Monotone and cash-invariant convex functions and hulls

This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to some numeraire (‘cash’). As a main result, for any function f , we find the greatest closed convex monotone and cash-invariant function majorized by f . We then apply our results to some well-known risk measures and problems arising in connection with insurance regulation.