Characterization of threshold utilities for which a given risk measure is Meyer

Characterize the set of threshold utility functions v (increasing, twice differentiable) for which a fixed monetary risk measure ρ on the space of bounded random variables is v-SD-consistent (i.e., for which ρ is a v-Meyer risk measure).

Background

Throughout the paper, the analysis fixes a threshold utility v and investigates conditions under which a risk measure ρ is v-SD-consistent. Representation theorems and impossibility results show strong ties between v-SD-consistency and the structure of v (e.g., CARA vs. non-CARA), but a general inverse characterization—starting from a given ρ and identifying all v yielding v-SD-consistency—has not been established.

This inverse problem would map each risk measure to the collection of threshold utilities that make it consistent with the corresponding fractional stochastic dominance order, thereby clarifying the scope of applicability of a given risk measure within the v-SD framework.