STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS AND MARKOVIAN REGIME SWITCHING SYSTEM

Wen，Jiaqiang1; Li，Xun2; Xiong，Jie1; Zhang，Xin3

2023-04-01

10.1137/22M1481415

SIAM Journal on Control and Optimization   影响因子和分区

0363-0129

1095-7138

This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random. We prove the solvability of the stochastic Riccati equation under the uniform convexity condition and obtain the closed-loop representation of the open-loop optimal control using the unique solvability of the corresponding stochastic Riccati equation. Moreover, by applying Itô's formula with jumps, we get a representation of the cost functional on a Hilbert space, characterized as the adapted solutions of some forward-backward stochastic differential equations. We show that the necessary condition of the open-loop optimal control is the convexity of the cost functional, and the sufficient condition of the open-loop optimal control is the uniform convexity of the cost functional. In addition, we study the properties of the stochastic value flow of the stochastic linear-quadratic optimal control problem. Finally, as an application, we present a continuous-time mean-variance portfolio selection problem and prove its unique solvability.

Markovian regime switching mean-variance portfolio selection random coefficient stochastic linear-quadratic optimal control stochastic Riccati equation

SCI ; EI

英语

第一

National Natural Science Foundation of China[11831010];National Natural Science Foundation of China[12101291];National Natural Science Foundation of China[12171086];Ocean Park Conservation Foundation, Hong Kong[15215319];Ocean Park Conservation Foundation, Hong Kong[15216720];Ocean Park Conservation Foundation, Hong Kong[15221621];Applied Basic Research Foundation of Yunnan Province[2022A1515012017];National Key Research and Development Program of China[2022YFA1006102];National Key Research and Development Program of China[2022YFA1006102];Fundamental Research Funds for the Central Universities[2242021R41082];Ocean Park Conservation Foundation, Hong Kong[4-ZZHX];

Automation & Control Systems ; Mathematics

Automation & Control Systems ; Mathematics, Applied

WOS:000995819400020

SIAM PUBLICATIONS

20232114136499

Continuous time systems ; Costs ; Equations of state ; Optimal control systems ; Quadratic programming ; Riccati equations

Control Systems:731.1 ; Cost and Value Engineering; Industrial Economics:911 ; Calculus:921.2 ; Systems Science:961

ENGINEERING

2-s2.0-85159765684

Scopus

1.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
2.Department of Applied Mathematics,Hong Kong Polytechnic University,Hong Kong
3.School of Mathematics,Southeast University,Nanjing,Jiangsu Province,211189,China

Wen，Jiaqiang,Li，Xun,Xiong，Jie,et al. STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS AND MARKOVIAN REGIME SWITCHING SYSTEM[J]. SIAM Journal on Control and Optimization,2023,61(2):949-979.

Wen，Jiaqiang,Li，Xun,Xiong，Jie,&Zhang，Xin.(2023).STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS AND MARKOVIAN REGIME SWITCHING SYSTEM.SIAM Journal on Control and Optimization,61(2),949-979.

Wen，Jiaqiang,et al."STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS AND MARKOVIAN REGIME SWITCHING SYSTEM".SIAM Journal on Control and Optimization 61.2(2023):949-979.