Advanced Search
Article Contents
Article Contents

A mesoscopic stock market model with hysteretic agents

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: 91B55, 91B25, 35Q84, 47J40.


    \begin{equation} \\ \end{equation}
  • [1]

    Y. Amihud and H. Mendelson, Trading mechanism and stock returns: An empirical investigation, J. Finance, 42 (1987), 533-555.doi: 10.1111/j.1540-6261.1987.tb04567.x.


    J. Bect, H. Baili and G. Fleury, Generalized Fokker-Planck equation for piecewise-diffusion processes with boundary hitting resets, in "Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems," Kyoto, (2006), 1360-1367.


    B. Biais, "The Organization of Financial Markets," Rotman School's Distinguished Lecture Series, University of Toronto, Toronto, 2008.


    B. Biais, L. Glosten and C. Spratt, Market microstructure: A survey of microfoundations, empirical results and policy implications, J. Financial Markets, 8 (2005), 217-264.doi: 10.1016/j.finmar.2004.11.001.


    I. Brocas and J. D. Carrillo, From perception to action: An economic model of brain processes, mimeo., Univ. of South Carolina, 2010.


    J. S. Chang and G. Cooper, A practical difference scheme for Fokker-Planck equations, J. Comp. Phys., 6 (1970), 1-16.


    S. Cordier, L. Pareschi and C. Piatecki, Mesoscopic modelling of financial markets, J. Stat. Phys., 134 (2009), 161-184.


    R. Cross, V. Kozyakin, B. O'Callaghan, A. Pokrovskii, and A. Pokrovskiy, Periodic sequences of arbitrage: A tale of four currencies, Metroeconomica, 62 (2011), 1-45.


    R. Cross, M. Grinfeld and H. Lamba, A mean-field model of investor behaviour, J. Phys. Conf. Ser., 55 (2006), 55-62.


    R. Cross, M. Grinfeld and H. Lamba, Hysteresis and economics, IEEE Control Systems Magazine, 29 (2009), 30-43.


    R. Cross, M. Grinfeld, H. Lamba and T. Seaman, A threshold model of investor psychology, Physica A, 354 (2005), 463-478.


    R. Cross, M. Grinfeld, H. Lamba and T. Seaman, Stylized facts from a threshold-based heterogeneous agent model, Eur. J. Phys. B, 57 (2007), 213-218.doi: 10.1140/epjb/e2007-00108-5.


    B. Düring and G. Toscani, Hydrodynamics from kinetic models of conservative economies, Physica A, 384 (2007), 493-506.


    M. D. Evans and R. K. Lyons, How is the macro news transmitted to exchange rates?, J. Financial Econ., 88 (2008), 26-50.


    J. Gyntelberg, M. Loretan, T. Subhanij and E. Chan, Private information, stock markets and exchange rates, BIS Discussion paper, Basel, Switzerland, August 2009.


    L. Harris, "Trading and Exchange," Oxford University Press, Oxford, 2003.


    F. de Jong and B. Rindi, "The Microstructure of Financial Markets," Cambridge University Press, New York, 2009.


    D. B. Keim and A. Madhavan, The costs of institutional equity trades: an overview, Financial Analysis J., 54 (1998), 50-69.


    H. Lamba, A queueing theory description of cascades in financial markets and fat-tailed price returns, Euro. Physics J. B, 77 (2010), 297-304.doi: 10.1140/epjb/e2010-00248-5.


    H. Lamba and T. Seaman, Rational expectations, psychology and inductive learning via moving thresholds, Physica A, 387 (2008), 3904-3909.doi: 10.1016/j.physa.2008.01.061.


    R. Naes and S. Skjeltorp, Is the market microstructure of stock markets important?, Norges Bank Econ. Bull., 77 (2006), 123-132.


    A. Omurtag and L. Sirovich, Modeling a large population of traders: Mimesis and stability, J. Econ. Behav. Organiz., 61 (2006), 562-576.


    B. Park and V. Petrosian, Fokker-Planck equations of stochastic acceleration: A study of numerical methods, Astrophys. J. Supp. Ser., 103 (1996), 255-267.doi: 10.1086/192278.

  • 加载中

Article Metrics

HTML views() PDF downloads(94) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint