307
个编辑
更改
→Basic tools
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 10<sup>8</sup> 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.
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 10<sup>8</sup> 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“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。
==Influence==
==Influence==