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 of non-negligible sets\mathcal{S , which we call Arbitrage de la classe S. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular for }  S being the open sets we show that the absence of arbitrage opportunities, with respect to an opportune filtration enlargement, guarantees the existence of full support martingale measures. Finally we provide a dual representation  in terms of weakly open sets of probability measures, which highlights the robust nature of our approach .
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 \mathcal{S , which we call Arbitrage de la classe S. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular : for S= \Omega} absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for 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 .
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of non-negligible sets\mathcal{S
\mathcal{S
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de la classe
de la classe
R
for
: for S=
A
\Omega
A
absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for
R
we show that the absence of arbitrage opportunities, with respect to an opportune filtration enlargement, guarantees
, absence of Open Arbitrage is equivalent to
R
Finally we provide
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
of Open Arbitrage
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our approach
this concept