2020/02/19 by Christelle Dleuna Nyoumbi, Nyoumbi, Christelle Dleuna, Antoine Tambue +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2002.08464
openalex publication_date 2020/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.