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 .
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 .
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