Alternative Approaches to Comparative n th-Degree Risk Aversion

This paper extends the three main approaches to comparative risk aversion—the risk premium approach and the probability premium approach of Pratt (1964) [Risk aversion in the small and in the large. Econometrica 32(1-2):122–136] and the comparative statics approach of Jindapon and Neilson (2007) [Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach. J. Econom. Theory 136(1):719–728]—to study comparative n th-degree risk aversion. These extensions can accommodate trading off an n th-degree risk increase and an m th-degree risk increase for any m , such that 1 ≤ m < n . It goes on to show that, in the expected utility framework, all of these general notions of comparative n th-degree risk aversion are equivalent and can be characterized by the concept of ( n/m )th-degree Ross more risk aversion of Liu and Meyer (2013) [Substituting one risk increase for another: A method for measuring risk aversion. J. Econom. Theory 148(6):2706–2718].