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Another good example is random matrix theory, which can be used to identify the noise in financial correlation matrices.  One paper has argued that this technique can improve the performance of portfolios, e.g., in applied in portfolio optimization.

Another good example is random matrix theory, which can be used to identify the noise in financial correlation matrices.  One paper has argued that this technique can improve the performance of portfolios, e.g., in applied in portfolio optimization.

There are, however, various other tools from physics that have so far been used, such as fluid dynamics, classical mechanics and quantum mechanics (including so-called classical economy, quantum economics and quantum finance), and the path integral formulation of statistical mechanics.

There are, however, various other tools from physics that have so far been used, such as fluid dynamics, classical mechanics and quantum mechanics (including so-called classical economy, quantum economics and quantum finance), and the path integral formulation of statistical mechanics.

然而，到目前为止，还有其他各种各样的物理学工具被使用，例如流体动力学、经典力学和量子力学(包括所谓的古典经济学、量子经济学和量子金融学) ，以及路径积分表述统计力学。

然而，到目前为止，还有其他各种各样的物理学工具被使用，例如'''<font color="#ff8000">流体动力学 fluid dynamics</font>'''、'''<font color="#ff8000">经典力学 classical mechanics</font>'''和'''<font color="#ff8000">量子力学 quantum mechanics</font>'''(包括所谓的'''<font color="#ff8000">古典经济学 classical economy</font>'''、'''<font color="#ff8000">量子经济学 quantum economics</font>'''和'''<font color="#ff8000">量子金融学 quantum finance</font>''') ，以及'''<font color="#ff8000">路径积分表述 path integral formulation</font>'''统计力学。

The concept of economic complexity index, introduced by the MIT physicist Cesar A. Hidalgo and the Harvard economist Ricardo Hausmann and made available at MIT's Observatory of Economic Complexity, has been devised as a predictive tool for economic growth. According to the estimates of Hausmann and Hidalgo, the ECI is far more accurate in predicting GDP growth than the traditional governance measures of the World Bank.

The concept of economic complexity index, introduced by the MIT physicist Cesar A. Hidalgo and the Harvard economist Ricardo Hausmann and made available at MIT's Observatory of Economic Complexity, has been devised as a predictive tool for economic growth. According to the estimates of Hausmann and Hidalgo, the ECI is far more accurate in predicting GDP growth than the traditional governance measures of the World Bank.

经济复杂性指数的概念，由麻省理工学院的物理学家 Cesar a. Hidalgo 和哈佛大学的经济学家 Ricardo Hausmann 提出，并在麻省理工学院的经济复杂性观察站提供，已经被设计成经济增长的预测工具。根据 Hausmann 和 Hidalgo 的估计，与世界银行的传统治理措施相比，出口信贷保险在预测 GDP 增长方面要准确得多。

'''<font color="#ff8000">经济复杂性指数 economic complexity index</font>'''的概念，由麻省理工学院的物理学家'''<font color="#ff8000">塞萨尔·A·希达尔戈 Cesar a. Hidalgo</font>'''和哈佛大学的经济学家'''<font color="#ff8000">里卡多·豪斯曼 Ricardo Hausmann </font>''' 提出，并在麻省理工学院的'''<font color="#ff8000">经济复杂性观察站 Observatory of Economic Complexity</font>'''提供，已经被设计成'''<font color="#ff8000">经济增长的预测工具 predictive tool for economic growth</font>'''。根据 Hausmann 和 Hidalgo 的估计，与'''<font color="#ff8000">世界银行 World Bank</font>'''的传统治理措施相比，出口信贷保险在预测 GDP 增长方面要准确得多。

There are also analogies between finance theory and diffusion theory. For instance, the Black–Scholes equation for option pricing is a diffusion-advection equation (see however  for a critique of the Black–Scholes methodology). The Black–Scholes theory can be extended to provide an analytical theory of main factors in economic activities. Other economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics. More recently, Vernon L. Smith, one of the founders of experimental economics and Nobel Memorial Prize in Economic Sciences laureate, has used these techniques and claimed they show a lot of promise. Also several scaling laws have been found in various economic data.

There are also analogies between finance theory and diffusion theory. For instance, the Black–Scholes equation for option pricing is a diffusion-advection equation (see however  for a critique of the Black–Scholes methodology). The Black–Scholes theory can be extended to provide an analytical theory of main factors in economic activities. Other economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics. More recently, Vernon L. Smith, one of the founders of experimental economics and Nobel Memorial Prize in Economic Sciences laureate, has used these techniques and claimed they show a lot of promise. Also several scaling laws have been found in various economic data.

在金融理论和扩散理论之间也有相似之处。例如，期权定价的布莱克-斯科尔斯方程是一个扩散-对流方程(见对布莱克-斯科尔斯方法论的批判)。布莱克-斯科尔斯理论可以扩展为经济活动中主要因素的分析理论。其他经济学家，包括毛罗 · 加勒盖蒂，史蒂夫 · 基恩，保罗 · 奥默罗德和艾伦 · 基尔曼对此表现出了更多的兴趣，但也批评了经济物理学的一些趋势。最近，实验经济学创始人之一、诺贝尔经济学奖得主弗农 · l · 史密斯使用了这些技术，并声称它们显示了很大的希望。在各种经济数据中也发现了一些标度律。

在金融理论和'''<font color="#ff8000">扩散 Diffusion</font>'''理论之间也有相似之处。例如，期权定价的'''<font color="#ff8000">布莱克-斯科尔斯方程 Black–Scholes equation</font>'''是一个'''<font color="#ff8000">扩散-对流 diffusion-advection</font>'''方程(见对布莱克-斯科尔斯方法论的批判)。布莱克-斯科尔斯理论可以扩展为经济活动中主要因素的分析理论。其他经济学家，包括毛罗 · 加勒盖蒂，史蒂夫 · 基恩，保罗 · 奥默罗德和艾伦 · 基尔曼对此表现出了更多的兴趣，但也批评了经济物理学的一些趋势。最近，实验经济学创始人之一、诺贝尔经济学奖得主弗农·L·史密斯使用了这些技术，并声称它们表现出良好的前景。在各种经济数据中也发现了一些标度律。

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“胖尾”解释为一种普遍的自相似标度性质(即“胖尾”)。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10 < sup > 8 </sup > 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“胖尾”解释为一种普遍的自相似标度性质(即“胖尾”)。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。

==Influence==

==Influence==