We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stability, by...

We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process--the equivalent of an equivalent martingale measure. This result fails in the presence of transaction costs. A...

The paper considers trading with proportional transaction costs. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed, and show, in general, how to represent its closure in such a way that it is the cone of claims attainable for zero...

In the first part of this paper, we introduce the notion of switch-stability for set of probabilities and prove that it is equivalent to the notion of optional m-stability. In the second part this notion is generalized to set of processes and prove that it is linked to the former notion.