The present paper extends to higher degrees the well-known separation theorem decomposing a shift in the increasing convex order into a combination of a shift in the usual stochastic order followed by another shift in the convex order. An application in decision making under risk is provided to...

The utility premium is generally defined as the pain or reduction in expected utility caused by an nth-degree risk increase, where n≥2. While it is a very useful concept in understanding a decision maker’s choice in uncertain situations, the utility premium is not interpersonally comparable....

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an mth degree risk increase, where nm⩾1. The paper shows that the rate of substitution...