Before revision:  Then, assuming individual utility functions for the assets, utility-based shortfall and divergence risk measures are defined , which form two classes of  set-valued convex risk measures . Minimal penalty functions are computed in terms of the vector versions of the well-known divergence functionals (generalized relative entropy). As special cases, set-valued versions of the entropic risk measure and the average value at risk are obtained.
After revision:  Then, assuming individual utility functions for the assets, utility-based shortfall and divergence risk measures are defined , which form two classes of set-valued versions of the entropic risk measure and the average value at risk are obtained.