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A Mathematical Model of Financial Bubbles: A Behavioral Approach

Author

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  • Andrei Afilipoaei

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada)

  • Gustavo Carrero

    (Centre for Science, Faculty of Science and Technology, Athabasca University, Athabasca, AB T9S 3A3, Canada)

Abstract

In this work, we propose a mathematical model to describe the price trends of unsustainable growth, abrupt collapse, and eventual stabilization characteristic of financial bubbles. The proposed model uses a set of ordinary differential equations to depict the role played by social contagion and herd behavior in the formation of financial bubbles from a behavioral standpoint, in which the market population is divided into neutral, bull (optimistic), bear (pessimistic), and quitter subgroups. The market demand is taken to be a function of both price and bull population, and the market supply is taken to be a function of both price and bear population. In such a manner, the spread of optimism and pessimism controls the supply and demand dynamics of the market and offers a dynamical characterization of the asset price behavior of a financial bubble.

Suggested Citation

  • Andrei Afilipoaei & Gustavo Carrero, 2023. "A Mathematical Model of Financial Bubbles: A Behavioral Approach," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4102-:d:1249796
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    References listed on IDEAS

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    1. Gadi Barlevy, 2007. "Economic theory and asset bubbles," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 31(Q III), pages 44-59.
    2. Kenneth R. Ahern, 2014. "Do Common Stocks Have Perfect Substitutes? Product Market Competition and the Elasticity of Demand for Stocks," The Review of Economics and Statistics, MIT Press, vol. 96(4), pages 756-766, October.
    3. Brons, Martijn & Pels, Eric & Nijkamp, Peter & Rietveld, Piet, 2002. "Price elasticities of demand for passenger air travel: a meta-analysis," Journal of Air Transport Management, Elsevier, vol. 8(3), pages 165-175.
    4. Westphal, Rebecca & Sornette, Didier, 2020. "Market impact and performance of arbitrageurs of financial bubbles in an agent-based model," Journal of Economic Behavior & Organization, Elsevier, vol. 171(C), pages 1-23.
    5. Penghang Liu & Kshama Dwarakanath & Svitlana S Vyetrenko & Tucker Balch, 2022. "Limited or Biased: Modeling Sub-Rational Human Investors in Financial Markets," Papers 2210.08569, arXiv.org, revised Mar 2024.
    6. Alexander Kiselev & Lenya Ryzhik, 2010. "A simple model for asset price bubble formation and collapse," Papers 1009.0299, arXiv.org.
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    Cited by:

    1. Ignas Mikalauskas & Darius Karaša, 2025. "The Risk of Financial Bubbles in Renewable Energy Markets," Energies, MDPI, vol. 18(6), pages 1-20, March.

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