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摘要翻译：
我们通过证明金融时间序列中趋势的存在来解决数量金融学中的一个长期争论，这要归功于P.Cartier和Y.Perrin的一个定理，该定理用非标准分析的语言表达（有限集上的积分，F.&M.Diener（编辑）：非标准分析在实践中，Springer，1995年，第195-204页）。这些趋势可能与一些改变的随机游走范式和有效市场假说并存，但似乎很难与著名的布莱克-斯科尔斯模型相协调。它们是通过来自控制和信号理论的最新技术来估计的。描述了对各种金融数量预测的几个相当令人信服的计算机模拟。我们通过讨论概率论的R^ole来总结。
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英文标题：
《A mathematical proof of the existence of trends in financial time series》
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作者：
Michel Fliess (LIX, INRIA Saclay - Ile de France), C\'edric Join
(INRIA Saclay - Ile de France, CRAN)
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Computer Science 计算机科学
二级分类：Computational Engineering, Finance, and Science 计算工程、金融和科学
分类描述：Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的，集中在技术和工具，使挑战性的计算模拟能够执行，其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4（经济学）中的材料。
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一级分类：Mathematics 数学
二级分类：Classical Analysis and ODEs 经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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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：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the r\^ole of probability theory.
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PDF链接：
https://arxiv.org/pdf/0901.1945
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