Before revision:  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 eligible assets.
After revision:  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 a general defaultable bond. In this paper we fill this gap allowing for general eligible assets.