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 (RA-n) utility premium as a measure of pain associated with facing the passage from one risk to a riskier one....

This paper shows that temperance is the highest order risk preferences condition for which spreading N independent and unfair risks provides the highest level of welfare than any other possible allocations of risks. These results are also interpreted through the concept of N-superadditivity of...