Consistent Risk Measure on L 0 : NA Condition, Pricing and Dual Representation

The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on L0 is fixed to characterize the family of acceptable wealths that play the role of non negative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices of an European option. Moreover we provide an example where it is possible to obtain a dual representation of the risk-measure on L0 .