Stock Price Fluctuation as a Diffusion in a Random Environment

The fluctuation of stock prices is modelled as a sequence of temporary equilibria on a financial market with different types of agents. We summarize joint work with M. Schweizer on the class of Ornstein-Uhlenbeck processes in a random environment which appears in the diffusion limit. Moreover, we show how the random environment may be generated by the interaction of a large set of agents modelled by Markov chains as they appear in the theory of probabilistic cellular automata.