Capital adequacy tests and limited liability of financial institutions

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate the class of surplus-invariant acceptance sets. We argue that surplus invariance is a reasonable requirement from a regulatory perspective, since the corresponding capital adequacy tests do not depend on the surplus of a financial institution, which benefits exclusively its shareholders, but only on the default profile, which affects its liability holders. We provide a detailed analysis of surplus-invariant acceptance sets and their associated risk measures and we discuss the link with loss-based and excess-invariant risk measures, recently studied by Cont et al. (2013) and by Staum (2013), respectively.