The fundamental theorem of asset pricing for continuous processes under small transaction costs. (English) Zbl 1239.91190

The question of identification of the necessary and sufficient conditions for proving a version of the fundamental theorem of asset pricing for arbitrary small transaction costs is addressed. In continuous-time setting, a notion of absence of arbitrage admitting a clear-cut economic interpretation to the existence of consistent price system, which correspond to equivalent martingale measure in the frictionless case, is studied. A comparison between numeraire-free and numeraire-based notions of admissibility is provided, and the corresponding martingale and local martingale properties for the consistent price systems are stated as well.


91G80 Financial applications of other theories
91B25 Asset pricing models (MSC2010)
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