“经济物理学”的版本间的差异

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2020年5月12日 (二) 17:34的版本

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Econophysics is a heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Some of its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics. Econophysics is closely related to social physics.

Econophysics is a heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Some of its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics. Econophysics is closely related to social physics.

经济物理学是一个非正统的科际整合，它应用物理学家最初为了解决经济学问题而开发的理论和方法，通常包括不确定性或随机过程和非线性动力学。它在金融市场研究中的一些应用也被称为统计金融学，因为它源于统计物理学。经济物理学与社会物理学密切相关。


History

Physicists' interest in the social sciences is not new; Daniel Bernoulli, as an example, was the originator of utility-based preferences. One of the founders of neoclassical economic theory, former Yale University Professor of Economics Irving Fisher, was originally trained under the renowned Yale physicist, Josiah Willard Gibbs.[1] Likewise, Jan Tinbergen, who won the first Nobel Memorial Prize in Economic Sciences in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with Paul Ehrenfest at Leiden University. In particular, Tinbergen developed the gravity model of international trade that has become the workhorse of international economics.

Physicists' interest in the social sciences is not new; Daniel Bernoulli, as an example, was the originator of utility-based preferences. One of the founders of neoclassical economic theory, former Yale University Professor of Economics Irving Fisher, was originally trained under the renowned Yale physicist, Josiah Willard Gibbs. Likewise, Jan Tinbergen, who won the first Nobel Memorial Prize in Economic Sciences in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with Paul Ehrenfest at Leiden University. In particular, Tinbergen developed the gravity model of international trade that has become the workhorse of international economics.

物理学家对社会科学的兴趣并不是什么新鲜事; 例如，丹尼尔·伯努利就是基于效用的偏好的鼻祖。新古典主义经济理论的创始人之一，前耶鲁大学经济学教授 Irving Fisher，最初受训于著名的耶鲁大学物理学家约西亚·威拉德·吉布斯。同样，Jan Tinbergen，因为开发和应用经济过程分析的动力学模型而获得1969年诺贝尔经济学奖，在莱顿大学和 Paul Ehrenfest 一起学习物理学。特别是，廷伯根发展了国际贸易的引力模型，这个模型已经成为国际经济学的主力。


Econophysics was started in the mid-1990s by several physicists working in the subfield of statistical mechanics. Unsatisfied with the traditional explanations and approaches of economists – which usually prioritized simplified approaches for the sake of soluble theoretical models over agreement with empirical data – they applied tools and methods from physics, first to try to match financial data sets, and then to explain more general economic phenomena.

Econophysics was started in the mid-1990s by several physicists working in the subfield of statistical mechanics. Unsatisfied with the traditional explanations and approaches of economists – which usually prioritized simplified approaches for the sake of soluble theoretical models over agreement with empirical data – they applied tools and methods from physics, first to try to match financial data sets, and then to explain more general economic phenomena.

经济物理学是在20世纪90年代中期由几个在统计力学物理学领域工作的物理学家发起的。他们不满足于经济学家的传统解释和方法——这种方法通常优先考虑简化的方法，以便于理解理论模型，而不是与实证数据取得一致——他们应用物理学的工具和方法，首先试图匹配金融数据集，然后解释更普遍的经济现象。


One driving force behind econophysics arising at this time was the sudden availability of large amounts of financial data, starting in the 1980s. It became apparent that traditional methods of analysis were insufficient – standard economic methods dealt with homogeneous agents and equilibrium, while many of the more interesting phenomena in financial markets fundamentally depended on heterogeneous agents and far-from-equilibrium situations.

One driving force behind econophysics arising at this time was the sudden availability of large amounts of financial data, starting in the 1980s. It became apparent that traditional methods of analysis were insufficient – standard economic methods dealt with homogeneous agents and equilibrium, while many of the more interesting phenomena in financial markets fundamentally depended on heterogeneous agents and far-from-equilibrium situations.

当时经济物理学兴起的一个推动力是，自1980年代开始，突然出现了大量的金融数据。显然，传统的分析方法是不够充分的——标准的经济方法处理的是同质的行为者和均衡，而金融市场中许多更有趣的现象从根本上依赖于异质的行为者和远离均衡的情况。


The term "econophysics" was coined by H. Eugene Stanley, to describe the large number of papers written by physicists in the problems of (stock and other) markets, in a conference on statistical physics in Kolkata (erstwhile Calcutta) in 1995 and first appeared in its proceedings publication in Physica A 1996.[2][3] The inaugural meeting on econophysics was organised in 1998 in Budapest by János Kertész and Imre Kondor. The first book on econophysics was by R. N. Mantegna & H. E. Stanley in 2000.[4]

The term "econophysics" was coined by H. Eugene Stanley, to describe the large number of papers written by physicists in the problems of (stock and other) markets, in a conference on statistical physics in Kolkata (erstwhile Calcutta) in 1995 and first appeared in its proceedings publication in Physica A 1996. The inaugural meeting on econophysics was organised in 1998 in Budapest by János Kertész and Imre Kondor. The first book on econophysics was by R. N. Mantegna & H. E. Stanley in 2000.

“经济物理学”一词是由 h · 尤金 · 斯坦利于1995年在加尔各答的一次统计物理学会议上发明的，用来描述物理学家们在(股票和其他)市场问题上撰写的大量论文，这些论文首次出现在1996年在 Physica 出版的会议记录中。经济物理学会议于1998年在布达佩斯由 j nos kert sz 和 Imre Kondor 组织。2000年，r. n. Mantegna & h. e. Stanley 出版了第一本关于经济物理学的书。


The almost regular meeting series on the topic include: ECONOPHYS-KOLKATA (held in Kolkata & Delhi),[5] Econophysics Colloquium, ESHIA/ WEHIA.

The almost regular meeting series on the topic include: ECONOPHYS-KOLKATA (held in Kolkata & Delhi), Econophysics Colloquium, ESHIA/ WEHIA.

关于这一主题的几乎定期会议系列包括: ECONOPHYS-KOLKATA (在加尔各答和德里举行)、 econophyics 座谈会、 ESHIA / WEHIA。


In recent years network science, heavily reliant on analogies from statistical mechanics, has been applied to the study of productive systems. That is the case with the works done at the Santa Fe Institute in European Funded Research Projects as Forecasting Financial Crises and the Harvard-MIT Observatory of Economic Complexity

In recent years network science, heavily reliant on analogies from statistical mechanics, has been applied to the study of productive systems. That is the case with the works done at the Santa Fe Institute in European Funded Research Projects as Forecasting Financial Crises and the Harvard-MIT Observatory of Economic Complexity

近年来，严重依赖统计力学类比的网络科学已经应用于生产系统的研究。圣菲研究所在欧洲资助的研究项目中所做的预测金融危机和哈佛-麻省理工学院经济复杂性天文台的工作就是如此


If "econophysics" is taken to denote the principle of applying statistical mechanics to economic analysis, as opposed to a particular literature or network, priority of innovation is probably due to Emmanuel Farjoun and Moshé Machover (1983). Their book Laws of Chaos: A Probabilistic Approach to Political Economy proposes dissolving (their words) the transformation problem in Marx's political economy by re-conceptualising the relevant quantities as random variables.[6]

If "econophysics" is taken to denote the principle of applying statistical mechanics to economic analysis, as opposed to a particular literature or network, priority of innovation is probably due to Emmanuel Farjoun and Moshé Machover (1983). Their book Laws of Chaos: A Probabilistic Approach to Political Economy proposes dissolving (their words) the transformation problem in Marx's political economy by re-conceptualising the relevant quantities as random variables.

如果把“经济物理学”用来表示将统计力学应用于经济分析的原则，而不是某一特定的文献或网络，那么创新的优先权可能应归功于 Emmanuel Farjoun 和 mosh Machover (1983)。他们在《混沌定律: 政治经济学的概率方法》一书中提出，通过将相关数量重新概念化为随机变量，来解决(他们的话)马克思政治经济学中的转换问题。


If, on the other hand, "econophysics" is taken to denote the application of physics to

If, on the other hand, "econophysics" is taken to denote the application of physics to

另一方面，如果把“经济物理学”看作是物理学在物理学中的应用

economics, one can consider the works of Léon Walras and Vilfredo Pareto as part of it. Indeed, as shown by Bruna Ingrao and Giorgio Israel, general equilibrium theory in economics is based on the physical concept of mechanical equilibrium.

economics, one can consider the works of Léon Walras and Vilfredo Pareto as part of it. Indeed, as shown by Bruna Ingrao and Giorgio Israel, general equilibrium theory in economics is based on the physical concept of mechanical equilibrium.

从经济学的角度来看，我们可以把 l 关于瓦尔拉斯和维尔弗雷多 · 帕雷托的著作看作是经济学的一部分。事实上，正如 Bruna Ingrao 和 Giorgio Israel 所表明的那样，经济学中的一般均衡理论是基于力学平衡的物理概念。


Econophysics has nothing to do with the "physical quantities approach" to economics, advocated by Ian Steedman and others associated with neo-Ricardianism. Notable econophysicists are Jean-Philippe Bouchaud, Bikas K Chakrabarti, J. Doyne Farmer, Diego Garlaschelli, Dirk Helbing, János Kertész, Francis Longstaff, Rosario N. Mantegna, Matteo Marsili, Joseph L. McCauley, Enrico Scalas, Didier Sornette, H. Eugene Stanley, Victor Yakovenko and Yi-Cheng Zhang. Particularly noteworthy among the formal courses on econophysics is the one offered by Diego Garlaschelli at the Physics Department of the Leiden University,[7][8] from where the first Nobel-laureate in economics Jan Tinbergen came. From September 2014 King's College has awarded the first position of Full Professor in Econophysics.

Econophysics has nothing to do with the "physical quantities approach" to economics, advocated by Ian Steedman and others associated with neo-Ricardianism. Notable econophysicists are Jean-Philippe Bouchaud, Bikas K Chakrabarti, J. Doyne Farmer, Diego Garlaschelli, Dirk Helbing, János Kertész, Francis Longstaff, Rosario N. Mantegna, Matteo Marsili, Joseph L. McCauley, Enrico Scalas, Didier Sornette, H. Eugene Stanley, Victor Yakovenko and Yi-Cheng Zhang. Particularly noteworthy among the formal courses on econophysics is the one offered by Diego Garlaschelli at the Physics Department of the Leiden University, from where the first Nobel-laureate in economics Jan Tinbergen came. From September 2014 King's College has awarded the first position of Full Professor in Econophysics.

经济物理学与 Ian Steedman 和其他与新李嘉图学派相关的人提出的经济学的物理量方法没有任何关系。Notable econophysicists are Jean-Philippe Bouchaud, Bikas K Chakrabarti, J. Doyne Farmer, Diego Garlaschelli, Dirk Helbing, János Kertész, Francis Longstaff, Rosario N. Mantegna, Matteo Marsili, Joseph L. McCauley, Enrico Scalas, Didier Sornette, H. Eugene Stanley, Victor Yakovenko and Yi-Cheng Zhang.在经济物理学的正规课程中，特别值得一提的是莱顿大学物理系的 Diego Garlaschelli 开设的一门课程，他就是第一位诺贝尔经济学奖得主 Jan Tinbergen 的出身。由2014年9月起，英皇书院荣获 Econophysics 首个全职教授职位。


Basic tools

Basic tools of econophysics are probabilistic and statistical methods often taken from statistical physics.

Basic tools of econophysics are probabilistic and statistical methods often taken from statistical physics.

经济物理学的基本工具是通常取自统计物理学的概率和统计方法。


Physics models that have been applied in economics include the kinetic theory of gas (called the kinetic exchange models of markets [9]), percolation models, chaotic models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for earthquake prediction.[10] Moreover, there have been attempts to use the mathematical theory of complexity and information theory, as developed by many scientists among whom are Murray Gell-Mann and Claude E. Shannon, respectively.

Physics models that have been applied in economics include the kinetic theory of gas (called the kinetic exchange models of markets ), percolation models, chaotic models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for earthquake prediction. Moreover, there have been attempts to use the mathematical theory of complexity and information theory, as developed by many scientists among whom are Murray Gell-Mann and Claude E. Shannon, respectively.

应用于经济学的物理模型包括气体动力学理论(称为市场动力学交换模型)、逾渗模型、用于研究心脏骤停的混沌模型、具有自组织临界性的模型以及用于地震预测的其他模型。此外，还有人尝试使用复杂性数学理论和信息理论，这两种理论是由许多科学家发展起来的，其中分别有默里·盖尔曼和克劳德·香农。


For potential games, it has been shown that an emergence-producing equilibrium based on information via Shannon information entropy produces the same equilibrium measure (Gibbs measure from statistical mechanics) as a stochastic dynamical equation, both of which are based on bounded rationality models used by economists. The fluctuation-dissipation theorem connects the two to establish a concrete correspondence of "temperature", "entropy", "free potential/energy", and other physics notions to an economics system. The statistical mechanics model is not constructed a-priori - it is a result of a bounded rational assumption and modeling on existing neoclassical models. It has been used to prove the "inevitability of collusion" result of Huw Dixon in a case for which the neoclassical version of the model does not predict collusion.引用错误：没有找到与</ref>对应的<ref>标签

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Here the demand is increasing, as with Veblen goods or stock buyers with the "hot hand" fallacy preferring to buy more successful stocks and sell those that are less successful.

Here the demand is increasing, as with Veblen goods or stock buyers with the "hot hand" fallacy preferring to buy more successful stocks and sell those that are less successful.

这里的需求正在增加，就像 Veblen 的产品或有“热手”谬论的股票买家，他们更愿意买入更多成功的股票，卖出那些不那么成功的股票。

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Quantifiers derived from information theory were used in several papers by econophysicist Aurelio F. Bariviera and coauthors in order to assess the degree in the informational efficiency of stock markets. In a paper published in Physica A[11]

Quantifiers derived from information theory were used in several papers by econophysicist Aurelio F. Bariviera and coauthors in order to assess the degree in the informational efficiency of stock markets. In a paper published in Physica A

经济物理学家[ http://www.aureliofernandez.net/ · 奥雷里奥 · 巴里维埃拉]和合著者在几篇论文中使用了来自信息论的量词来评估股票市场信息效率的程度。在 Physica 发表的一篇论文中


Zunino et al. use an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This Cartesian representation establish an efficiency ranking of different markets and distinguish different bond market dynamics. Moreover, the authors conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. A similar study developed by Bariviera et al.[12] explore the relationship between credit ratings and informational efficiency of a sample of corporate bonds of US oil and energy companies using also the complexity–entropy causality plane. They find that this classification agrees with the credit ratings assigned by Moody's.

Zunino et al. use an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This Cartesian representation establish an efficiency ranking of different markets and distinguish different bond market dynamics. Moreover, the authors conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. A similar study developed by Bariviera et al. explore the relationship between credit ratings and informational efficiency of a sample of corporate bonds of US oil and energy companies using also the complexity–entropy causality plane. They find that this classification agrees with the credit ratings assigned by Moody's.

祖尼诺等人。在金融文献中使用创新的统计工具: 复杂性-熵因果关系平面。这个笛卡尔坐标表示建立了不同市场的效率排名，并区分了不同的债券市场动态。此外，从复杂熵因果关系平面导出的分类结果与主权证券评级公司对主权证券的评级结果是一致的。由 Bariviera 等人开发的一个类似的研究。以美国石油和能源公司债券为样本，运用复杂熵因果关系平面，探讨了信用评级与信息效率之间的关系。他们发现，这一分类与穆迪给予的信用评级相一致。


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.[13]

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.

另一个很好的例子是随机矩阵理论，它可以用来识别金融相关矩阵中的噪声。一篇论文认为，这种技术可以改善投资组合的性能，例如，应用于投资组合优化。


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),[14] and the path integral formulation of statistical mechanics.[15]

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。


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.[16]

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。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。


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 [17][18] 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.[15]

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.

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。


Influence

Papers on econophysics have been published primarily in journals devoted to physics and statistical mechanics, rather than in leading economics journals. Mainstream economists have generally been unimpressed by this work.[19] Some economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics.

Papers on econophysics have been published primarily in journals devoted to physics and statistical mechanics, rather than in leading economics journals. Mainstream economists have generally been unimpressed by this work. Some economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics.

关于经济物理学的论文主要发表在专门研究物理学和统计力学的期刊上，而不是主要的经济学期刊上。主流经济学家普遍对这项研究不以为然。一些经济学家，包括 Mauro garyati，Steve Keen，Paul Ormerod 和 Alan Kirman 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。


In contrast, econophysics is having some impact on the more applied field of quantitative finance, whose scope and aims significantly differ from those of economic theory. Various econophysicists have introduced models for price fluctuations in financial markets or original points of view on established models.[17][20][21] Also several scaling laws have been found in various economic data.[22][23][24]

In contrast, econophysics is having some impact on the more applied field of quantitative finance, whose scope and aims significantly differ from those of economic theory. Various econophysicists have introduced models for price fluctuations in financial markets or original points of view on established models. Also several scaling laws have been found in various economic data.

相比之下，经济物理学对定量金融学的应用领域产生了一些影响，定量金融学的范围和目标与经济学理论有很大的不同。各种经济物理学家已经介绍了金融市场价格波动的模型或已建立模型的原始观点。在各种经济数据中也发现了一些标度律。


Main results

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),[25] 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]\displaystyle{ 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".[26]  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.[26]  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]\displaystyle{ 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".  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(即自相似标度性质)。这是由于个别市场竞争对手或他们的整体趋势有系统地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。这些“胖尾巴”不仅在数学上很重要，因为它们包含了风险，一方面，风险可能很小，以至于人们可能会忽略它们，但另一方面，它们一点也不可忽视。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定律，例如，只有数学 p 的失效概率，/ 数学 x 是一个越来越大的变量，在尾部区域的分布考虑(即。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“保险离开”。 在大宗商品市场也可以看到“肥尾”。


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 approximations, e.g. the 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 approximations, e.g. the 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.

正如在量子场论中一样，“胖尾”可以通过复杂的“非微扰”方法得到，主要是通过数值方法，因为它们包含了通常的高斯近似的偏差，例如:。布莱克-斯科尔斯理论。然而，肥尾也可能是由其他现象引起的，比如中心极限定理中的随机数项，或者其他任何非经济物理学模型。由于这些模型难以检验，因此在传统的经济分析中很少受到重视。


See also

模板:Portal


References

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  2. ↑ Interview of H. E. Stanley on Econophysics (Published in "IIM Kozhikode Society & Management Review", Sage publication (USA), Vol. 2 Issue 2 (July), pp. 73-78 (2013))
  3. ↑ Econophysics Research in India in the last two Decades (1993-2013) (Published in "IIM Kozhikode Society & Management Review", Sage publication (USA), Vol. 2 Issue 2 (July), pp. 135-146 (2013))
  4. ↑ "An Introduction to Econophysics", Cambridge University Press, Cambridge (2000)
  5. ↑ "Econophysics of Wealth Distributions", Eds. A. Chatterjee et al., New Economic Windows, Springer, Milan (2005), & the subsequent eight Proc. Volumes published in 2006, 2007, 2010, 2011, 2013, 2014, 2015 & 2019 in the New Economic Windows series of Springer
  6. ↑ Farjoun and Machover disclaim complete originality: their book is dedicated to the late Robert H. Langston, who they cite for direct inspiration (page 12), and they also note an independent suggestion in a discussion paper by E.T. Jaynes (page 239)
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  10. ↑ Didier Sornette (2003). Why Stock Markets Crash?. Princeton University Press. 
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  12. ↑ Bariviera, A.F., Zunino, L., Guercio, M.B., Martinez, L.B. and Rosso, O.A. (2013). "Efficiency and credit ratings: a permutation-information-theory analysis" (PDF). Journal of Statistical Mechanics: Theory and Experiment. 2013 (8): P08007. arXiv:1509.01839. Bibcode:2013JSMTE..08..007F. doi:10.1088/1742-5468/2013/08/P08007. hdl:11336/2007.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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  21. ↑ Y. Shapira; Y. Berman; E. Ben-Jacob (2014). "Modelling the short term herding behaviour of stock markets". New Journal of Physics. 16 (5): 053040. Bibcode:2014NJPh...16e3040S. doi:10.1088/1367-2630/16/5/053040.
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  25. ↑ The physicists noted the scaling behaviour of "fat tails" through a letter to the scientific 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)
  26. ↑ 26.0 26.1 See for example Preis, Mantegna, 2003.


Further reading

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