Greater Arrow–Pratt (Absolute) risk aversion of higher orders

Abstract

Higher-order risk attitudes are related to higher-order moments of risk, and are unequivocally characterized by the signs and levels of higher-order derivatives of utility functions. In contrast to the direction of higher-degree risk aversion, the intensity of higher-degree risk aversion beyond the Arrow–Pratt measure of absolute risk aversion is far from conclusive. The purpose of this paper is to develop a unified framework of greater (m,n)th-degree mixed risk aversion in the Arrow–Pratt tradition, which includes many competing notions of greater higher-degree (absolute) risk aversion proposed in the extant literature as special cases. Properties of greater (m,n)th-degree mixed risk aversion are studied, a choice-based characterization is established, and several applications are presented.