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First-order risk aversion and non-differentiability

Authors:	Uzi Segal and Avia Spivak

Institution:	(1) Department of Economics, University of Western Ontario, N6A 5C2 London, Canada;(2) Department of Economics, Ben Gurion University, 84105 Beer Sheva, Israel

Abstract:	Summary First-order risk aversion happens when the risk premium a decision maker is willing to pay to avoid the lottery $t \cdot \tilde \varepsilon , E\tilde \varepsilon ] = 0$ , is proportional, for smallt, tot. Equivalently, $\partial \pi /\partial t\|_{ t = 0^ + } > 0$ . We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina 7]).We are grateful to the Social Sciences and Humanities Research Council of Canada for financial support and to Kim Border, Larry Epstein, Mark Machina and Joe Ostroy for helpful discussions and suggestions.

Keywords:	D8
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