  The classical discrete time model of proportional transaction costs relies on
the assumption that a feasible portfolio process has solvent increments at each
step. We extend this setting in two directions, allowing for convex transaction
costs and assuming that increments of the portfolio process belong to the sum
of a solvency set and a family of multivariate acceptable positions, e.g. with
respect to a dynamic risk measure. We describe the sets of superhedging prices,
formulate several no (risk) arbitrage conditions and explore connections
between them. 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 become stronger. The mathematical technique
relies on results for unbounded and possibly non-closed random sets in
Euclidean space.
