Arbitrage in Continuous Complete Markets

Eckhard Platen ()

No 72, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: continuous financial market; arbitrage amount; mutual fund theorem; growth optimal portfolio; numeraire portfolio; contingent claim pricing; forward rate equation (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2001-12-01
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Citations: View citations in EconPapers (85)

Published as: Platen, E., 2002. "Arbitrage in Continuous Complete Markets", Advances in Applied Probability, 34(3), 540-558.

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