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Price systems constructed by optimal dynamic portfolios

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  • Manfred Schäl

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. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Manfred Schäl, 2000. "Price systems constructed by optimal dynamic portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 375-397, August.
    • Handle: RePEc:spr:mathme:v:51:y:2000:i:3:p:375-397
    DOI: 10.1007/s001860000049
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