英文标题：
《Pricing Financial Derivatives using Radial Basis Function generated
Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts》
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作者：
Slobodan Milovanovi\\\'c
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最新提交年份：
2018
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英文摘要：
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfully apply it to two types of multidimensional partial differential equations in finance: a two-asset European call basket option under the Black--Scholes--Merton model, and a European call option under the Heston model. We also show that the performance of the improved method is equally high when it comes to pricing American options. By studying convergence, computational performance, and conditioning of the discrete systems, we show the superiority of the introduced approaches over previously used versions of the RBF-FD method in financial applications.
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中文摘要：
在本文中，我们研究了使用多谐样条曲线和平滑变化密度的节点布局来开发稳健高效的径向基函数生成有限差分（RBF-FD）方法用于金融衍生品定价的好处。我们提出了一个显著改进的RBF-FD方案，并成功地将其应用于金融领域的两类多维偏微分方程：Black-Scholes-Merton模型下的双资产欧洲看涨期权和Heston模型下的欧洲看涨期权。我们还表明，改进后的方法在美式期权定价方面的性能同样高。通过研究离散系统的收敛性、计算性能和条件，我们展示了引入的方法在金融应用中优于先前使用的RBF-FD方法。
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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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