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arXiv · 1406.5414

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

Christa Cuchiero·Josef Teichmann
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Abstract

We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining this insight with well known results from J. Mémin and L. Słominski \cite{MS:91} leads to a short variant of the proof of the fundamental theorem of asset pricing initially proved by F. Delbaen and W. Schachermayer \cite{DS:94}. The results are formulated in the general setting of admissible portfolio wealth processes as laid down by Y. Kabanov in \cite{kab:97}.

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Christa Cuchiero, Josef Teichmann. 2014-07-10. A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing. https://arxiv.org/abs/1406.5414

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