英文标题：
《Micro-foundation using percolation theory of the finite-time singular
  behavior of the crash hazard rate in a class of rational expectation bubbles》
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作者：
Maximilian Seyrich and Didier Sornette
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最新提交年份：
2016
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英文摘要：
  We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power sa (with a > 1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power sa of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite-time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modelling the density of traders on the percolation network by an Ornstein-Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes.
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中文摘要：
我们提出了一个似是而非的微观模型，用于在理性预期泡沫的Johansen-Ledoit-Sornette模型中假设的碰撞危险率的幂律有限时间奇异形式。该模型基于交易者网络的渗透图，以及关联交易者集群共享相同观点的概念。关键因素是这样一种观念，即一个足够大的交易者群体的立场从买方转移到卖方，可能会引发崩盘。这提供了一个公式，通过对超过簇大小s的最小幂sa（a>1）的逾渗簇求和来估计碰撞危险率，类似于广义逾渗敏感性。集群规模的功率sa来自于群体活动作为群体规模函数的超线性依赖性，这在之前的文献中已有记载。当控制参数（占用场地的比例或网络中交易者的密度）接近渗透阈值pc时，碰撞危险率表现出爆炸性的有限时间奇异行为。通过奥恩斯坦-乌伦贝克过程对渗透网络中交易者的密度进行建模，生成真实的动力学，它的记忆控制着接近气泡形成临界区域的控制参数的自发漂移。我们的数值模拟恢复了JLS模型的主要程式化特性，该模型具有被碰撞中断的间歇性爆炸性超指数气泡。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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