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.