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. M\'emin and L. S{ \l}ominski \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}.
Categories: math.PR q-fin.MF