摘要翻译：
借助Dirichlet形式方法，我们研究了完全和不完全金融模型之间的转换点。我们将Bouleau开发的最新技术应用到套期保值过程中，以便在波动率参数固定但对交易者不确定的情况下扰动参数和随机过程；我们称之为扰动Black Scholes模型(PBS)。我们证明了该模型可以同时再现微笑效应和买卖价差；当考虑vanilla期权时，我们给出了与PBS模型等价的局部波动率模型相关的波动率函数。最后，我们给出了利用Dirichlet形式的误差理论与效用函数理论之间的联系。
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英文标题：
《Perturbative Approach on Financial Markets》
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作者：
Simone Scotti
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最新提交年份：
2008
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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
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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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英文摘要：
  We study the point of transition between complete and incomplete financial models thanks to Dirichlet Forms methods. We apply recent techniques, developped by Bouleau, to hedging procedures in order to perturbate parameters and stochastic processes, in the case of a volatility parameter fixed but uncertain for traders; we call this model Perturbed Black Scholes (PBS) Model. We show that this model can reproduce at the same time a smile effect and a bid-ask spread; we exhibit the volatility function associated to the local-volatility model equivalent to PBS model when vanilla options are concerned.   Lastly, we present a connection between Error Theory using Dirichlet Forms and Utility Function Theory.
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PDF链接：
https://arxiv.org/pdf/0806.0287