Universal arbitrage aggregator in discrete-time markets under uncertainty

Journal article

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 classeS$\mathcal{S}$. 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.

Authors: Burzoni, M; Frittelli, M; Maggis, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Finance and Stochastics
• Volume: 20
• Pages: 1-50
• Publication date: 2015-11-12
• Acceptance date: 2015-05-03
• DOI: 10.1007/s00780-015-0283-x
• EISSN: 1432-1122
• ISSN: 0949-2984
• Keywords: SBTMR