No arbitrage of the first kind and local martingale numéraires

Yuri Kabanov, Constantinos Kardaras and Shiqi Song
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

JEL-codes: C1 (search for similar items in EconPapers)
Date: 2016-10-01
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Citations: View citations in EconPapers (17)

Published in Finance and Stochastics, 1, October, 2016, 20(4), pp. 1097-1108. ISSN: 0949-2984

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Journal Article: No arbitrage of the first kind and local martingale numéraires (2016)
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