scholarly journals Verification theorems for stochastic optimal control problems via a time dependent Fukushima–Dirichlet decomposition

2006 ◽  
Vol 116 (11) ◽  
pp. 1530-1562 ◽  
Author(s):  
Fausto Gozzi ◽  
Francesco Russo
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Time Dependent ◽  
Control Problems

scholarly journals A New Approach to Solving Stochastic Optimal Control Problems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1207 ◽  
Author(s):  
Pablo T. Rodriguez-Gonzalez ◽  
Vicente Rico-Ramirez ◽  
Ramiro Rico-Martinez ◽  
Urmila M. Diwekar
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Objective Function ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Biodiesel Production ◽  
Time Dependent ◽  
Control Problems ◽  
Model Calculations ◽  
New Approach

A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from the optimality conditions. An alternative approach consists of using continuous random variables to capture uncertainty through sampling-based methods embedded within an optimization strategy for the decision variables; such a technique may also fail due to the computational intensity involved in excessive model calculations for evaluating the objective function and its derivatives for each sample. This paper presents a new approach to solving stochastic optimal control problems with time-dependent uncertainties based on BONUS (Better Optimization algorithm for Nonlinear Uncertain Systems). The BONUS has been used successfully for non-linear programming problems with static uncertainties, but we show here that its scope can be extended to the case of optimal control problems with time-dependent uncertainties. A batch reactor for biodiesel production was used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles were better than those obtained by the maximum principle.

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
Sign in / Sign up

Export Citation Format

Share Document