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

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Abstract

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.

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Authors and Affiliations

  1. Stat-Math Unit, Indian Statistical Institute, Kolkata, 700 108, India

    Gopal K. Basak

  2. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Mrinal K. Ghosh

  3. Unitedworld School of Business, Plot G1, Block EP & GP, Sector-V, Salt Lake, Kolkata, 700 091, India

    Diganta Mukherjee

Authors
  1. Gopal K. Basak
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  2. Mrinal K. Ghosh
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  3. Diganta Mukherjee
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Corresponding author

Correspondence to Gopal K. Basak.

Additional information

We would like to thank many patient readers and audiences of several international conferences for their helpful comments which helped us to improve the manuscript. We would also like to thank one of our former students, Subhadip Mitra for his numerical work regarding payoff functions during his Masters’ project.

The work of G.K. Basak is supported in part by an internal research grant from ISI.

The work of M.K. Ghosh was supported in part by a grant from UGC through DSA-SAP Phase IV.

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Basak, G.K., Ghosh, M.K. & Mukherjee, D. Influence of Big Traders on the Stock Market: Theory and Simulation. Dyn Games Appl 1, 220–252 (2011). https://doi.org/10.1007/s13235-011-0011-x

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