Robust Fundamental Theorem for Continuous Processes

Sara Biagini, Bruno Bouchard (), Constantinos Kardaras and Marcel Nutz
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Sara Biagini: UniPi - University of Pisa [Italy] = Università di Pisa [Italia] = Université de Pise [Italie]
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
Constantinos Kardaras: LSE - London School of Economics and Political Science
Marcel Nutz: Dept. of Mathematics - Columbia University [New York]

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Abstract: We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA1(P) of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: NA1(P) holds if and only if every P ∈ P admits a martingale measure which is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures.

Keywords: Superhedging duality; Nondominated Model AMS 2010 Subject Classification 91B25; Arbitrage of the First Kind; Fundamental Theorem of Asset Pricing; 60G44; 93E20 (search for similar items in EconPapers)
Date: 2017-10-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01076062v1
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Citations: View citations in EconPapers (32)

Published in Mathematical Finance, 2017, 27 (4), pp.963-987. ⟨10.1111/mafi.12110⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01076062

DOI: 10.1111/mafi.12110

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