Relationship Between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic Approach

2000 ◽  
Vol 38 (5) ◽  
pp. 1392-1407 ◽  
Author(s):  
Michael Kohlmann ◽  
Xun Yu Zhou
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Linear Quadratic ◽  
Stochastic Controls

scholarly journals Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Chen ◽  
Zhen Wu ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Delay System ◽  
Linear Quadratic ◽  
Stochastic Linear System ◽  
And Control

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

scholarly journals A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients

2004 ◽  
Vol 2004 (6) ◽  
pp. 461-477
Author(s):  
Omid. S. Fard ◽  
Ali V. Kamyad
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Term ◽  
Piecewise Linear ◽  
Backward Stochastic Differential Equation ◽  
Numerical Approach ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Controls ◽  
The Relationship ◽  
Uniformly Continuous

We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE corresponding to the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.

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