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摘要翻译：
在本文中，给定一个演化的混合概率密度，我们定义了一个候选扩散过程，其边缘律遵循相同的演化。作为一个特例，我们导出了一个具有唯一强解的随机微分方程(SDE)，它的密度演化为高斯密度的混合物。我们给出了一个有趣的结果，即所得到的过程与其平方扩散系数之间的瞬时关联和终端关联的比较。作为数学金融学的一个应用，我们构造了边际密度为对数正态密度混合的扩散过程。我们解释了如何使用这些过程来建模市场微笑现象。我们证明了对数正态混合动力学是一个合适的不确定波动率模型的一维扩散版本，并适当地重新解释了早期的相关结果。我们从数值上探讨了扩散型和不确定波动型的未来微笑结构之间的关系。
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英文标题：
《The general mixture-diffusion SDE and its relationship with an
uncertain-volatility option model with volatility-asset decorrelation》
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作者：
Damiano Brigo
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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：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 the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE) admitting a unique strong solution and whose density evolves as a mixture of Gaussian densities. We present an interesting result on the comparison between the instantaneous and the terminal correlation between the obtained process and its squared diffusion coefficient. As an application to mathematical finance, we construct diffusion processes whose marginal densities are mixtures of lognormal densities. We explain how such processes can be used to model the market smile phenomenon. We show that the lognormal mixture dynamics is the one-dimensional diffusion version of a suitable uncertain volatility model, and suitably reinterpret the earlier correlation result. We explore numerically the relationship between the future smile structures of both the diffusion and the uncertain volatility versions.
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PDF链接：
https://arxiv.org/pdf/0812.4052
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