Equilibrium and stability of a stock market game with big traders

Differential Equations and Dynamical Systems - Tập 17 - Trang 283-299 - 2010
Gopal K. Basak1, Mrinal K. Ghosh2, Diganta Mukherjee3
1Stat-Math Unit, Indian Statistical Institute, Kolkata, India
2Department of Mathematics, Indian Institute of Science, Bangalore, India
3Usha Martin Academy, Salt Lake Electronic Complex, Kolkata, India

Tóm tắt

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.

Tài liệu tham khảo

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