Zeroth Order Risk Aversion and Its Measures

Abstract

We define zeroth order risk neutrality, risk aversion, risk loving, and mixed risk attitude based on risk-taking behaviors and show that an agent displays the four zeroth order risk attitudes if and only if his local utility function is continuous, right continuous but left discontinuous, left continuous but right discontinuous, or left and right discontinuous, respectively. We then derive five zeroth order risk aversion measures and show how these measures, together with the first and second order risk aversion measures, determine risk premium, probability premium, the sign of utility premium, and portfolio decisions.

Keywords: zeroth order risk attitude, zeroth order risk aversion measures, discontinuous utility functions.

JEL Classification: D81, G11