Non-ergodic Behavior in a Financial Market with Interacting Investors

We identify possible long-run market shares and the long-run asset price dynamics of financial markets with heterogenous interacting agents. This involves stability conditions for a class of difference equation in a random environment, where the random environment is endogenously generated by agents' investment behavior. Depending on the evaluation of a performance measure of an investment, asset prices may behave in a non-ergodic manner. That is, the price processes converge in distribution, but the limiting distribution is not necessarily uniquely determined. The long-run market shares of two competing financial mediators may strongly depend on the random environment which is endogenously generated by a noise traders