Dilatation monotonous Choquet integrals

Choquet integrals allow to define the utility, respectively a risk-adjusted value, of a bounded random payment, or alternatively a (coherent) risk measure by changing the sign. We show that a necessary and sufficient condition for dilatation monotonicity of a Choquet integral is the convexity of the corresponding capacity with respect to the underlying probability measure. It follows that utility functionals with respect to a Choquet integral are dilatation monotonous iff the defining Choquet integral is dilatation monotonous.