英文标题：
《A Method of Reducing Dimension of Space Variables in Multi-dimensional
Black-Scholes Equations》
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作者：
Hyong-chol O, Yong-hwa Ro, Ning Wan
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最新提交年份：
2014
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英文摘要：
We study a method of reducing space dimension in multi-dimensional Black-Scholes partial differential equations as well as in multi-dimensional parabolic equations. We prove that a multiplicative transformation of space variables in the Black-Scholes partial differential equation reserves the form of Black-Scholes partial differential equation and reduces the space dimension. We show that this transformation can reduce the number of sources of risks by two or more in some cases by giving remarks and several examples of financial pricing problems. We also present that the invariance of the form of Black-Scholes equations is based on the invariance of the form of parabolic equation under a change of variables with the linear combination of variables.
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中文摘要：
研究了多维Black-Scholes偏微分方程和多维抛物型方程的降维方法。证明了Black-Scholes偏微分方程中空间变量的乘法变换保留了Black-Scholes偏微分方程的形式，并降低了空间维数。我们通过评论和几个金融定价问题的例子来说明，在某些情况下，这种转变可以将风险源的数量减少两个或更多。我们还证明了Black-Scholes方程形式的不变性是基于抛物型方程形式在变量变化和变量线性组合情况下的不变性。
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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：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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