Decreasing Ross risk aversion: Higher-order generalizations and implications

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. Meanwhile, the utility functional form of the agent with decreasing (n+1)-th degree Ross risk aversion is specified. Our result also implies decreasing 3-rd degree Ross risk aversion can be used to characterize the sufficient condition of risk vulnerability. Moreover, our analysis shows the implication of decreasing n/m-th (n>m≥1) Ross risk aversion.