  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 $L^0$ 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 (called risk-hedging prices) of a European option. Moreover, we show
that the set of all risk-hedging prices is closed under NA. At last, we provide
a dual representation of the risk-measure on $L^0$ under some conditions.
