scholarly journals Time-inconsistent optimal control problems and the equilibrium HJB equation

2012 ◽  
Vol 2 (3) ◽  
pp. 271-329 ◽  
Author(s):  
Jiongmin Yong ◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Hjb Equation ◽  
Control Problems ◽  
Time Inconsistent

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.

A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation

2018 ◽  
Vol 24 (2) ◽  
pp. 639-676
Author(s):  
Jianjun Zhou
Keyword(s):  
Optimal Control ◽  
Viscosity Solution ◽  
Optimal Control Problems ◽  
Nonlinear Partial Differential Equation ◽  
Infinite Horizon ◽  
Hjb Equation ◽  
Second Order ◽  
Control Problems ◽  
Stochastic Delay ◽  
Hamilton Jacobi Bellman

In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including timetand identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.

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