First-order risk aversion and non-differentiability (*)

Uzi Segal and Avia Spivak
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Avia Spivak: Department of Economics, Ben Gurion University, Beer Sheva 84105, ISRAEL

Economic Theory, 1996, vol. 9, issue 1, 179-183

Abstract: First-order risk aversion happens when the risk premium a decision maker is willing to pay to avoid the lottery $t\cdot {\tilde \epsilon }, E[{\tilde \epsilon }]=0,$ is proportional, for small t, to t. Equivalently, $\partial \pi /\partial t\mid_{t=0^{+}}> 0.$ We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).

Date: 1996
Note: Received: June 26, 1995; revised version November 20, 1995
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