We present 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 special spaces of random variables. In this paper we develop a theory of surplus invariance in the framework of vector lattices. Besides providing a unifying perspective on the existing literature, this greater level of generality makes our results applicable to model spaces where a dominating probability is not available, which are becoming increasingly popular in the field of "robust finance". We establish a variety of new results, including structural results for surplus-invariant acceptance sets and powerful dual representations for surplus-invariant risk measures.
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