  In markets with transaction costs, consistent price systems play the same
role as martingale measures in frictionless markets. We prove that if a
continuous price process has conditional full support, then it admits
consistent price systems for arbitrarily small transaction costs. This result
applies to a large class of Markovian and non-Markovian models, including
geometric fractional Brownian motion. Using the constructed price systems, we
show, under very general assumptions, the following ``face-lifting'' result:
the asymptotic superreplication price of a European contingent claim $g(S_T)$
equals $\hat{g}(S_0)$, where $\hat{g}$ is the concave envelope of $g$ and $S_t$
is the price of the asset at time $t$. This theorem generalizes similar results
obtained for diffusion processes to processes with conditional full support.
