Geodesic
A complement to the Grigoriev theorem for the Kabanov model
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 409-419 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] B. Bouchard, Yu. M. Kabanov, N. Touzi, “Option pricing by large risk aversion utility under transaction costs”, Decis. Econ. Finance, 24:2 (2001), 127–136 | DOI | MR | Zbl

[2] L. Campi, W. Schachermayer, “A super-replication theorem in Kabanov's model of transaction costs”, Finance Stoch., 10:4 (2006), 579–596 | DOI | MR | Zbl

[3] A. Cherny, “General arbitrage pricing model. II. Transaction costs”, Séminaire de probabilités XL, Lecture Notes in Math., 1899, Springer, Berlin, 2007, 447–461 | DOI | MR | Zbl

[4] D. De Vallière, E. Denis, Y. Kabanov, “Hedging of American options under transaction costs”, Finance Stoch., 13:1 (2009), 105–119 | DOI | MR | Zbl

[5] R. C. Dalang, A. Morton, W. Willinger, “Equivalent martingale measures and no-arbitrage in stochastic securities market models”, Stochastics Stochastics Rep., 29:2 (1990), 185–201 | DOI | MR | Zbl

[6] P. Grigoriev, “On low dimensional case in the fundamental asset pricing theorem with transaction costs”, Statist. Decisions, 23:1 (2005), 33–48 | DOI | MR | Zbl

[7] P. Guasoni, E. Lépinette, M. Rásonyi, “The fundamental theorem of asset pricing under transaction costs”, Finance Stoch., 16:4 (2012), 741–777 | DOI | MR | Zbl

[8] P. Guasoni, M. Rásonyi, W. Schachermayer, “The fundamental theorem of asset pricing for continuous processes under small transaction costs”, Ann. Finance, 6:2 (2010), 157–191 | DOI | Zbl

[9] Hao Zhang, S. Hodges, An extended model of effective bid-ask spread, 2012, 32 pp. http://www.cass.city.ac.uk/__data/assets/pdf_file/0007/128068/H.Zhang.pdf

[10] E. Jouini, H. Kallal, “Martingales and arbitrage in securities markets with transaction costs”, J. Econom. Theory, 66:1 (1995), 178–197 | DOI | MR | Zbl

[11] R. Przemysław, “Arbitrage in markets with bid-ask spreads. The fundamental theorem of asset pricing in finite discrete time markets with bid-ask spreads and a money account”, Ann. Finance, 11:3-4 (2015), 453–475 | DOI | MR | Zbl

[12] W. Schachermayer, “The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time”, Math. Finance, 14:1 (2004), 19–48 | DOI | MR | Zbl

[13] Yu. Kabanov, M. Safarian, Markets with transaction costs. Mathematical theory, Springer Finance, Springer-Verlag, Berlin, 2009, xiv+294 pp. | DOI | MR | Zbl

[14] Yu. Kabanov, E. Denis, “Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs”, Finance Stoch., 16:1 (2012), 135–154 | DOI | MR | Zbl

[15] E. Lépinette, Tuan Tran, “General financial market model defined by a liquidation value process”, Stochastics, 88:3 (2016), 437–459 | DOI | MR | Zbl

[16] M. Rásonyi, “Arbitrage under transaction costs revisited”, Optimality and risk — modern trends in mathematical finance, Springer, Berlin, 2009, 211–225 | DOI | MR | Zbl