Convex risk measures on Lp

Convex risk measures are best known on L∞. In this paper we argue that Lp, for p ∈ [1,∞), is a more appropriate model space. We provide a comprehensive but concise exposure of the topological properties of con-vex risk measures on Lp. Our main result is the complete characterization of the extension and restriction operations of convex risk measures from and to L ∞ and Lp, respectively. In particular, it turns out that there is a one-to-one correspondence between law-invariant convex risk measures on L ∞ and L1. Key words: convex risk measures, extension and restriction opera-tions, law-invariant convex functions