Before revision:  As special cases, set-valued versions of the entropic risk measure and the average value at risk are obtained. The general results on the effect of market frictions are applied to the utility-based framework and conditions concerning applicability are presented .
After revision:  As special cases, set-valued versions of the entropic risk measure and the average value at risk . As a second step, the minimization of these risk measures subject to trading opportunities is studied in a general convex market in discrete time. The optimal value of the minimization problem, called the market risk measure, is also a set-valued risk measure. A dual representation for the market risk measure that decomposes the effects of the original risk measure and the frictions of the market is proved .