scholarly journals On stochastic relaxed control for partially observed diffusions

1984 ◽  
Vol 93 ◽  
pp. 71-108 ◽  
Author(s):  
W. H. Fleming ◽  
M. Nisio
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Control Region ◽  
The State ◽  
Probability Measures ◽  
Control Problems ◽  
Relaxed Control ◽  
Observation Process ◽  
Partially Observed ◽  
Partially Observed Diffusions

In this paper we are concerned with stochastic relaxed control problems of the following kind. Let X(t), t ≥ 0, denote the state of a process being controlled, Y(t), t ≥ 0, the observation process and p(t, ·) a relaxed control, that is a process with values probability measures on the control region Г. The state and observation processes are governed by stochastic differential equationsandwhere B and W are independent Brownian motions with values in Rn and Rm respectively, (put m = 1 for simplicity).

scholarly journals Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui Min ◽  
Ying Peng ◽  
Yongli Qin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Backward Stochastic Differential Equations ◽  
Maximum Principles ◽  
Control Problems ◽  
Linear Quadratic Optimal Control ◽  
Fully Coupled

We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. The stochastic maximum principles are derived and the related mean-field linear quadratic optimal control problems are also discussed.

scholarly journals Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations

2011 ◽  
Vol 43 (02) ◽  
pp. 572-596 ◽  
Author(s):  
Bernt Øksendal ◽  
Agnès Sulem ◽  
Tusheng Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Backward Stochastic Differential Equation ◽  
Maximum Principles ◽  
Optimal Consumption ◽  
Control Problems ◽  
Stochastic Delay ◽  
Stochastic Delay Equations

We study optimal control problems for (time-)delayed stochastic differential equations with jumps. We establish sufficient and necessary stochastic maximum principles for an optimal control of such systems. The associated adjoint processes are shown to satisfy a (time-)advanced backward stochastic differential equation (ABSDE). Several results on existence and uniqueness of such ABSDEs are shown. The results are illustrated by an application to optimal consumption from a cash flow with delay.

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