Characterization of acceptance sets for co-monotone risk measures

•We study acceptance sets of co-monotone, convex risk measures.•In the case of finite state-spaces we give a complete geometric characterization.•Applications in low dimensional situations are discussed in detail.

We present a geometric characterization of acceptance sets for monotone, co-monotone and convex risk measures on finite state spaces. Geometrically, such acceptance sets can be represented by convex polygons with edges only on certain hyperplanes. We also provide some lower dimensional examples, and study acceptance sets for value at risk and expected shortfall.