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Finance and Stochastics

, Volume 19, Issue 4, pp 685–717 | Cite as

The existence of dominating local martingale measures

  • Peter ImkellerEmail author
  • Nicolas Perkowski
Article

Abstract

We prove that for locally bounded processes the absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of filtration enlargements.

Keywords

Dominating local martingale measure Arbitrage of the first kind Fundamental theorem of asset pricing Supermartingale densities Föllmer’s measure Enlargement of filtration Jacod’s criterion 

Mathematics Subject Classification

60G44 60G48 91B70 46N10 

JEL Classification

G10 

Notes

Acknowledgements

We wish to express our gratitude to the anonymous referees for their careful reading of the manuscript and for their detailed comments which helped to correct a mistake in Sect. 5 and to improve the presentation. N.P. thanks Asgar Jamneshan for the introduction to filtration enlargements. We are grateful to Stefan Ankirchner, Kostas Kardaras and Johannes Ruf for their helpful comments on earlier versions of this paper. We thank Alexander Gushchin for pointing out the reference [45]. Part of the research was carried out during a 2011 visit at the University of Illinois at Urbana-Champaign. We are grateful for the hospitality at UIUC.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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