A Mathematical Model of Financial Bubbles: A Behavioral Approach

Author:

Afilipoaei Andrei1,Carrero Gustavo2ORCID

Affiliation:

1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada

2. 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.

Funder

Athabasca University ARF

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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