A Mathematical Model of Financial Bubbles: A Behavioral Approach

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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.

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Afilipoaei, A., & Carrero, G. (2023). A Mathematical Model of Financial Bubbles: A Behavioral Approach. Mathematics, 11(19). https://doi.org/10.3390/math11194102

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