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Arbitrage possibilities in Bessel processes and their relations to local martingales
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  • Published: September 1995

Arbitrage possibilities in Bessel processes and their relations to local martingales

  • F. Delbaen1 &
  • W. Schachermayer2 

Probability Theory and Related Fields volume 102, pages 357–366 (1995)Cite this article

  • 313 Accesses

  • 67 Citations

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Summary

We show that, if we allow general admissible integrands as trading strategies, the three dimensional Bessel process, Bes3, admits arbitrage possibilities. This is in contrast with the fact that the inverse process is a local martingale and hence is arbitrage free. This leads to some economic interpretation for the analysis of the property of arbitrage in foreign exchange rates. This notion (relative to general admissible integrands) does depend on the fact, which of the two currencies under consideration is chosen as numéraire. The results rely on a general construction of strictly positive local martingales. The construction is related to the Föllmer measure of a positive super-martingale.

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Author information

Authors and Affiliations

  1. Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussels, Belgium

    F. Delbaen

  2. Universität Wien, Brünnerstrasse 72, A-1210, Wien, Austria

    W. Schachermayer

Authors
  1. F. Delbaen
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  2. W. Schachermayer
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Additional information

Part of this research was supported by the European Community Stimulation Plan for Economic Science contract Number SPES-CT91-0089

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Delbaen, F., Schachermayer, W. Arbitrage possibilities in Bessel processes and their relations to local martingales. Probab. Th. Rel. Fields 102, 357–366 (1995). https://doi.org/10.1007/BF01192466

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  • Received: 01 April 1994

  • Revised: 17 March 1995

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01192466

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Mathematics Subject Classifcation (1991)

  • 90A09
  • 60G44
  • 46N10
  • 47N10
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