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O-equivalent measures and arbitrage
In this talk we introduce the notion of O-equivalence between probability measures. This is a weaker, but similar notion to the usual equivalence between measures. We prove that this notion of O-equivalence, combined with certain topological property of portfolios, can be used to transfer arbitrage properties between models, in a similar way that equivalence between probability measures is used traditionally in finance for that purpose. We consider different topologies on the canonical spaces corresponding to various models. We show that arbitrage can be excluded within certain large classes of portfolios, even under non-semimartingale models for which equivalent martingale measures do not exist.