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No arbitrage of the first kind and local martingale numéraires

Kabanov, Yuri, Kardaras, Constantinos ORCID: 0000-0001-6903-4506 and Song, Shiqi (2016) No arbitrage of the first kind and local martingale numéraires. Finance and Stochastics, 20 (4). pp. 1097-1108. ISSN 0949-2984

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Identification Number: 10.1007/s00780-016-0310-6

Abstract

A supermartingale deflator (resp. local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp. local martingales). A supermartingale numéraire (resp. local martingale numéraire) is a wealth process whose reciprocal is a supermartingale deflator (resp. local martingale deflator). It has been established in previous works that absence of arbitrage of the first kind ( NA1NA1 ) is equivalent to the existence of the (unique) supermartingale numéraire, and further equivalent to the existence of a strictly positive local martingale deflator; however, under NA1NA1 , a local martingale numéraire may fail to exist. In this work, we establish that under NA1NA1 , a supermartingale numéraire under the original probability PP becomes a local martingale numéraire for equivalent probabilities arbitrarily close to PP in the total variation distance.

Item Type: Article
Official URL: http://link.springer.com/journal/780
Additional Information: © 2016 Springer
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 11 Oct 2016 11:13
Last Modified: 20 Oct 2021 00:32
URI: http://eprints.lse.ac.uk/id/eprint/68002

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