论文标题
随机最佳控制问题的拟合有限体积方法
A fitted finite volume method for stochastic optimal control Problems
论文作者
论文摘要
在本文中，我们提供了一种基于拟合有限体积方法的数值方法，以近似于来自随机最佳控制问题的汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程。计算挑战是由于HJB方程的性质造成的，这可能是二阶退化部分微分方程以及优化。在工作中，我们使用拟合有限体积方法将HJB方程离散化，并表明由空间离散化产生的矩阵是M-Matrix。使用迭代方法在每个时间步骤求解优化问题。给出了数值结果，以显示与标准有限差方法相比，拟合有限体积数值方法的鲁棒性。
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.
