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Department of Mathematical Sciences

Staff

Publication details for Hasanjan Sayit

Maris, F. & Sayit, H. (2012). Consistent Price Systems in Multiasset Markets. International Journal of Stochastic Analysis 2012: 687376.

Author(s) from Durham

Abstract

Let Xt be any d-dimensional continuous process that takes values in an open connected domain
O in Rd. In this paper, we give equivalent formulations of the conditional full support CFS
property of Xt in O.We use them to show that the CFS property of X in O implies the existence of a
martingale M under an equivalent probability measure such that M 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.