Dynamic Games and Applications

, Volume 1, Issue 2, pp 220–252 | Cite as

Influence of Big Traders on the Stock Market: Theory and Simulation

  • Gopal K. BasakEmail author
  • Mrinal K. Ghosh
  • Diganta Mukherjee


We study the influence of large traders in the stock market in the presence of a fringe of marginal “noise traders”. We formulate a trade model relating stock price to the demand strategies of these traders who wish to maximize their payoffs. Using the Nash equilibrium concept, we compute the optimal value functions for the large traders and study the stability of the state process (log price) under equilibrium strategies of the large traders. In the process, we propose two measures. The first one is to measure the big traders’ total faith on the market’s valuation (φ 0), and the second one is to measure the big traders’ interaction between themselves (φ 1). We discuss what values of the measures might indicate a collusion of the big traders to corner the market for their benefit and illustrate this with numerical examples. We also illustrate, with diagrams, the historical and instantaneous correlation among the value processes for these large traders to highlight certain interesting features that influence the market.


Financial market Stochastic differential game Nash equilibrium Stability of stock market 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basak GK (1991) A class of limit theorems for singular diffusions. J Multivar Anal 39:44–59 MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Basak GK, Bhattacharya RN (1992) Stability in distribution for a class of singular diffusions. Ann Probab 20:312–321 MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Basak GK, Ghosh MK, Mukherjee D (2009) Equilibrium and stability of a stock market game with big traders. Differ Equ Dyn Syst 17(3):283–299 MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Berkelaar AB, Kouwenberg R, Post T (2004) Optimal portfolio choice under loss aversion. Rev Econ Stat 86(4):973–987 CrossRefGoogle Scholar
  5. 5.
    Bollerslev T, Chou RY, Kroner KF (1992) ARCH modeling in finance: a review of the theory and empirical evidence. J Econom 52:5–59 zbMATHCrossRefGoogle Scholar
  6. 6.
    Borkar VS (1989) Optimal control of diffusion processes. Pitman research notes in mathematics. Longman Scientific and Technical, Harlow zbMATHGoogle Scholar
  7. 7.
    Borkar VS, Ghosh MK (1992) Stochastic differential games: an occupation measure based approach. J Optim Theory Appl 73:359–385. Errata corrige, ibid, 88:251–252 (1996) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Buckdahn R, Cardaliaguet P, Rainer C (2004) Nash equilibrium payoffs for nonzero-sum stochastic differential games. Mimeo, Universite de Bretagne Occidentale Google Scholar
  9. 9.
    Chan LKC, Lakonishok J (1993) Institutional trades and intraday stock price behavior. J Financ Econ 33(2):173–199 CrossRefGoogle Scholar
  10. 10.
    Chan LKC, Lakonishok J (1995) The behavior of stock prices around institutional trades. J Finance 50(4):1147–1174 CrossRefGoogle Scholar
  11. 11.
    Engle RF (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation. Econometrica 50:987–1008 MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Friedman A (1976) Stochastic differential equations, vol 2. Academic Press, New York zbMATHGoogle Scholar
  13. 13.
    Gokarn S (1996) Indian capital market reforms, 1992–96, an assessment. Economic and Political Weekly, April 13, 1996, pp 956–961 Google Scholar
  14. 14.
    Heston SL (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud 6:327–343 CrossRefGoogle Scholar
  15. 15.
    Jin H, Zhou X (2008) Behavioral portfolio selection in continuous time. Math Finance 18:385–426 MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Jin H, Zhou X (2009) Greed, leverage, and potential losses: an application of portfolio choice under prospect theory. SSRN eLibrary Google Scholar
  17. 17.
    Jin H, Zhou X (2011) Greed, leverage, and potential losses: a prospect theory perspective. SSRN eLibrary, January Google Scholar
  18. 18.
    Jin H, Zhang S, Zhou X (2010) Behavioral portfolio selection with loss control. SSRN eLibrary, February Google Scholar
  19. 19.
    Kakati M (1999) Price performance of initial public offerings. Int J Dev Bank 17(2):59–75 Google Scholar
  20. 20.
    Keim DB, Madhavan A (1995) Anatomy of the trading process: empirical evidence on the motivation for and execution of institutional equity trades. J Financ Econ 37:371–398 CrossRefGoogle Scholar
  21. 21.
    Keim DB, Madhavan A (1996) The upstairs market for large-block transactions: analysis and measurement of price effects. Rev Financ Stud 9:1–36 CrossRefGoogle Scholar
  22. 22.
    Keim DB, Madhavan A (1997) Transaction costs and investment style: an inter-exchange analysis of institutional equity trades. J Financ Econ 3:265–292 CrossRefGoogle Scholar
  23. 23.
    Krawczyk JB (2005) Numerical solutions to lump-sum pension problems that can yield left-skewed fund return distributions. In: Deissenburg C, Hartl RF (eds) Optimal control and dynamic games. Advances in computational management science, vol 7. Springer, New York, pp 155–176. Chap 10 CrossRefGoogle Scholar
  24. 24.
    Krawczyk JB (2008) On loss-avoiding payoff distribution in a dynamic portfolio management problem. J Risk Finance 9(2):151–172 CrossRefGoogle Scholar
  25. 25.
    Madhusoodanan TP (1997) Risk and return: a new look at the Indian stock market. Finance India XI(2):285–304 Google Scholar
  26. 26.
    Nelson DB (1996) Asymptotically optimal smoothing with ARCH models. Econometrica 64:561–573 MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Nelson DB, Foster DP (1994) Asymptotic filtering theory for univariate ARCH models. Econometrica 62:1–41 MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Oksendal B (2003) Stochastic differential equations. Springer, Heidelberg CrossRefGoogle Scholar
  29. 29.
    Tirole J (1995) The theory of industrial organisation. MIT Press, Cambridge Google Scholar
  30. 30.
    Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323 zbMATHCrossRefGoogle Scholar
  31. 31.
    Varian HR (1992) Microeconomic analysis, 3rd edn. WW Norton, New York Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Gopal K. Basak
    • 1
    Email author
  • Mrinal K. Ghosh
    • 2
  • Diganta Mukherjee
    • 3
  1. 1.Stat-Math UnitIndian Statistical InstituteKolkataIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Unitedworld School of BusinessKolkataIndia

Personalised recommendations