Evolutionary Stable Stock Markets

This paper shows that a stock market is evolutionary stable if andonly if stocks are evaluated by expected relative dividends. Any othermarket can be invaded by portfolio rules that will gain market wealthand hence change the valuation. In the model the valuation of assetsis given by the wealth average of the portfolio rules in the market. Thewealth dynamics is modelled as a random dynamical system. Neces-sary and sufficient conditions are derived for the evolutionary stabilityof portfolio rules when (relative) dividend payoffs form a stationaryMarkov process. These local stability conditions lead to a unique evo-lutionary stable strategy according to which assets are evaluated byexpected relative dividends.