英文标题：
《Algebraic Structure of Vector Fields in Financial Diffusion Models and
  its Applications》
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作者：
Yusuke Morimoto and Makiko Sasada
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最新提交年份：
2015
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英文摘要：
  High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical methods. The authors found a special Lie algebraic structure on the vector fields in the major financial diffusion models. Using this structure, we can solve the flows associated with vector fields analytically and efficiently. Numerical examples show that our method saves the computation time drastically.
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中文摘要：
Kusuoka、Lyons Victoir、Ninomia Victoir和Ninomia Ninomia介绍了使用自由李代数值随机变量的SDE高阶离散格式。这些方案称为KLNV方法。它们涉及求解与SDE相关的向量场流，通常通过数值方法完成。作者在主要金融扩散模型的向量场上发现了一种特殊的李代数结构。利用这种结构，我们可以解析且高效地求解与向量场相关的流。数值算例表明，该方法大大节省了计算时间。
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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