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Existence of solution to a class of stochastic Riccati equations with constraint
HAN Yue-cai 1, Xu Jie 2
1. School of Mathematics, Jilin University, Changchun, 130012
2. School of Mathematics, Jilin University, Changchun, 130012; College of Sciences, Jilin Institute of Chemical Technology, Jilin, 132022
*Correspondence author
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Funding: RFDP （No.20120061110002）
Opened online:17 June 2016
Accepted by: none
Citation: HAN Yue-cai, Xu Jie.Existence of solution to a class of stochastic Riccati equations with constraint[OL]. [17 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697832
 
 
In this paper, the authors investigate a class of stochastic Riccati equation with constraint. Stochastic Riccati equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. Because of its complex structure, and the equation is matrix-valued, the solvability of the stochastic Riccati equation is very difficult, but is the key to solve the stochastic linear quadratic optimal control problem. The main idea is to replace the stochastic Riccati equation by a backward stochastic differential equation (without including algebraic constraint), and the existence of solution for backward stochastic differential equation enforces the algebraic constraint to be satisfied automatically.
Keywords:stochastic Riccati equation; constraint condition; backward stochastic differential equation; stochastic linear quadratic optimal control
 
 
 

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