Before revision:  To every convex regular risk measure \rho on {\cal C}_b(\Omega), we associate a canonical c_{\rho of probability measures . Furthermore{\cal   the convex risk measure admits a dual representation in terms of a weakly relatively compact set of probability measures absolutely continuous with respect to some probability measure belonging to the canonical c_{\rho .
After revision:  To every convex regular risk measure \rho on {\cal C}_b(\Omega), we associate a canonical c_{\rho of probability measures on Borel sets, characterizing the riskless non positive elements of{\cal the convex risk measure admits a dual representation in terms of a weakly relatively compact set of probability measures absolutely continuous with respect to some probability measure belonging to the canonical c_{\rho .