摘要翻译：
给出了Black-Scholes方程的非线性修正的精确解族。这种风险调整定价方法模型(RAPM)既考虑了交易成本，又考虑了波动性投资组合的风险。利用李群分析，得到了RAPM方程所承认的李代数。它给出了描述一个最优子代数系统的可能性，并相应地给出了该模型的不变解集。这样，我们就可以描述非线性RAPM模型可能约简的全集。以不同的二阶常微分方程的形式给出了约化。在所有情况下，我们提供了这些方程的精确或参数形式的解。我们讨论了这些约化的性质和相应的不变解。
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英文标题：
《Study of the risk-adjusted pricing methodology model with methods of
  Geometrical Analysis》
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作者：
Ljudmila A. Bordag
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最新提交年份：
2010
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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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英文摘要：
  Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.
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PDF链接：
https://arxiv.org/pdf/0911.0113