A representation of risk measures

We provide a representation theorem for risk measures satisfying (1) monotonicity, (2) positive homogeneity and (3) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition, sub-additive; see Artzner et al. in Math Finance 9:203–228, 1999).