Skorokhod Transition in the Conic Market Model

We examine the applicability of the Skorokhod representation theorem on filtrated probability spaces to the utility maximization problem in the Kabanov conic model of multiasset markets with proportional transaction costs. Filtrations on different stochastic bases are generally not related to one another under Skorokhod transitions, and hence the corresponding strategies may cease to be adapted. Consequently, the solutions obtained on the new probability space may not correspond to those on the original space. We show that, under fairly general conditions, the Bellman function of the control problem is preserved under changes of the underlying probability space.