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arXiv 0901.1945q-fin.STcs.CEmath.CAmath.PRq-fin.CPstat.AP
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金融时间序列趋势存在性的数学证明

A mathematical proof of the existence of trends in financial time series

Michel Fliess, Cédric Join

摘要:

通过证明金融时间序列中趋势的存在,我们正在解决量化金融中的一个长期争论,这要归功于卡地亚和Y。Perrin,用非标准分析的语言表达(有限集上的积分,F。& M. Diener(Eds):Nonstandard Analysis in Practice,Springer,1995,pp. 195- 204)。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共存,但似乎很难与著名的布莱克-斯科尔斯模型相协调。他们估计通过最近的技术源于控制和信号理论。对各种金融量的预测进行了几个相当有说服力的计算机模拟。最后,我们讨论概率论的作用。

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 rôle of probability theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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