Equilibrium and stability of a stock market game with big traders

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


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.


Financial market Stochastic differential game Nash equilibrium Stability 

Mathematics Subject Classification (2000)

91A23 91B28 49J55 49N70 


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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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