Geodesic
A~complement to the Grigoriev theorem for the Kabanov model
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 409-419

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We provide an equivalent characterization of the absence of arbitrage opportunity for the bid and ask financial market model. This result, which is an analogue of the Dalang–Morton–Willinger theorem formulated for discrete-time financial market models without friction, supplements and improves the Grigoriev theorem for conic models in the two-dimensional case by showing that the set of all terminal liquidation values is closed.
Keywords: proportional transaction costs, absence of arbitrage opportunities, bid and ask prices, consistent price systems.
Mots-clés : liquidation value 
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     author = {J. Zhao and E. Lepinette},
     title = {A~complement to the {Grigoriev} theorem for the {Kabanov} model},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {409--419},
     publisher = {mathdoc},
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     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a6/}
}
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J. Zhao; E. Lepinette. A~complement to the Grigoriev theorem for the Kabanov model. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 409-419. http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a6/