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Equilibrium and stability of a stock market game with big traders

  • Gopal K. Basak
  • Mrinal K. GhoshEmail author
  • Diganta Mukherjee
Original Research

Abstract

This paper addresses a stochastic differential game arising in a stock market largely controlled by big traders. We model stock price behaviour as a standard geometric Brownian motion and the stock market as characterized by the presence of a few large traders and a fringe of marginal “noise traders”. Using the concept of Nash equilibrium we compute the equilibrium strategies and optimal value functions for the large traders. We also establish the stability of the state process under equilibrium strategies of the large traders. Finally we illustrate our results through some numerical examples for each variation of our model.

Keywords

Financial market Stochastic differential game Nash equilibrium Stability 

Mathematics Subject Classification (2000)

91A23 91B28 49J55 49N70 

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References

  1. 1.
    Basak G. K. and Bhattacharya R. N., Stability in distribution for a class of singular diffusions, Annals of Probability, 20, 312–321, (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cadbury Report, The Financial Aspects of Corporate Governance, Burgess Science Press, (1992)Google Scholar
  3. 3.
    Cochrane J. H., Asset Pricing, Princeton University Press, Princeton, (2000)Google Scholar
  4. 4.
    Cvitanic J. and Zapatero F., Introduction to the Economics and Mathematics of Financial Markets. The MIT Press, Cambridge, Massachusetts, (2004)zbMATHGoogle Scholar
  5. 5.
    Friedman A., Stochastic Differential Equations, Vol. 2, Academic Press, (1976)Google Scholar
  6. 6.
    Gokarn S., Indian Capital Market Reforms, 1992–96, An Assessment, Economic and Political Weekly, April 13, 956–961, (1996)Google Scholar
  7. 7.
    Kakati M, Price Performance of Initial Public Offerings, International Journal of Development Banking, 17(2), 59–75, (1999)Google Scholar
  8. 8.
    Madhusoodanan T. P., Risk and Return: A New Look at the Indian Stock Market, Finance India, XI(2), June, 285–304, (1997)Google Scholar
  9. 9.
    Oksendal B., Stochastic Differential Equations, Springer-Verlag, Heidelberg, (2003)Google Scholar
  10. 10.
    Tirole J., The Theory of Industrial Organisation, MIT Press, (1995)Google Scholar

Copyright information

© Foundation for Scientific Research and Technological Innovation 2009

Authors and Affiliations

  • Gopal K. Basak
    • 1
  • Mrinal K. Ghosh
    • 2
    Email author
  • Diganta Mukherjee
    • 3
  1. 1.Stat-Math UnitIndian Statistical InstituteKolkataIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Usha Martin AcademySalt Lake Electronic ComplexKolkataIndia

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