Price systems constructed by optimal dynamic portfolios

Price systems constructed by optimal dynamic portfolios

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Article ID: iaor20013398
Country: Germany
Volume: 51
Issue: 3
Start Page Number: 375
End Page Number: 397
Publication Date: Jan 2000
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors:
Keywords: portfolio management
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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