A fitted finite volume method for stochastic optimal control Problems
Numerical Analysis
2020-02-21 v1 Numerical Analysis
Analysis of PDEs
Abstract
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature of the HJB equation, which may be a second-order degenerated partial differential equation coupled with optimization. In the work, we discretize the HJB equation using the fitted finite volume method and show that matrix resulting from spatial discretization is an M-matrix. The optimization problem is solved at every time step using iterative method. Numerical results are presented to show the robustness of the fitted finite volume numerical method comparing to the standard finite difference method.
Cite
@article{arxiv.2002.08464,
title = {A fitted finite volume method for stochastic optimal control Problems},
author = {Christelle Dleuna Nyoumbi and Antoine Tambue},
journal= {arXiv preprint arXiv:2002.08464},
year = {2020}
}