Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty

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.

References in corpus (2)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• A model-free version of the fundamental theorem of asset pricing and the super-replication theorem

Cited by in corpus (3)

• On robust pricing-hedging duality in continuous time
• Arbitrage theory without a numéraire
• Consistent Price Systems under Model Uncertainty