The risk aversion measure without the independence axiom

✍ Scribed by Aldo Montesano

• Book ID: 104642571
• Publisher: Springer US
• Year: 1988
• Tongue: English
• Weight: 604 KB
• Volume: 24
• Category: Article
• ISSN: 0040-5833
• DOI: 10.1007/bf00148959

✦ Synopsis

The risk premium (conveniently normalized) is defined as the measure of risk aversion. This measure does not require any relevant assumption in the theory of choice under uncertainty except the existence of a certainty equivalent. In particular, the independence axiom is not required. The measure of risk aversion of an action is provided not only for the case with one commodity and two consequences but also for the case with many commodities and consequences. The measure of mean risk aversion of all actions with given consequences is introduced and the local measure of risk aversion is obtained by making all these consequences approach the consequence under consideration. This measure is demonstrated to be zero when the yon Neumann-Morgenstern utility function exists. In this case a measure of risk aversion of the second order is introduced, which turns out to be equal to the Arrow-Pratt absolute index when there is only one commodity and similar to the generalized measures proposed by several authors when there are many commodities and two consequences.