Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks
25 Pages Posted: 10 Feb 2012 Last revised: 5 Apr 2019
Date Written: February 11, 2013
This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessarily mean independent, and may be conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross for mean independent risks. Our theoretical results propose new insights into comparing the welfare costs of business cycles and are related to utility functions having the n-switch independence property. They can be applied to many other economic situations implying a background risk.
Keywords: Comparative cross Ross risk aversion, dependent background risk, partial risk premium, decreasing cross Ross risk aversion, n-switch independence property
JEL Classification: D81
Suggested Citation: Suggested Citation