## Consistent price systems and face-lifting pricing under transaction costs.(English)Zbl 1133.91422

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.
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:

 91G80 Financial applications of other theories 60G99 Stochastic processes 91B24 Microeconomic theory (price theory and economic markets)
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### References:

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