Abstracts

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. Our objective is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the fact that acceptability does not depend on the positive part, or surplus, of a capital position. We argue that surplus invariance is a reasonable requirement from a regulatory perspective, because it focuses on the interests of liability holders of a fi nancial institution. We provide a dual characterization of surplus-invariant, convex acceptance sets, and show that the combination of surplus invariance and coherence leads to a narrow range of capital adequacy tests, essentially limited to scenario-based tests. Finally, we analyze the relationship between surplus-invariant acceptance sets and loss-based and excess-invariant risk measures.