Decreasing Ross Risk Aversion: Higher-Order Generalizations and Implications

Abstract

We define decreasing higher-degree Ross risk aversion and provide an intuitive interpretation for it. We show that all deteriorations of background risk in the sense of n-th risk increase raise risk aversion in the Arrow-Pratt sense if and only if decreasing (n 1)-th degree Ross risk aversion holds; Our result implies that (i) any zero-mean background risk leads more risk aversion if and only if decreasing downside risk aversion holds; (ii) decreasing Arrow-Pratt absolute risk aversion and decreasing downside risk aversion are equivalent to risk vulnerability.

Keywords: Decreasing n-th Ross risk aversion, n-th risk increase, background Risk, risk

JEL Classification: D81