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Arbitrage in Continuous Complete Markets

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Abstract

This paper introduces a benchmark approach for the modelling of continuous, complete financial markets when an equivalent risk neutral measure does not exist. This approach is based on the unique characterization of a benchmark portfolio, the growth optimal portfolio, which is obtained via a generalization of the mutual fund theorem. The discounted growth optimal portfolio with minimum variance drift is shown to follow a Bessel process of dimension four. Some form of arbitrage can be explicitly measured by arbitrage amounts. Fair contingent claim prices are derived as conditional expectations under the real world probability measure. The Heath-Jarrow-Morton forward rate equation remains valid despite the absence of an equivalent risk neutral measure.

Suggested Citation

  • Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:72
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp72.pdf
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    Keywords

    continuous financial market; arbitrage amount; mutual fund theorem; growth optimal portfolio; numeraire portfolio; contingent claim pricing; forward rate equation;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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