Orders of Probabilistic Risk Aversion

Abstract

In this paper we extend Segal and Spivak's (1990) discussion of orders of risk aversion to probabilistic risk attitudes, i.e., risk preferences represented by the transformation of (de)cumulative probability distribution functions, and discuss orders of probabilistic risk aversion. We define zeroth order probabilistic risk neutrality, risk aversion, risk loving, and mixed risk attitude; first order probabilistic risk neutrality, risk aversion, and risk loving; and second order probabilistic risk neutrality, risk aversion, and risk loving. We present a necessary and sufficient condition for each of these concepts and characterize corresponding risk taking behaviors, explaining the implications of discontinuity and nonsmoothness of probability weighting functions for risk preferences.

Keywords: zeroth order probabilistic risk aversion, first order probabilistic risk aversion, second order probabilistic risk aversion

JEL Classification: D81