On a multi-asset version of the Kusuoka limit theorem of option superreplication under transaction costs

Abstract

We consider, using the geometric description, a sequence of models of multi-asset financial markets with proportional transaction costs vanishing in the limit. We assume that the price processes are He-type multinomial approximations of a process whose components are correlated geometric Brownian motions. For a given vector-valued contingent claim, defined as a continuous function of the price trajectories, we consider for each model the hedging set, that is, the set of all vector-valued initial endowments permitting to superreplicate the contingent claim by the final position of a self-financing portfolio. We calculate the limit of the hedging sets in the closed topology, obtaining in this way a set-valued version of the Kusuoka limit theorem.