On the Existence of Consistent Price Systems
arXiv:0911.3789
Abstract
We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs for certain processes that fail to have the CFS property. In particular this condition gives sufficient conditions, under which a continuous function of a process with CFS admits a CPS, while the CFS property might be lost.
To appear in "Stochastic Analysis and Applications". Keywords: Consistent pricing systems, No-arbitrage, Transaction costs, Full support, Conditional Full Support, Stability under Composition with Continuous Functions