摘要翻译：
我们提供了一个令人惊讶的经典逼近理论的新应用到一个基本的资产定价模型的数学金融。具体来说，我们计算了指数布朗运动与其时间平均值之间的相关系数的解析值，我们发现分差的使用极大地阐明了公式，为几个新的结果提供了途径。作为应用，我们发现该相关系数总是至少为$1/\sqrt{2}$,并通过Hermite-Genocchi积分关系证明了时间平均值的所有矩都是指数函数的某些分差。我们还证明了这些矩与Oshanin和Yor得到的更复杂的公式一致。
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英文标题：
《Functionals of Exponential Brownian Motion and Divided Differences》
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作者：
Brad Baxter and Raymond Brummelhuis
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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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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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：
  We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and its time average, and we find the use of divided differences greatly elucidates formulae, providing a path to several new results. As applications, we find that this correlation coefficient is always at least $1/\sqrt{2}$ and, via the Hermite--Genocchi integral relation, demonstrate that all moments of the time average are certain divided differences of the exponential function. We also prove that these moments agree with the somewhat more complex formulae obtained by Oshanin and Yor.
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PDF链接：
https://arxiv.org/pdf/1006.1996