Evolution of Portfolio Rules in Incomplete Markets

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Abstract
The paper considers the evolution of portfolio rules in markets with stationary returns and endogenous prices. The ultimate success of a portfolio rule is measured by the wealth share the rule is eventually able to conquer in competition with other portfolio rules. We give nec-essary and sufficient conditions for portfolio rules to be evolutionary stable. In the case of i.i.d. returns we identify a simple portfolio rule to be the unique evolutionary stable strategy. Moreover we demonstrate that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.

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