We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov et al. (Finance Stoch 6(3):371–382, 2002; Finance Stoch 7(3):403–411, 2003) and...

In this note, we consider a general discrete time ¯nancial market with pro- portional transaction costs as in Kabanov and Stricker [4], Kabanov et al. [5], Kabanov et al. [6] and Schachermayer [10]. We provide a dual formulation for the set of initial endowments which allow to super-hedge some...

We introduce a new class of control problems in which the gain depends on the solu- tion of a stochastic differential equation (SDE) reflected at the boundary of a bounded domain, along directions which are controlled by a bounded variation process. We provide a PDE characterization of the...

We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constrained to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a...

We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi [B....