英文标题：
《Pricing Derivatives under Multiple Stochastic Factors by Localized
Radial Basis Function Methods》
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作者：
Slobodan Milovanovi\\\'c and Victor Shcherbakov
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最新提交年份：
2018
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英文摘要：
We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing problems arising from market models with multiple stochastic factors. We demonstrate the useful features of the proposed methods, such as high accuracy, sparsity of the differentiation matrices, mesh-free nature and multi-dimensional extendability, and show how to apply these methods for solving time-dependent higher-dimensional PDEs in finance. We test these methods on several problems that incorporate stochastic asset, volatility, and interest rate dynamics by conducting numerical experiments. The results illustrate the capability of both methods to solve the problems to a sufficient accuracy within reasonable time. Both methods exhibit similar orders of convergence, which can be further improved by a more elaborate choice of the method parameters. Finally, we discuss the parallelization potentials of the proposed methods and report the speedup on the example of RBF-FD.
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中文摘要：
我们提出了两种局部径向基函数（RBF）方法，即径向基函数单位分割法（RBF-PUM）和径向基函数生成有限差分法（RBF-FD），用于解决由多随机因素市场模型引起的金融衍生品定价问题。我们展示了所提方法的有用特性，如高精度、微分矩阵的稀疏性、无网格性和多维可扩展性，并展示了如何将这些方法应用于求解金融领域中与时间相关的高维偏微分方程。我们通过进行数值实验，在几个包含随机资产、波动性和利率动态的问题上测试这些方法。结果表明，这两种方法都能够在合理的时间内以足够的精度解决问题。这两种方法表现出相似的收敛顺序，可以通过更精细地选择方法参数来进一步改进。最后，我们讨论了所提方法的并行化潜力，并以RBF-FD为例报告了加速效果。
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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：Computer Science 计算机科学
二级分类：Computational Engineering, Finance, and Science 计算工程、金融和科学
分类描述：Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的，集中在技术和工具，使挑战性的计算模拟能够执行，其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4（经济学）中的材料。
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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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