Dynamic instabilities from information annihilation in speculative markets

金融市场表现出极端的价格波动。他们的统计数据遵循比例法则，这在不同的市场和时间段几乎是普遍的。这些“程式化事实”的根本原因尚不清楚。（新）古典经济理论只考虑由于外部信息进入市场而引起的重大波动。这就是“新闻”。否则，市场应该处于均衡状态。相反，许多实证研究得出结论，大多数重大的价格变化不能归因于外部消息，“程式化的事实”往往与物理学中已知的“临界现象”有关。然而，到目前为止，它们还不能从不同市场共享的第一原则中得到充分解释。相反，近年来发展了一系列具有不同机制和缺陷的非均衡模型。通过一个抽象模型，我们可能迈出了对“程式化事实”更基本理解的第一步，该模型表明，主要吸收自我生成信息的投机市场可能同时表现出：向信息效率均衡状态的演化以及随后的不稳定。这些动态再现了对数回报的经验标度，量化了价格变化，以及它们的长期时间聚集。虽然这个抽象的理论有可能调和关于金融市场运行状态的相互冲突的观点--信息效率和复杂的失衡动态--但它在现实世界中的相关性是未知的。因此，我的目标是将理论转化为对真实的高频交易的有形描述。我将与Jean-Philippe Bouchaud合作，他是统计物理和金融领域的著名研究员。他也是资本基金管理公司（CFM）的董事长，该公司将提供高质量的数据，这些数据将有助于开发和测试现实的模型。我假设，“风格化的事实”遵循的一般属性的动态平衡的影响，相反的市场力量。因此，我也将调查信息传递在不同的时间尺度和可能的概括的理论。我的目标是开发一个一致的框架来描述金融市场在不同层次的抽象多代理模型，并达到宏观描述的形式diffusion processes. Further，我假设一个一般的原则可以解释类似的现象，在许多复杂的自适应系统，功能的自适应平衡的对立力量。这一原则的一个例子是人类的棍子平衡，吸收可预测的趋势可以减少平均波动，但也增加了罕见的极端错误的风险。与Klaus Pawelzik一起，我以前在运动控制模型和人体平衡实验中证明了这一原则。因此，我们计划合作识别这种信息湮灭不稳定性（IAI）的系统独立特征。

Financial markets exhibit extreme price fluctuations. Their statistics follow scaling-laws which are nearly universal across different markets and time periods. The underlying causes for these "stylised facts" are unknown. (Neo-)classical economic theories only allow for significant fluctuations due to external information entering the market. That is, "news". Otherwise, markets should be in equilibrium. Many empirical studies, in contrast, concluded that most large price changes cannot be attributed to external news.The "stylised facts" are often associated with the "critical phenomena" known from physics. So far, however, they cannot be fully explained from first principles shared across different markets. Instead, a zoo of out-of-equilibrium models with different mechanisms and shortcomings has been developed over recent years.A possible first step towards a more fundamental understanding of the "stylised facts" was taken with an abstract model demonstrating that speculative markets which absorb predominantly self-generated information may exhibit both: evolution towards information-efficient equilibrium states as well as their subsequent destabilisation. These dynamics reproduce the empirical scaling of log returns, which quantify price changes, and their long-ranged temporal clustering.While this abstract theory has the potential to reconcile conflicting views on the state of operation of financial markets - information efficiency and complex out-of-equilibrium dynamics - its real-world relevance is unknown. Hence I aim to transfer the theory onto a tangible description of real high-frequency trading. I will collaborate with Jean-Philippe Bouchaud, a renown researcher in statistical physics and finance. He is also chairman of Capital Fund Management (CFM), which will provide high-quality data that will serve to develop and test realistic models.I hypothesise that the "stylised facts" follow from general properties of a dynamical balance of the impacts of opposing market forces. I will therefore investigate also information transfer over different time-scales and possible generalisations of the theory. I aim to develop a consistent framework for describing financial markets across different levels of abstractions in multi-agent models, and up to macroscopic descriptions in the form of diffusion processes.Moreover, I hypothesise that a general principle can account for similar phenomena in many complex adaptive systems that feature an adaptive balance of opposing forces. One instantiation of this principle is human stick-balancing where absorption of predictable trends can reduce mean fluctuations, but also increase the risk for rare, extreme errors. Together with Klaus Pawelzik, I previously demonstrated this principle in a motor control model and in human balancing experiments. Therefore, we plan to collaborate on the identification of system-independent features of this Information Annihilation Instability (IAI).