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

Christa Cuchiero () and Josef Teichmann ()

Finance and Stochastics, 2015, vol. 19, issue 4, 743-761

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 ). Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Fundamental theorem of asset pricing; Emery topology; (NUPBR) condition; (P-UT) property; 60G48; 91B70; 91G99; G10 (search for similar items in EconPapers)
Date: 2015
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