  We consider a financial market in discrete time and study pricing and hedging
conditional on the information available up to an arbitrary point in time. In
this conditional framework, we determine the structure of arbitrage-free
prices. Moreover, we characterize attainability and market completeness. We
derive a conditional version of the second fundamental theorem of asset
pricing, which, surprisingly, is not available up to now. The main tool we use
are time consistency properties of dynamic nonlinear expectations, which we
apply to the super- and subhedging prices. The results obtained extend existing
results in the literature, where the conditional setting is considered in most
cases only on finite probability spaces.
