Before revision:  We allow for general acceptance sets and general positive eligible (or "reference") assets, which include defaultable bonds, options, or limited liability assets . Since the payoff of these assets is not  bounded away from zero the resulting capital requirements cannot be transformed into cash-invariant risk measures by a simple change of numeraire.
After revision:  We allow for general acceptance sets and general positive eligible (or "reference") assets, which include defaultable bonds, options, or limited liability assets . Since the payoff of these assets is not bounded away from zero the resulting risk measures cannot be transformed into cash-invariant risk measures by a simple change of numeraire.