Abstract.
The paper studies connections between arbitrage and utility maximization in a discrete-time financial market. The market is incomplete. Thus one has several choices of equivalent martingale measures to price contingent claims. Davis determines a unique price for a contingent claim which is based on an optimal dynamic portfolio by use of a `marginal rate of substitution' argument. Here conditions will be given such that this price is determined by a martingale measure and thus by a consistent price system. The underlying utility function U is defined on the positive half-line. Then dynamic portfolios are admissible if the terminal wealth is positive. In case of the logarithmic utility function, the optimal dynamic portfolio is the numeraire portfolio.
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Manuscript received: November 1999 / Final version received: February 2000
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Schäl, M. Price systems constructed by optimal dynamic portfolios. Mathematical Methods of OR 51, 375–397 (2000). https://doi.org/10.1007/s001860000049
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DOI: https://doi.org/10.1007/s001860000049