Geodesic
An extended version of
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 503-521

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This work considers an extension of the Dalang–Morton–Willinger theorem (the first fundamental theorem of asset pricing) in the presence of random convex constraints on the asset portfolio. The arbitrage-free assumption is characterized both in terms of a natural generalization of the notion of the martingale measure and in terms of supports of conditional distributions of price increments. The proposed approach relies on the well-known results for the case of a perfect market and is connected with the theory of measurable set-valued mappings.
Mots-clés : arbitrage, Doob decompositionю.
Keywords: free lunch, measurable set-valued mappings, support of a conditional distribution, martingale measures 
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     author = {D. B. Rokhlin},
     title = {An extended version of},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a4/}
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D. B. Rokhlin. An extended version of. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 503-521. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a4/