We investigate the asset prices dynamics and the long-run market shares of two competing financial mediators who are selected
by consumers. We demonstrate that the social interaction among consumers constitutes an endogenous path-depending source of
risk in a financial market. Depending on consumers’ evaluation of the mediator’s investment, asset prices may behave in a
non-ergodic manner: the price process converges in distribution but the limiting distribution is not necessarily uniquely
determined, its multiplicity being characterized by the multiplicity of possible long-run market shares. The convergence of
the process is sensitive to initial conditions and depends on the history of noise-trader transactions. Long-run portfolio
holdings may be in-efficient since investors holding mean-variance efficient portfolios may not be identified.
Keywords CAPM - Financial markets - Social interaction - Random difference equations
JEL Classification Numbers C62 - D85 - G12
We would like to thank Volker Böhm, Hans Föllmer, Roger Guesnerie, Alan Kirman, Thorsten Pampel, participants at the workshops
on Interactions and Markets (Pisa), Stochastic Modelling in Mathematical Finance (Montreal), and Aggregation and Disaggregation
(Banff), and seminar participants at various institutions for valuable comments and suggestions. We are indebted to Andreas
Starke for computational assistance. Financial support from the Deutsche Forschungsgemeinschaft under grant GRK11134/1: International Research Training Group ‘Economic Behavior and Interaction Models (EBIM)’ and NSERC is gratefully acknowledged. An earlier version was entitled “Non-ergodic behavior in financial markets with interacting
investors ”.