Comparative higher-order risk aversion and higher-order prudence

In this paper, we define the nth-degree utility premium as the pain associated with facing the passage from a more favorable risk to a less favorable risk, where the risk increase is specified by the notion of more nth-degree risk. We further define the nth-degree prudence utility premium as the increase in pain when the individual suffers a sure loss. We show that the nth-degree utility premium, normalized by the (n - 1)th derivative of the utility function evaluated at the initial wealth, can explain comparative risk aversion of higher orders. On the other hand, the nth-degree prudence utility premium, normalized by the nth derivative of the utility function evaluated at the initial wealth, can explain comparative prudence of higher orders. (C) 2018 Elsevier B.V. All rights reserved.