No marginal arbitrage of the second kind for high production regimes in discrete time production-investment models with proportional transaction costs

Bruno Bouchard () and Adrien Nguyen Huu ()
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Bruno Bouchard: 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, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Adrien Nguyen Huu: 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, EDF - EDF, FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF
Authors registered in the RePEc Author Service: Adrien Nguyen-Huu

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Abstract: We consider a class of production-investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no-arbitrage of the second kind condition introduced by M. Rasonyi [13]. We show that this condition implies the closedness of the set of attainable claims and is equivalent to the existence of a strictly consistent price system under which the evaluation of future production profits are strictly negative. This allows to discuss the closedness of the set of terminal wealth in models with non-linear production functions which may admit arbitrages of the second kind for low production regimes but not marginally for high production regimes.

Keywords: Consistent price systems; Financial markets with transaction costs; Non-linear returns; No-arbitrage of the second kind (search for similar items in EconPapers)
Date: 2013-04-01
Note: View the original document on HAL open archive server: https://hal.science/hal-00487030v2
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Citations: View citations in EconPapers (5)

Published in Mathematical Finance, 2013, 23 (2), pp.366--386. ⟨10.1111/j.1467-9965.2011.00493.x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00487030

DOI: 10.1111/j.1467-9965.2011.00493.x

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