Geodesic
Constructive no-arbitrage criterion under transaction costs in the case of finite discrete time
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 41-59 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain a constructive criterion for robust no-arbitrage in discrete-time market models with transaction costs. This criterion is expressed in terms of the supports of the regular conditional upper distributions of the solvency cones. We also consider the model with a bank account. A method for construction of arbitrage strategies is proposed.
Mots-clés : robust no-arbitrage
Keywords: transaction costs, arbitrage portfolios, measurable set-valued maps, supports of the regular conditional distributions. 
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D. B. Rokhlin. Constructive no-arbitrage criterion under transaction costs in the case of finite discrete time. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 41-59. http://geodesic.mathdoc.fr/item/TVP_2007_52_1_a2/

[1] Beer G., “A Polish topology for the closed subsets of a Polish space”, Proc. Amer. Math. Soc., 113:4 (1991), 1123–1133 | DOI | MR | Zbl

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

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

[4] Himmelberg C. J., “Measurable relations”, Fund. Math., 87 (1975), 53–72 | MR | Zbl

[5] Jacod J., Shiryaev A. N., “Local martingales and the fundamental asset pricing theorems in the discrete-time case”, Finance Stoch., 2:3 (1998), 259–273 | DOI | MR | Zbl

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

[7] Kabanov Y. M., “Hedging and liquidation under transaction costs in currency markets”, Finance Stoch., 3:2 (1999), 237–248 | DOI | MR | Zbl

[8] Kabanov Y., Rásonyi M., Stricker C., “No-arbitrage criteria for financial markets with efficient friction”, Finance Stoch., 6:3 (2002), 371–382 | DOI | MR | Zbl

[9] Kabanov Y., Rásonyi M., Stricker C., “On the closedness of sums of convex cones in $L^0$ and the robust no-arbitrage property”, Finance Stoch., 7:3 (2003), 403–411 | DOI | MR | Zbl

[10] Kabanov Y., Stricker C., “The Harrison–Pliska arbitrage pricing theorem under transaction costs”, J. Math. Econom., 35:2 (2001), 185–196 | DOI | MR | Zbl

[11] Kusraev A. G., Kutateladze S. S., Subdifferentsialy. Teoriya i prilozheniya, Ch. I, Izd-vo IM SO RAN, Novosibirsk, 2002, 381 pp. | MR | Zbl

[12] Levin V. L., Vypuklyi analiz v prostranstvakh izmerimykh funktsii i ego primeneniya v matematike i ekonomike, Nauka, M., 1985, 352 pp. | MR

[13] Rokafellar R., Vypuklyi analiz, Mir, M., 1973, 469 pp.

[14] Rokhlin D. B., “Rasshirennaya versiya teoremy Dalanga–Mortona–Villindzhera pri vypuklykh ogranicheniyakh na portfel”, Teoriya veroyatn. i ee primen., 49:3 (2004), 503–521 | MR | Zbl

[15] Rokhlin D. B., “Zadacha o martingalnom vybore v sluchae konechnogo diskretnogo vremeni”, Teoriya veroyatn. i ee primen., 50:3 (2005), 480–500 | MR

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

[17] Srivastava S. M., A Course on Borel Sets, Grad. Texts in Math., 180, Springer-Verlag, New York, 1998, 261 pp. | MR | Zbl