Gibbs measure and Markov chain modeling for stock markets

  • Jun-ichi Maskawa
Conference paper


We reviewed the recent work on Gibbs measure (statistical physics model) describing the collective price jumps in stock markets. We started with the study of a multivariate Markov chain model as a. stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes were coded into the sequences of up and down spins according to their signs. As the stationary state of the Markov chain, Gibbs measure was naturally derived, which formally coincides with spin glass model of disordered magnetic systems. The linear response of the system to external fields was examined to prove the fluctuation response theorem, Finally, the analysis of actual portfolios based on this model was briefly summarized.


Markov Chain Stock Market Stock Issue Price Change Spin Glass 
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  1. 1.
    Gopikrishnan P, Rosenow B, Plerou V, Stanley H E (2001) Quantifying and interpreting collective behavior in financial markets. Phys. Rev. E 64:035106(R)CrossRefGoogle Scholar
  2. 2.
    Mantegna R N (1999) Hierarchical structure in financial markets. Eur. Phys. J. B 11:193–197ADSCrossRefGoogle Scholar
  3. 3.
    Mantegna R N, Stanley H E (2000) An Introduction to Econophysics. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Markowitz H M (1991) Portofolio Selection. Blackwell, OxfordGoogle Scholar
  5. 5.
    Maskawa J (2002a) Spin-Glass like network model for stock market. In: Takatasu H (Ed) Empirical Science of Financial Fluctuation. Springer-Verlag, TokyoGoogle Scholar
  6. 6.
    Maskawa J (2002b) Ordered phase and non-equilibrium fluctuation in stock market. Physics A 311:563MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Maskawa J (2003) Multivariate Markov chain modeling for stock markets. Physica A in pressGoogle Scholar
  8. 8.
    Sherrington D,Kirkpatrick S;(1975) Solvable model of a spin glass. Phys. Rev. Lett. 35:1972CrossRefGoogle Scholar
  9. 9.
    Thouless D J,Anderson P W, Palmer R G (1977) Solution of solvable model of a spin glass. Phil. Mag. 35:593–601ADSCrossRefGoogle Scholar

Copyright information

© Springer Japan 2004

Authors and Affiliations

  • Jun-ichi Maskawa
    • 1
  1. 1.Department of Management InformationFukuyama Heisei UniversityFukuyamaJapan

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