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摘要翻译：
本文提出了一种简单易行的方法，用于求解一类比较一般的Hamilton-Jacobi-Bellman(HJB)方程。在许多情况下，所考虑的问题只有粘性解，幸运的是，许多直观的（例如基于有限差分的）离散可以收敛到粘性解。然而，特别是当采用具有良好稳定性的全隐式时间步长格式时，人们仍然面临着求解由此产生的非线性离散系统的艰巨任务。本文给出了一种在罚参数下将非线性离散系统近似为一阶的罚方法，并证明了用一种迭代格式可以在有限步内求解罚离散问题。我们包括了数学金融学中的一些例子，对于这些例子，所描述的方法产生了一个严格的数值格式并给出了数值结果。
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英文标题：
《A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman
(HJB) Equations in Finance》
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作者：
Jan Hendrik Witte and Christoph Reisinger
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最新提交年份：
2010
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分类信息：
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
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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
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英文摘要：
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.
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PDF链接：
https://arxiv.org/pdf/1008.0401
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