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Zbl 1133.91422
Guasoni, Paolo; Rásonyi, Miklós; Schachermayer, Walter
Consistent price systems and face-lifting pricing under transaction costs. (English)
[J] Ann. Appl. Probab. 18, No. 2, 491-520 (2008). ISSN 1050-5164

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.\par 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.

MSC 2000:: *91B28 Finance etc.
60G99 Stochastic processes

Keywords: transaction costs; superreplication; fractional Brownian motion

Cited in: Zbl 1151.91490 Zbl 1151.91517

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