摘要翻译：
我们的主要研究对象是描述非线性Black-Scholes模型对称性的四维李代数。该模型实现了一个反馈效应，这是一个典型的非流动性市场。李代数的结构依赖于一个参数，即我们与一个单参数代数族有关。我们用Patera-Winternitz方法给出了这些代数的分类。描述了非线性Black-Scholes方程对称代数族的一维、二维和三维子代数的最优系统。最优系统使我们有可能描述方程的一个完整的不变解集。
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英文标题：
《Optimal systems of subalgebras for a nonlinear Black-Scholes equation》
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作者：
Maxim Bobrov
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最新提交年份：
2009
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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：
  The main object of our study is a four dimensional Lie algebra which describes the symmetry properties of a nonlinear Black-Scholes model. This model implements a feedback effect which is typical for an illiquid market. The structure of the Lie algebra depends on one parameter, i.e. we have to do with a one-parametric family of algebras. We provide a classification of these algebras using Patera--Winternitz method. Optimal systems of one-, two- and three- dimensional subalgebras are described for the family of symmetry algebras of the nonlinear Black-Scholes equation. The optimal systems give us the possibility to describe a complete set of invariant solutions to the equation.
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PDF链接：
https://arxiv.org/pdf/0901.2826