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The numéraire portfolio in semimartingale financial models

Karatzas, Ioannis and Kardaras, Constantinos (2007) The numéraire portfolio in semimartingale financial models. Finance and Stochastics, 11 (4). pp. 447-493. ISSN 0949-2984

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Identification Number: 10.1007/s00780-007-0047-3


We study the existence of the numéraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numéraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient conditions for the existence of the numéraire portfolio are obtained in terms of the triplet of predictable characteristics of the asset price process. This characterization is then used to obtain further necessary and sufficient conditions, in terms of a no-free-lunch-type notion. In particular, the full strength of the “No Free Lunch with Vanishing Risk” (NFLVR) condition is not needed, only the weaker “No Unbounded Profit with Bounded Risk” (NUPBR) condition that involves the boundedness in probability of the terminal values of wealth processes. We show that this notion is the minimal a-priori assumption required in order to proceed with utility optimization. The fact that it is expressed entirely in terms of predictable characteristics makes it easy to check, something that the stronger NFLVR condition lacks.

Item Type: Article
Official URL:
Additional Information: © 2007 Springer-Verlag
Divisions: Statistics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Date Deposited: 04 Dec 2017 09:23
Last Modified: 20 Aug 2021 01:40

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