摘要翻译：
本文将Weideman[IMA J.Numer.Anal.]最近提出的积分半离散对流扩散偏微分方程的等高线积分方法推广应用于数学金融学中的一些重要方程。利用空间算子的数值范围估计，从理论上导出了最优轮廓参数，并进行了数值验证。给出的测试例子是一维的Black-Scholes偏微分方程和二维的Heston偏微分方程。在后一种情况下，效率与ADI分裂方案相比较，以解决这个问题。算例表明，在中高精度要求的范围内，等高线积分法具有较好的优越性。对目前等高线积分方法的实现提出了进一步的改进建议。
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英文标题：
《Appraisal of a contour integral method for the Black-Scholes and Heston
  equations》
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作者：
K.J. in 't Hout and J.A.C. Weideman
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最新提交年份：
2011
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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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英文摘要：
  A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parameters are derived theoretically and tested numerically. Test examples presented are the Black-Scholes PDE in one space dimension and the Heston PDE in two dimensions. In the latter case efficiency is compared to ADI splitting schemes for solving this problem. In the examples it is found that the contour integral method is superior for the range of medium to high accuracy requirements. Further improvements to the current implementation of the contour integral method are suggested.
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PDF链接：
https://arxiv.org/pdf/0912.0434