英文标题：
《Analysis of the nonlinear option pricing model under variable
  transaction costs》
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作者：
Daniel Sevcovic and Magdalena Zitnanska
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最新提交年份：
2016
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英文摘要：
  In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying asset price and the Gamma of the option. We show that the generalizations of the classical Black--Scholes model can be analyzed by means of transformation of the fully nonlinear parabolic equation into a quasilinear parabolic equation for the second derivative of the option price. We show existence of a classical smooth solution and prove useful bounds on the option prices. Furthermore, we construct an effective numerical scheme for approximation of the solution. The solutions are obtained by means of the efficient numerical discretization scheme of the Gamma equation. Several computational examples are presented.
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中文摘要：
本文分析了可变交易成本下期权定价的非线性Black-Scholes模型。假设价格$V$的非线性抛物线方程的扩散系数是基础资产价格和期权伽马的函数。我们证明了经典Black-Scholes模型的推广可以通过将完全非线性的抛物方程转化为期权价格二阶导数的拟线性抛物方程来分析。我们证明了经典光滑解的存在性，并证明了期权价格的有用界。此外，我们构造了一个有效的数值格式来逼近该解。利用伽马方程的高效数值离散格式得到了这些解。给出了几个算例。
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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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