For a set-valued stochastic sequence $(G_n)_{ n=0}^N$ with relatively open convex values $G_n(\omega)$ we give a criterion for the existence of an adapted sequence $(x_n)_{ n=0}^N$ of selectors, admitting an equivalent martingale measure. Mentioned criterion is expressed in terms of supports of the regular conditional upper distributions of the elements $G_n$. This result is a refinement of the main result of author's previous paper (Teor. Veroyatnost. i Primen., 2005, 50:3, 480--500), where the sets $G_n(\omega)$ were assumed to be open and where were asked if the openness condition can be relaxed.
Categories: math.PR