No-arbitrage in Discrete-time Markets with Proportional Transaction Costs and General Information structure

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 Schachermayer (Math Finance 14(1):19–48, 2004) to the case where bid-ask spreads are not known with certainty. In the “no-friction” case, we retrieve the result of Kabanov and Stricker (Preprint 2003). Additionally, we propose a new modelization based on simple orders which appears to be powerful whatever the information structure is.