Evolutionary stability of portfolio rules in incomplete markets
This paper studies the evolution of market shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of continuous reinvestment of wealth is determined by the market share eventually conquered in competition with other portfolio rules. Using random dynamical systems theory, we derive necessary and sufficient conditions for the evolutionary stability of portfolio rules. In the case of Markov (in particular i.i.d.) payoffs these local stability conditions lead to a simple portfolio rule that is the unique evolutionary stable strategy. This rule possesses an explicit representation. Moreover, it is demonstrated that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.
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- Klaus Reiner Schenk-Hoppï¿½, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
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- Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2002. "Market Selection Of Financial Trading Strategies: Global Stability," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 329-339.
- Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppï¿½, "undated". "Market Selection of Financial Trading Strategies: Global Stability," IEW - Working Papers 083, Institute for Empirical Research in Economics - University of Zurich.
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