Journal
ANNALS OF APPLIED PROBABILITY
Volume 18, Issue 2, Pages 491-520Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/07-AAP461
Keywords
transaction costs; superreplication; fractional Brownian motion
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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 (g) over cap (S-0), where (g) over cap 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.
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