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Title: Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks
Authors: Dionne, Georges
Li, Jingyuan
Keywords: Comparative cross Ross risk aversion
Quadrant dependent background risk
Partial risk premium
Decreasing cross Ross risk aversion
n-switch utility functions
Issue Date: 2012-06
Series/Report no.: Cahiers du CIRPÉE;12-26
Abstract: This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Although the literature covers this question extensively, 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 necessary mean independent, and may be quadrant dependent. We show that our order of cross Ross risk aversion is equivalent to that of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to that of a decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross (1981) for mean independent risks. Finally, we show that decreasing cross Ross risk aversion gives rise to the utility function family belonging to the class of n-switch utility functions.
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