Evolutionary beliefs and financial markets

Why do investors keep different opinions even though they learn from their own failures and successes? Why do investors keep different opinions even though they observe each other and learn from their relative failures and successes? We analyze beliefs dynamics when beliefs result from a very general learning process that favors beliefs leading to higher absolute or relative utility levels. We show that such a process converges to the Nash equilibrium in a game of strategic belief choices. The asymptotic beliefs are subjective and heterogeneous across the agents. Optimism (resp. overconfidence) as well as pessimism (resp. doubt) both emerge from the learning process. Furthermore, we obtain a positive correlation between pessimism (resp. doubt) and risk-tolerance. Under reasonable assumptions, beliefs exhibit a pessimistic bias and, as a consequence, the risk premium is higher than in a standard setting.