Geodesic
On the Existence of an Equivalent Supermartingale Density for a Fork-Convex Family of Stochastic Processes
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 594-603

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We prove that a fork-convex family $\mathbb W$ of nonnegative stochastic processes has an equivalent supermartingale density if and only if the set $H$ of nonnegative random variables majorized by the values of elements of $\mathbb W$ at fixed instants of time is bounded in probability. A securities market model with arbitrarily many main risky assets, specified by the set $\mathbb W(\mathbb S)$ of nonnegative stochastic integrals with respect to finite collections of semimartingales from an arbitrary indexed family $\mathbb S$, satisfies the assumptions of this theorem.
Keywords: stochastic process, fork-convex family, supermartingale, semimartingale, securities market, probability space, convergence in probability, stochastic integral. 
@article{MZM_2010_87_4_a10,
     author = {D. B. Rokhlin},
     title = {On the {Existence} of an {Equivalent} {Supermartingale} {Density} for a {Fork-Convex} {Family} of {Stochastic} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {594--603},
     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a10/}
}
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D. B. Rokhlin. On the Existence of an Equivalent Supermartingale Density for a Fork-Convex Family of Stochastic Processes. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 594-603. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a10/