摘要翻译：
我们考虑了一个简单的随机微分方程来建模社会背景下的泡沫。一个主要的例子是资产定价的泡沫，但类似的机制可能会控制一系列由心理因素驱动的社会现象（例如，摇滚乐队的受欢迎程度，或某一专业的学生人数）。我们的目标是研究最简单的模型，其中每个术语都有明确的含义，并展示几个关键行为。进入的主要因素是均值向稳定值回归的趋势、趋势跟随引发的投机性社会反应和随机波动。这三种力量的相互作用可能导致泡沫的形成和崩溃。数值模拟表明，该方程随参数的取值有不同的状态。我们对弱随机区域进行了严格的分析，并研究了基本面变化在点燃泡沫中的作用。
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英文标题：
《A simple model for asset price bubble formation and collapse》
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作者：
Alexander Kiselev and Lenya Ryzhik
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Mathematics        数学
二级分类：Analysis of PDEs        偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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英文摘要：
  We consider a simple stochastic differential equation for modeling bubbles in social context. A prime example is bubbles in asset pricing, but similar mechanisms may control a range of social phenomena driven by psychological factors (for example, popularity of rock groups, or a number of students pursuing a given major). Our goal is to study the simplest possible model in which every term has a clear meaning and which demonstrates several key behaviors. The main factors that enter are tendency of mean reversion to a stable value, speculative social response triggered by trend following and random fluctuations. The interplay of these three forces may lead to bubble formation and collapse. Numerical simulations show that the equation has distinct regimes depending on the values of the parameters. We perform rigorous analysis of the weakly random regime, and study the role of change in fundamentals in igniting the bubble.
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PDF链接：
https://arxiv.org/pdf/1009.0299