Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks

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 are related to utility functions having the n-switch independence property.