Sticky continuous processes have consistent price systems
arXiv:1310.7857 · doi:10.1239/jap/1437658617
Abstract
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)].
10 pages, v3: incorporates minor corrections and the proof of the main result has been clarified, to appear in Journal of Applied Probability