Consistent price systems and face-lifting pricing under transaction costs

By Paolo Guasoni, Miklós Rásonyi, Walter Schachermayer. 2008

139 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/f1c77046cf0a236df785b4a38b67959500ed0bcd

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Citations in the corpus

The fundamental theorem of asset pricing for continuous processes under small transaction costs (2010, background): “In [10] the following result has been shown:”
Fractional Processes as Models in Stochastic Finance (2010, background): “[24] that conditional full support implies the existence of an ε-consistent price system for every ε > 0.”
Modelling energy spot prices by volatility modulated Levy-driven Volterra processes (2013, background): “It turns out that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs, see Guasoni, Rásonyi and Schachermayer [47].”
Asymptotics and duality for the Davis and Norman problem (2010, background): “The pairs (S̃, Z) correspond to the consistent price systems of [9, 22].”