A stochastic feedback system model of a stock exchange

Stock exchanges are modelled as nonlinear feedback systems where the plant dynamics is defined by known stock market regulations but the actions of agents are unknown. It is assumed though that each agent submits transaction requests according to his/her beliefs on the price dynamics and his/her behavior. The action of the agents may contain a random element, thus we get a non-linear stochastic feedback system. The market is in equilibrium when the actions of the agents reinforce their beliefs on the price dynamics. Assuming that an AR(k) predictor is 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, Métivier and Priouret, [1].