A mesoscopic stock market model with hysteretic agents

Michael Grinfeld; Harbir Lamba; Rod Cross

doi:10.3934/dcdsb.2013.18.403

Article Contents

2013, Volume 18, Issue 2: 403-415. Doi: 10.3934/dcdsb.2013.18.403

This issue Previous Article Hysteresis and post Walrasian economics Next Article Reduction and identification of dynamic models. Simple example: Generic receptor model

A mesoscopic stock market model with hysteretic agents

1.
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH
2.
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030
3.
Department of Economics, University of Strathclyde, Sir William Duncan Building, 130 Rottenrow, Glasgow G4 0GE

Received: October 2011

Revised: June 2012

Published: March 2013

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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:

Mathematics Subject Classification: 91B55, 91B25, 35Q84, 47J40.

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