2003-09-30Buch DOI: 10.18452/2935
Intertemporal mean-variance efficiency with a Markovian state price density
Ziemba, William T.
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
This paper extends Merton's continuous time (instantaneous) mean-variance analysis and the mutual fund separation theory. Given the existence of a Markovian state price density process, the optimal portfolios from concave utility maximization are instantaneously mean-variance efficient independent of the concave utility function's form. The Capital Asset Pricing Model holds with the market portfolio induced by the growth optimal portfolio. The Markowitz-Tobin mutual fund separation is extended to include the lognormal assumption for asset prices as a special case. Closed form solutions to the expected utility maximization of terminal portfolio value are derived. We present an example in which the state price processes are specified as a multivariate geometric Brownian motion and the asset prices follow a multivariate diffusion process with relatively general parameters.
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