Linear-quadratic optimal control for backward stochastic differential equations with random coefficients

Sun, Jingrui1; Wang, Hanxiao2

2021-05-26

10.1051/cocv/2021049

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS   影响因子和分区

1292-8119

1262-3377

This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem for backward stochastic differential equations (BSDEs, for short), where the coefficients of the backward control system and the weighting matrices in the cost functional are allowed to be random. By a variational method, the optimality system, which is a coupled linear forward-backward stochastic differential equation (FBSDE, for short), is derived, and by a Hilbert space method, the unique solvability of the optimality system is obtained. In order to construct the optimal control, a new stochastic Riccati-type equation is introduced. It is proved that an adapted solution (possibly non-unique) to the Riccati equation exists and decouples the optimality system. With this solution, the optimal control is obtained in an explicit way.

Linear-quadratic optimal control backward stochastic differential equation random coefficient stochastic Riccati equation

SCI ; EI

英语

第一

NSFC[11901280] ; Guangdong Basic and Applied Basic Research Foundation[2021A1515010031] ; SUSTech start-up funds["Y01286128","Y01286228"] ; Singapore MOE AcRF Grants[R-146-000-271-112]

Automation & Control Systems ; Mathematics

Automation & Control Systems ; Mathematics, Applied

WOS:000654512300001

EDP SCIENCES S A

20212310447944

Optimal control systems ; Quadratic programming ; Riccati equations ; Stochastic control systems

Control Systems:731.1 ; Calculus:921.2

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

Sun, Jingrui,Wang, Hanxiao. Linear-quadratic optimal control for backward stochastic differential equations with random coefficients[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS,2021,27.

Sun, Jingrui,&Wang, Hanxiao.(2021).Linear-quadratic optimal control for backward stochastic differential equations with random coefficients.ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS,27.

Sun, Jingrui,et al."Linear-quadratic optimal control for backward stochastic differential equations with random coefficients".ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 27(2021).