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No arbitrage of the first kind and local martingale numéraires

Kabanov, Yuri, Kardaras, Constantinos 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
Sets: Departments > Statistics
Date Deposited: 11 Oct 2016 11:13
Last Modified: 20 May 2019 02:10
URI: http://eprints.lse.ac.uk/id/eprint/68002

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