A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

2010 ◽  
Author(s):  
Walailuck Chavanasporn ◽  
Christian-Oliver Ewald
Keyword(s):  
Optimal Control ◽  
Numerical Method ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Linear Control ◽  
Control Problems

Dynamic Path Synthesis and Optimal Control

1974 ◽  
Vol 96 (1) ◽  
pp. 19-24
Author(s):  
P. J. Starr
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Fourth Order ◽  
Optimal Control Problems ◽  
Singular Control ◽  
Physical Nature ◽  
Linear Control ◽  
Control Problems ◽  
Dynamic Path ◽  
Path Synthesis

Dynamic Path Synthesis refers to a class of linkage synthesis problems in which constraint paths between specified positions are determined in such a way as to optimize some measure of the resulting dynamic behavior. These problems can be transformed into nonlinear optimal control problems which are generally non-autonomous. The physical nature of the system allows general comments to be made regarding uniqueness, controllability, and singular control. The ideas are developed in the context of a two-link device yielding a fourth order non-linear control problem, for which a numerical example is presented.

scholarly journals A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems

2021 ◽  
Author(s):  
Christelle Dleuna Nyoumbi ◽  
Antoine Tambue
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Finite Difference Method ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Hjb Equation ◽  
High Dimensional ◽  
Control Problems ◽  
Volume Method

AbstractStochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton–Jacobi–Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the only tools to provide accurate approximations. The aims of this paper is to introduce a novel fitted finite volume method to solve high dimensional degenerated HJB equation from stochastic optimal control problems in high dimension ($$ n\ge 3$$ n ≥ 3 ). The challenge here is due to the nature of our HJB equation which is a degenerated second-order partial differential equation coupled with an optimization problem. For such problems, standard scheme such as finite difference method losses its monotonicity and therefore the convergence toward the viscosity solution may not be guarantee. We discretize the HJB equation using the fitted finite volume method, well known to tackle degenerated PDEs, while the time discretisation is performed using the Implicit Euler scheme.. We show that matrices resulting from spatial discretization and temporal discretization are M-matrices. Numerical results in finance demonstrating the accuracy of the proposed numerical method comparing to the standard finite difference method are provided.

scholarly journals A fitted finite volume method for stochastic optimal control problems in finance

2021 ◽  
Vol 6 (4) ◽  
pp. 3053-3079
Author(s):  
Christelle Dleuna Nyoumbi ◽  
◽  
Antoine Tambue ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Volume Method
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