Randomization in the two-armed bandit problem (Q750006)

This paper gives an elementary proof of the existence of optimal solutions to a general form of the continuous-time two-armed bandit. The formulation is the same as that used by \textit{G. Mazziotto} and \textit{A. Millet} [Stochastics 22, 251-288 (1987; Zbl 0643.60040)]; however the topological embedding of the set of randomized optimal increasing paths is new and enables a resolution of the problem that requires only straightforward topological arguments. Also, one of the conditions in Mazziotto and Millet's paper can be removed, yielding a stronger result.