英文标题：
《The G\\\"{a}rtner-Ellis theorem, homogenization, and affine processes》
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作者：
Archil Gulisashvili and Josef Teichmann
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最新提交年份：
2014
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英文摘要：
  We obtain a first order extension of the large deviation estimates in the G\\\"{a}rtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The construction of the special family of functions mentioned above is based on heat kernel expansions. Some of the ideas employed in the paper come from the theory of affine stochastic processes. For instance, we provide an explicit expansion with respect to the homogenization parameter of the rescaled cumulant generating function in the case of a generic continuous affine process. We also compute the coefficients in the homogenization expansion for the Heston model that is one of the most popular stock price models with stochastic volatility.
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中文摘要：
我们得到了G \\“{a}中大偏差估计的一阶推广埃利斯定理。此外，对于给定的测度族，我们发现了一个特殊的函数族，它的拉普拉斯原理展开式与原始测度族的拉普拉斯原理展开式相似，其阶数为1。上述特殊函数族的构造基于热核展开。本文采用的一些思想来自仿射随机过程理论。例如，在一般连续仿射过程的情况下，我们提供了关于重标度累积量生成函数的均匀化参数的显式展开。我们还计算了Heston模型的均匀化展开系数，Heston模型是最流行的随机波动性股票价格模型之一。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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