摘要翻译：
研究了Sircar和Papanicolaou引入的动态套期保值策略对资产价格的反馈效应的一类非线性定价模型。我们首先研究了模型中涉及的非线性需求函数的情形。利用李群分析，我们研究了这些非线性扩散方程的对称性。我们给出了子代数的最优系统和所研究的偏微分方程到偏微分方程的非等价约简的完备集。在大多数情况下，我们得到方程的精确解族或导出方程的特解。
---
英文标题：
《Pricing options in illiquid markets: optimal systems, symmetry
  reductions and exact solutions》
---
作者：
Ljudmila A. Bordag
---
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
--

---
英文摘要：
  We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function involved in the model. Using a Lie group analysis we investigate the symmetry properties of these nonlinear diffusion equations. We provide the optimal systems of subalgebras and the complete set of non-equivalent reductions of studied PDEs to ODEs. In most cases we obtain families of exact solutions or derive particular solutions to the equations.
---
PDF链接：
https://arxiv.org/pdf/1002.0864