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...

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...

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle...

We consider the problem of decomposing monetary risk in the presence of a fully traded market in {\it some} risks. We show that a mark-to-market approach to pricing leads to such a decomposition if the risk measure is time-consistent in the sense of Delbaen.

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.

The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk increments, leads to some natural dynamics. In this paper we...

We study a stochastic flow of -homeomorphisms of . At certain stopping times, the spatial derivative of the flow is a diffusion in the space variable and its generator is given. This answers several questions posed in a previous study by Bass and Burdzy (1999, Ann. Probab. 27, 50-108).