2000-06-13Buch DOI: 10.18452/2870
Mean-variance versus expected utility in dynamic investment analysis
Ziemba, William T.
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
This paper derives the mean-variance efficient frontier and optimal portfolio policies for a dynamic investment model. In the absence of arbitrage opportunities, the optimal expected portfolio value can be identified through the state price density in a frictionless market using martingale analysis. The efficient frontier for the dynamic model is linear in the space of the standard deviation and the expected value of the terminal portfolio in the presence of a riskless asset as in the static mean-variance case. A replication procedure is developed to obtain the optimal portfolio policies using a partial differential equation. A closed form solution is derived if asset prices jointly follow a multidimensional geometric Brownian motion. A comparison is made between the optimal policies of the expected utility approach and a mean-variance analysis in the continuous time setting. For investors interested in the mean-variance criterion, we discuss and derive the optimal choice of target wealth that maximizes the probability that the mean-variance analysis outperforms the expected utility approach.
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