Orders of nth Degree Risk Aversion and Their Measures

Abstract

We extend Segal and Spivak's (1990) discussion of orders of risk attitudes to higher degree risk aversion and define (n-2)th, (n-1)th, and nth orders of nth degree risk attitudes. We show that the nth degree Arrow-Pratt risk aversion measure is an nth order measure, which works well when utility functions are sufficiently smooth; however when utility functions are not n-1 times differentiable, we need an (n-1)th order measure, and when utility functions are not n-2 times differentiable, we further need two (n-2)th order measures. We derive these (n-2)th and (n-1)th order measures and then present a comparative statics analysis under nth degree risk aversion for utility functions which are not n-2 times differentiable.

Keywords: nth degree risk aversion, (n-2)th order, (n-1)th order, nth order

JEL Classification: D81