摘要翻译：
导出了具有随机波动的广义5D Black-Scholes微分方程。通过高维算子可以实现随机变量的随机演化从放大空间或超空间到普通空间的投影。与三维Merton-Garman方程相关的证券和波动性的随机性可以解释为额外维的影响。我们证明了Merton-Garman方程是包含无穷多个类Merton-Garman方程族中的第一激发态，即n=m=1。
---
英文标题：
《Extra-Dimensional Approach to Option Pricing and Stochastic Volatility》
---
作者：
Minh Q. Truong
---
最新提交年份：
2010
---
分类信息：

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
--
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
--

---
英文摘要：
  The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space or superspace onto an ordinary space can be achieved via higher-dimensional operators. The stochastic nature of the securities and volatility associated with the 3D Merton-Garman equation can then be interpreted as the effects of the extra dimensions. We showed that the Merton-Garman equation is the first excited state, i.e. n=m=1, within a family which contain an infinite numbers of Merton-Garman-like equations.
---
PDF链接：
https://arxiv.org/pdf/1001.4098