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 of significant sets, 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 = {Ω}, 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.
Universal arbitrage aggregator in discrete-time markets under uncertainty / M. Burzoni, M. Frittelli, M. Maggis. - In: FINANCE AND STOCHASTICS. - ISSN 0949-2984. - 20:1(2016), pp. 1-50. [10.1007/s00780-015-0283-x]
Universal arbitrage aggregator in discrete-time markets under uncertainty
M. BurzoniPrimo
;M. FrittelliSecondo
;M. MaggisUltimo
2016
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 of significant sets, 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 = {Ω}, 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.File | Dimensione | Formato | |
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