Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Tutorial: Walter Schachermayer

Title: Pricing and Hedging under Transaction Costs.

Abstract: 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 ) equals ^g(S0), where ^g 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.

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