更改

Presently, one of the main results of econophysics comprises the explanation of the "fat tails" in the distribution of many kinds of financial data as a universal self-similar scaling property (i.e. scale invariant over many orders of magnitude in the data), arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the  risks, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not negligible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a failure probability of only <math>P\propto x^{-4}\,,</math> where x is an increasingly large variable  in the tail region of the distribution considered (i.e. a price statistics with much more than 10⁸ data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away".&nbsp; The "fat tails" are also observed in commodity markets.

Presently, one of the main results of econophysics comprises the explanation of the "fat tails" in the distribution of many kinds of financial data as a universal self-similar scaling property (i.e. scale invariant over many orders of magnitude in the data), arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the  risks, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not negligible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a failure probability of only <math>P\propto x^{-4}\,,</math> where x is an increasingly large variable  in the tail region of the distribution considered (i.e. a price statistics with much more than 10⁸ data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away".&nbsp; The "fat tails" are also observed in commodity markets.

目前，经济物理学的主要研究成果之一是将多种金融数据分布中的“肥尾”解释为一种普遍的自相似标度性质(即“肥尾”)。由于个别市场竞争对手或他们的整体趋势有系统和最佳地利用当前的「微观趋势」(例如，价格上升或下跌)而引起的数量级。这些“肥尾”不仅在数学上很重要，因为它们包含了风险，这些风险一方面可能非常小，以至于人们可能会忽略它们，但另一方面，这些风险一点也不可忽视。它们永远不可能成指数微小，而是遵循一个可测量的代数递减幂律，例如，故障概率只有<math>P\propto x^{-4}\,,</math>其中x在所考虑的分布的尾部区域是一个越来越大的变量(例如，x = 0。一个价格统计数据远远超过10⁸数据)。也就是说，所考虑的事件不仅仅是“异常值” ，而是必须真正加以考虑，不能“保走”。大宗商品市场也出现了“肥尾”现象。

目前，经济物理学的主要研究成果之一是将多种金融数据分布中的“肥尾”解释为一种普遍的自相似标度性质(即“肥尾”)。由于个别市场竞争对手或他们的整体趋势有系统和最佳地利用当前的「微观趋势」(例如，价格上升或下跌)而引起的数量级。这些“肥尾”不仅在数学上很重要，因为它们包含了风险，这些风险一方面可能非常小，以至于人们可能会忽略它们，但另一方面，这些风险一点也不可忽视。它们永远不可能成指数微小，而是遵循一个可测量的代数递减幂律，例如，故障概率只有<math>P\propto x^{-4}\,,</math>其中x在所考虑的分布的尾部区域是一个越来越大的变量(例如，x = 0。一个价格统计数据远远超过10⁸)。也就是说，所考虑的事件不仅仅是“异常值” ，而是必须真正加以考虑，不能“保走”。大宗商品市场也出现了“肥尾”现象。

==Influence==

==Influence==

Presently, one of the main results of econophysics comprises the explanation of the [[Fat-tailed distribution|"fat tails"]] in the distribution of many kinds of financial data as a [[Universality class|universal]] self-similar [[scaling invariance|scaling]] property (i.e. scale invariant over many orders of magnitude in the data),<ref>The physicists noted the scaling behaviour of "fat tails" through a letter to the scientific journal ''[[Nature (journal)|Nature]]'' by Rosario N. Mantegna and H. Eugene Stanley: ''Scaling behavior in the dynamics of an economic index'', Nature Vol. 376, pages 46-49 (1995)</ref> arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the  [[risk]]s, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not negligible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a ''failure probability'' of only <math>P\propto x^{-4}\,,</math> where ''x'' is an increasingly large variable  in the tail region of the distribution considered (i.e. a price statistics with much more than 10⁸ data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away".<ref name="Preis" />&nbsp; It appears that it also plays a role that near a change of the tendency (e.g. from falling to rising prices) there are typical "panic reactions" of the selling or buying agents with algebraically increasing bargain rapidities and volumes.<ref name="Preis">See for example Preis, Mantegna, 2003.</ref>&nbsp; The "fat tails" are also observed in [[commodity market]]s.

Presently, one of the main results of econophysics comprises the explanation of the [[Fat-tailed distribution|"fat tails"]] in the distribution of many kinds of financial data as a [[Universality class|universal]] self-similar [[scaling invariance|scaling]] property (i.e. scale invariant over many orders of magnitude in the data),<ref>The physicists noted the scaling behaviour of "fat tails" through a letter to the scientific journal ''[[Nature (journal)|Nature]]'' by Rosario N. Mantegna and H. Eugene Stanley: ''Scaling behavior in the dynamics of an economic index'', Nature Vol. 376, pages 46-49 (1995)</ref> arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the  [[risk]]s, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not negligible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a ''failure probability'' of only <math>P\propto x^{-4}\,,</math> where ''x'' is an increasingly large variable  in the tail region of the distribution considered (i.e. a price statistics with much more than 10⁸ data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away".<ref name="Preis" />&nbsp; It appears that it also plays a role that near a change of the tendency (e.g. from falling to rising prices) there are typical "panic reactions" of the selling or buying agents with algebraically increasing bargain rapidities and volumes.<ref name="Preis">See for example Preis, Mantegna, 2003.</ref>&nbsp; The "fat tails" are also observed in [[commodity market]]s.

目前，经济物理学的主要研究成果之一是将多种金融数据分布中的'''<font color="#ff8000">肥尾 fat tails</font>'''解释为一种'''<font color="#ff8000">通用的 universal</font>'''自相似'''<font color="#ff8000">标度 scaling</font>'''性质(即“肥尾”)。由于个别市场竞争对手或他们的整体趋势有系统和最佳地利用当前的「微观趋势」(例如，价格上升或下跌)而引起的数量级。这些“肥尾”不仅在数学上很重要，因为它们包含了风险，这些风险一方面可能非常小，以至于人们可能会忽略它们，但另一方面，这些风险一点也不可忽视。它们永远不可能成指数微小，而是遵循一个可测量的代数递减幂律，例如，故障概率只有其中x在所考虑的分布的尾部区域是一个越来越大的变量(例如，x = 0。一个价格统计数据远远超过数据)。也就是说，所考虑的事件不仅仅是“异常值” ，而是必须真正加以考虑，不能“保走”。大宗商品市场也出现了“肥尾”现象

目前，经济物理学的主要研究成果之一是将多种金融数据分布中的'''<font color="#ff8000">肥尾 fat tails</font>'''解释为一种'''<font color="#ff8000">通用的 universal</font>'''自相似'''<font color="#ff8000">标度 scaling</font>'''性质(即“肥尾”)。由于个别市场竞争对手或他们的整体趋势有系统和最佳地利用当前的「微观趋势」(例如，价格上升或下跌)而引起的数量级。这些“肥尾”不仅在数学上很重要，因为它们包含了风险，这些风险一方面可能非常小，以至于人们可能会忽略它们，但另一方面，这些风险一点也不可忽视。它们永远不可能成指数微小，而是遵循一个可测量的代数递减幂律，例如，故障概率只有<math>P\propto x^{-4}\,,</math>其中x在所考虑的分布的尾部区域是一个越来越大的变量(例如，x = 0。一个价格统计数据远远超过10⁸)。也就是说，所考虑的事件不仅仅是“异常值” ，而是必须真正加以考虑，不能“保走”。大宗商品市场也出现了“肥尾”现象

As in quantum field theory the "fat tails" can be obtained by complicated "[[nonperturbative]]" methods, mainly by numerical ones, since they contain the deviations from the usual [[Gaussian distribution|Gaussian approximations]], e.g. the [[Black–Scholes model|Black–Scholes]] theory.  Fat tails can, however, also be due to other phenomena, such as a random number of terms in the central-limit theorem, or any number of other, non-econophysics models. Due to the difficulty in testing such models, they have received less attention in traditional economic analysis.

As in quantum field theory the "fat tails" can be obtained by complicated "[[nonperturbative]]" methods, mainly by numerical ones, since they contain the deviations from the usual [[Gaussian distribution|Gaussian approximations]], e.g. the [[Black–Scholes model|Black–Scholes]] theory.  Fat tails can, however, also be due to other phenomena, such as a random number of terms in the central-limit theorem, or any number of other, non-econophysics models. Due to the difficulty in testing such models, they have received less attention in traditional economic analysis.