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Universal arbitrage aggregator in discrete-time markets under uncertainty

Matteo Burzoni (matteo.burzoni@unimi.it), Marco Frittelli (marco.frittelli@unimi.it) and Marco Maggis (marco.maggis@unimi.it)

Finance and Stochastics, 2016, vol. 20, issue 1, 50 pages

Abstract: In a model-independent discrete-time financial market, we discuss the richness of the family of martingale measures in relation to different notions of arbitrage, generated by a class S $\mathcal{S}$ of significant sets, which we call arbitrage de la classe S $\mathcal{S}$ . The choice of S $\mathcal{S}$ reflects the intrinsic properties of the class of polar sets of martingale measures. In particular, for S = { Ω } $\mathcal{S}=\{ \Omega\} $ , absence of model-independent arbitrage is equivalent to the existence of a martingale measure; for S $\mathcal{S}$ being the open sets, absence of open arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a universal aggregator of all arbitrage opportunities. We further introduce the notion of market feasibility and provide its characterization via arbitrage conditions. We conclude providing a dual representation of open arbitrage in terms of weakly open sets of probability measures, which highlights the robust nature of this concept. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: Model uncertainty; First fundamental theorem of asset pricing; Feasible market; Open arbitrage; Full support martingale measure; 60G42; 91B24; 91G99; 60H99; 46A20; 46E27; G10; G12; G13 (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations: View citations in EconPapers (33)

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DOI: 10.1007/s00780-015-0283-x

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