标题： 资产价格泡沫形成与崩溃的简单模型 显示英文标题

标题： A simple model for asset price bubble formation and collapse

摘要： 我们考虑一个简单的随机微分方程，用于建模社会背景中的泡沫。 一个典型的例子是资产定价中的泡沫，但类似的机制可能控制由心理因素驱动的一系列社会现象（例如，摇滚乐队的受欢迎程度，或追求某个专业的学生人数）。 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，并且展示几种关键行为。 主要因素包括向稳定值回归的趋势、由趋势跟随引发的投机性社会反应以及随机波动。 这三个力量的相互作用可能导致泡沫的形成和崩溃。 数值模拟显示，该方程根据参数的不同值具有不同的区域。 我们对弱随机区域进行了严格分析，并研究了基本因素变化在引发泡沫中的作用。 显示英文摘要

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.