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Finance and Stochastics

, Volume 19, Issue 4, pp 743–761 | Cite as

A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing

  • Christa CuchieroEmail author
  • Josef Teichmann
Article

Abstract

We show that no unbounded profit with bounded risk (NUPBR) implies predictable uniform tightness (P-UT), a boundedness property in the Emery topology introduced by Stricker (Séminaire de Probabilités de Strasbourg XIX, pp. 209–217, 1985). Combining this insight with well-known results of Mémin and Słominski (Séminaire de Probabilités de Strasbourg XXV, pp. 162–177, 1991) leads to a short variant of the proof of the fundamental theorem of asset pricing initially proved by Delbaen and Schachermayer (Math. Ann. 300:463–520, 1994). The results are formulated in the general setting of admissible portfolio wealth processes as laid down by Kabanov (Statistics and Control of Stochastic Processes, pp. 191–203, World Sci. Publ., River Edge, 1997).

Keywords

Fundamental theorem of asset pricing Emery topology (NUPBR) condition (P-UT) property 

Mathematics Subject Classification

60G48 91B70 91G99 

JEL Classification

G10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of ViennaViennaAustria
  2. 2.ETH ZürichZürichSwitzerland

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