  This paper presents a systematic study of the notion of surplus invariance,
which plays a natural and important role in the theory of risk measures and
capital requirements. So far, this notion has been investigated in the setting
of some special spaces of random variables. In this paper we develop a theory
of surplus invariance in its natural framework, namely that of vector lattices.
Besides providing a unifying perspective on the existing literature, we
establish a variety of new results including dual representations and
extensions of surplus-invariant risk measures and structural results for
surplus-invariant acceptance sets. We illustrate the power of the lattice
approach by specifying our results to model spaces with a dominating
probability, including Orlicz spaces, as well as to robust model spaces without
a dominating probability, where the standard topological techniques and
exhaustion arguments cannot be applied.
