摘要翻译：
在数学金融学中，在某些Levy模型下，期权定价的一种流行方法是考虑标的物遵循泊松跳扩散过程。众所周知，这导致了部分积分微分方程(PIDE)，它通常不允许解析解，而数值解带来了一些问题。本文阐述了如何将PIDE转化为一类所谓的伪抛物方程的新方法，这类方程在数学中是已知的，但在数学金融学中是相对较新的。作为一个例子，我们讨论了Levy测度允许这种变换的几个跳扩散模型。
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英文标题：
《Using pseudo-parabolic and fractional equations for option pricing in
  jump diffusion models》
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作者：
Andrey Itkin, Peter Carr
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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：
  In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution while numerical solution brings some problems. In this paper we elaborate a new approach on how to transform the PIDE to some class of so-called pseudo-parabolic equations which are known in mathematics but are relatively new for mathematical finance. As an example we discuss several jump-diffusion models which Levy measure allows such a transformation.
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PDF链接：
https://arxiv.org/pdf/1002.1995