Annals of Applied Probability

Consistent price systems and face-lifting pricing under transaction costs

Paolo Guasoni, Miklós Rásonyi, and Walter Schachermayer

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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(ST) equals ĝ(S0), where ĝ 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.

Article information

Ann. Appl. Probab., Volume 18, Number 2 (2008), 491-520.

First available in Project Euclid: 20 March 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91B28
Secondary: 60G15: Gaussian processes 60G44: Martingales with continuous parameter

Transaction costs superreplication fractional Brownian motion


Guasoni, Paolo; Rásonyi, Miklós; Schachermayer, Walter. Consistent price systems and face-lifting pricing under transaction costs. Ann. Appl. Probab. 18 (2008), no. 2, 491--520. doi:10.1214/07-AAP461.

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