Under proportional transaction costs, a price process is said to have a
consistent price system, if there is a semimartingale with an equivalent
martingale measure that evolves within the bid-ask spread. We show that a
continuous, multi-asset price process has a consistent price system, under
arbitrarily small proportional transaction costs, if it satisfies a natural
multi-dimensional generalization of the stickiness condition introduced by
Guasoni [Math. Finance 16(3), 569-582 (2006)].