Stock exchanges are modeled as nonlinear closed-loop systems where
the plant dynamics is defined by known stock market regulations and the actions of
agents are based on their beliefs and behavior. The decision of the agents may contain
a random element, thus we get a nonlinear stochastic feedback system. The market
is in equilibrium when the actions of the agents reinforce their beliefs on the price
dynamics. Assuming that linear predictors are used for prediction of the price process,
a stochastic approximation procedure for finding market equilibrium is described.
The proposed procedure is analyzed using the theory of Benveniste et al. (Adaptive
algorithms and stochastic approximations. Springer, Berlin, 1990).Asimulation result
is also presented.