英文标题：
《Weakly chained matrices, policy iteration, and impulse control》
---
作者：
Parsiad Azimzadeh, Peter A. Forsyth
---
最新提交年份：
2017
---
英文摘要：
This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) semi-Lagrangian discretization schemes applied to the HJBQVI problem. Scheme (i) takes the form of a Bellman problem involving an operator which is not necessarily contractive. We consider the well-posedness of the Bellman problem and give sufficient conditions for convergence of the corresponding policy iteration. To do so, we use weakly chained diagonally dominant matrices, which give a graph-theoretic characterization of weakly diagonally dominant M-matrices. We compare schemes (i)--(iii) under the following examples: (a) optimal control of the exchange rate, (b) optimal consumption with fixed and proportional transaction costs, and (c) pricing guaranteed minimum withdrawal benefits in variable annuities. We find that one should abstain from using scheme (i).
---
中文摘要：
这项工作的动力来自于与组合随机和脉冲控制问题相关的Hamilton-Jacobi-Bellman拟变分不等式（HJBKVIS）的数值解。特别地，我们考虑（i）直接控制，（ii）惩罚，以及（iii）应用于HJBKVI问题的半拉格朗日离散化方案。方案（i）采用了一个贝尔曼问题的形式，涉及一个不一定是收缩的算子。我们考虑了Bellman问题的适定性，并给出了相应策略迭代收敛的充分条件。为此，我们使用弱链对角占优矩阵，它给出了弱对角占优M-矩阵的图论特征。我们比较了方案（i）——（iii）在以下示例下：（a）汇率的最优控制，（b）具有固定和比例交易成本的最优消费，以及（c）可变年金中有保证的最低提款利益的定价。我们发现应该避免使用方案（i）。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
--
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--

---
PDF下载：
-->