Geodesic
A Theorem on Martingale Selection for Relatively Open Convex Set-Valued Random Sequences
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 614-620

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For set-valued random sequences $(G_n)_{n=0}^N$ with relatively open convex values $G_n(\omega)$, we prove a new test for the existence of a sequence $(x_n)_{n=0}^N$ of selectors adapted to the filtration and admitting an equivalent martingale measure. The statement is formulated in terms of the supports of regular upper conditional distributions of $G_n$. This is a strengthening of the main result proved in our previous paper [1], where the openness of the set $G_n(\omega)$ was assumed and a possible weakening of this condition was discussed.
Keywords: representation, set-valued random sequence, martingale selection, measurable set-valued map, arbitrage theory, market model, pricing process. 
@article{MZM_2007_81_4_a13,
     author = {D. B. Rokhlin},
     title = {A {Theorem} on {Martingale} {Selection} for {Relatively} {Open} {Convex} {Set-Valued} {Random} {Sequences}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {614--620},
     publisher = {mathdoc},
     volume = {81},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a13/}
}
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D. B. Rokhlin. A Theorem on Martingale Selection for Relatively Open Convex Set-Valued Random Sequences. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 614-620. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a13/