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A simple model for asset price bubble formation and collapse

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  • Alexander Kiselev
  • Lenya Ryzhik

Abstract

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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  • Alexander Kiselev & Lenya Ryzhik, 2010. "A simple model for asset price bubble formation and collapse," Papers 1009.0299, arXiv.org.
    • Handle: RePEc:arx:papers:1009.0299
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    Cited by:

    1. Andrei Afilipoaei & Gustavo Carrero, 2023. "A Mathematical Model of Financial Bubbles: A Behavioral Approach," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    2. S'ebastien Gadat & Laurent Miclo & Fabien Panloup, 2013. "A stochastic model for speculative bubbles," Papers 1309.6287, arXiv.org.
    3. Angelos Dassios & Luting Li, 2018. "An Economic Bubble Model and Its First Passage Time," Papers 1803.08160, arXiv.org.

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