可解扩散的对偶随机变换

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摘要翻译：
我们对构造几族可解的一维时间齐次扩散的方法提出了新的扩展，这些扩散的跃迁密度可以解析地得到。我们的方法是基于所谓的扩散正则变换方法的双重应用，它结合了光滑单调映射和通过Doob-h变换的测度变化。这就产生了新的多参数可解扩散，一般分为两大类；第一类是通过具有仿射（线性）漂移和产生的各种非线性扩散系数函数来指定的，而第二类允许具有产生的非线性漂移函数的（通常是非线性的）扩散系数的几个规格。该理论适用于具有奇异和/或非奇异端点的扩散。作为本文结果的一部分，我们也给出了新发展的扩散族的完整边界分类和鞅刻划。
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英文标题：
《Dual Stochastic Transformations of Solvable Diffusions》
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作者：
Giuseppe Campolieti and Roman N. Makarov
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最新提交年份：
2014
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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 present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smooth monotonic mappings and measure changes via Doob-h transforms. This gives rise to new multi-parameter solvable diffusions that are generally divided into two main classes; the first is specified by having affine (linear) drift with various resulting nonlinear diffusion coefficient functions, while the second class allows for several specifications of a (generally nonlinear) diffusion coefficient with resulting nonlinear drift function. The theory is applicable to diffusions with either singular and/or non-singular endpoints. As part of the results in this paper, we also present a complete boundary classification and martingale characterization of the newly developed diffusion families.
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PDF链接：
https://arxiv.org/pdf/0907.2926

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关键词：Quantitative Constructing Differential Applications coefficient diffusions 方法 nonlinear several 线性