Consistent Price Systems in Multiasset Markets

Let Xt be any d-dimensional continuous process that takes values in an open connected domain O in R. In this paper, we give equivalent formulations of the conditional full support CFS property ofXt inO. We use them to show that the CFS property of X inO implies the existence of a martingaleM under an equivalent probability measure such thatM lies in the > 0 neighborhood of Xt for any given under the supremum norm. The existence of such martingales, which are called consistent price systems CPSs , has relevance with absence of arbitrage and hedging problems in markets with proportional transaction costs as discussed in the recent paper by Guasoni et al. 2008 , where the CFS property is introduced and shown sufficient for CPSs for processes with certain state space. The current paper extends the results in the work of Guasoni et al. 2008 , to processes with more general state space.