Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs

Emmanuel Denis and Yuri Kabanov ()
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Emmanuel Denis: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Yuri Kabanov: LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE]
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов and Emmanuel Lépinette

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Abstract: In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial endowments laying outside the solvency region but ending inside. Such a phenomenon was discovered by M. Rasonyi in the discrete-time framework. In this note we consider a rather abstract continuous-time setting and prove necessary and sufficient conditions for the property which we call No Free Lunch of the 2nd Kind, NFL2. We provide a number of equivalent conditions elucidating, in particular, the financial meaning of the property B which appeared as an indispensable 'technical' hypothesis in previous papers on hedging (super-replication) of contingent claims under transaction costs. We show that it is equivalent to another condition on the 'richness' of the set of consistent price systems, close to the condition PCE introduced by Rasonyi. In the last section we deduce the Rasonyi theorem from our general result using specific features of discrete-time models.

Keywords: transaction costs; arbitrage; no free lunch; consistent price systems; set-valued processes; martingales (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

Published in Finance and Stochastics, 2011, 16 (1), pp.135-154. ⟨10.1007/s00780-010-0144-6⟩

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Journal Article: Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00488288

DOI: 10.1007/s00780-010-0144-6

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