Journal title
FINANCE AND STOCHASTICS
DOI
10.1007/s00780-015-0283-x
Issue
1
Volume
20
Last updated
2020-04-13T16:18:27.993+01:00
Page
1-50
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 $\mathcal{S}$ of significant sets, which we
call Arbitrage de la classe $\mathcal{S}$. The choice of $\mathcal{S}$ 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
$\mathcal{S}$ 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.
richness of the family of martingale measures in relation to different notions
of Arbitrage, generated by a class $\mathcal{S}$ of significant sets, which we
call Arbitrage de la classe $\mathcal{S}$. The choice of $\mathcal{S}$ 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
$\mathcal{S}$ 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.
Symplectic ID
1063975
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Submitted to ORA
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Publication type
Journal Article
Publication date
January 2016