics Subject Classification: 49N10 / 93E20
Key words: Linear quadratic optimal control / markovian regime switching / riccati equations / open-loop solvability / closed-loop solvability
The first author is supported by National Natural Science Foundation of China (grant no. 11771079) and Fundamental Research Funds for the Central Universities (grant no. 2242021R41082), the second author is supported by RGC Grants (grant nos. 15209614, 15213218 and 15215319) and partially from CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, and the third author is supported by Southern University of Science and Technology Start up fund Y01286120 and National Natural Science Foundation of China (grant nos. 61873325, 11831010).
© 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.
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