The 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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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 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

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

Dates
First available in Project Euclid: 20 March 2008

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1206018195

Digital Object Identifier
doi:10.1214/07-AAP461

Zentralblatt MATH identifier
1133.91422

Mathematical Reviews number (MathSciNet)
MR2398764

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

Keywords
Transaction costs superreplication fractional Brownian motion

Citation

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. http://projecteuclid.org/euclid.aoap/1206018195.


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