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(ST ) equalŝ g(S0), whereĝ is the concave envelope of g and St is the price of the asset at time t. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support.

Transaction costs, No arbitragem, Consistent price systems, G10, G11, G12,

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We provide a rate for the strong convergence of Euler approximations for stochastic differential equations (SDEs) whose diffusion coefficient is not Lipschitz but only (1/2 + α)-Hölder continuous for some α ≥ 0.