Before revision:  Can the eligible asset be chosen in such a way that for every financial position the corresponding required capital is lower than if any other asset had been chosen? In contrast to most of the literature our discussion is not limited to convex or coherent acceptance sets and allows for eligible assets that are not necessarily bounded away from zero. This generality uncovers some unexpected phenomena and opens up the field for applications to acceptance sets based both on Value-at-Risk and on Tail Value-at-Risk .
After revision:  Can the eligible asset. Our examples and results on finiteness and continuity show that a theory of capital requirements allowing for general eligible assets is richer than that of cash-invariant capital requirements .