Before revision:  Given a set of acceptable financial positions and a pre-specified traded asset ( the eligible asset ), the associated capital requirement for a financial position represents to the amount of capital that needs to be raised and invested in the eligible asset to make the position acceptable. Our abstract approach allows to provide results that are applicable to a whole range of spaces of financial positions commonly used in the literature. Moreover, it allows to unveil the key properties of acceptance sets and of eligible assetsdriving the effectiveness and the robustness of the associated capital requirements.
After revision:  Given a set of acceptable financial positions and a pre-specified traded asset ( the eligible asset is assumed to be an arbitrary non-zero positive element, thus allowing for a wide range of choices. In the context of function spaces, these general capital requirements cannot be transformed into cash-additive capital requirements by a simple change of numeraire unless the payoff of the eligible asset is bounded away from zero. This excludes the possibility of choosing a defaultable security as the eligible asset which, given the potential unavailability of risk-free assets, constitutes an important gap in the existing theory of capital requirements. This paper fills this gap and provides a detailed analysis of the interplay between acceptance sets and of eligible assetsdriving the effectiveness and the robustness of the associated capital requirements.