Before revision:  If the acceptance sets consist of non-negative random vectors, that is the underlying dynamic risk measure is the conditional essential infimum, we extend many classical no arbitrage conditions in markets with transaction costs and provide their natural geometric interpretation .
After revision:  In the special case when multivariate positions are converted into a single fixed asset, our framework turns into the no good deals setting. However, in general, the possibilities of assessing the risk with respect to any asset or a basket of the assets lead to a decrease of superhedging prices and the no arbitrage conditions in markets with transaction costs and provide their natural geometric interpretation .