Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A mesoscopic stock market model with hysteretic agents

Pages: 403 - 415, Volume 18, Issue 2, March 2013      doi:10.3934/dcdsb.2013.18.403

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Michael Grinfeld - Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom (email)
Harbir Lamba - Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, United States (email)
Rod Cross - Department of Economics, University of Strathclyde, Sir William Duncan Building, 130 Rottenrow, Glasgow G4 0GE, United Kingdom (email)

Abstract: Following the approach of [22], we derive a system of Fokker-Planck equations to model a stock-market in which hysteretic agents can take long and short positions. We show numerically that the resulting mesoscopic model has rich behaviour, being hysteretic at the mesoscale and displaying bubbles and volatility clustering in particular.

Keywords:  Financial modeling, hysteresis, Fokker-Planck equations.
Mathematics Subject Classification:  91B55, 91B25, 35Q84, 47J40.

Received: October 2011;      Revised: June 2012;      Available Online: November 2012.