This paper investigates how welfare losses for facing risks change as the risk environment of the decision-maker is altered. To that aim, we define the risk apportionment of order n (RAn) utility premium as a measure of pain associated with facing the passage from one risk to a riskier one. Changes in risks are expressed through the concept of stochastic dominance of order n. Three configurations of risk exposures are considered. The paper first shows how the RAn utility premium is modified when initial wealth becomes riskier. Second, the paper provides conditions on individual preferences for superadditivity of the RAn utility premium. Third, the paper investigates welfare changes of merging increases in risks. These results offer new interpretations of the sign of higher derivatives of the utility function.