Consistent price systems and face-lifting pricing under transaction costs. (English) Zbl 1133.91422

Summary: 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.


91G80 Financial applications of other theories
60G99 Stochastic processes
91B24 Microeconomic theory (price theory and economic markets)
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