Evolutionary stable investment in stock markets

This paper studies the performance of portfolio rules in incomplete markets for long-lived assets with endogenous prices. The dynamics of wealth shares in the process of repeated reinvestment of wealth is modelled as a random dynamical systems. The performance of a portfolio rule is determined by the wealth share eventually conquered in competition with other rules. We derive necessary and sufficient conditions for the evolutionary stability of portfolio rules when dividends are Markov or, in particular, i.i.d. These local stability conditions leads to a unique evolutionary stable strategy for which an explicit representation is given. It is further demonstrated that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives