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# First-Order Risk Aversion and Non-Differentiability

Listed:
• Segal, U.
• Spivak, A.

## 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]).
(This abstract was borrowed from another version of this item.)

## Suggested Citation

• Segal, U. & Spivak, A., 1995. "First-Order Risk Aversion and Non-Differentiability," UWO Department of Economics Working Papers 9519, University of Western Ontario, Department of Economics.
• Handle: RePEc:uwo:uwowop:9519
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## Citations

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Cited by:

1. Zvi Safra & Uzi Segal, 2008. "Calibration Results for Non-Expected Utility Theories," Econometrica, Econometric Society, vol. 76(5), pages 1143-1166, September.
2. repec:kap:iaecre:v:17:y:2011:i:2:p:169-180 is not listed on IDEAS
3. Safra, Zvi & Segal, Uzi, 2002. "On the Economic Meaning of Machina's Frechet Differentiability Assumption," Journal of Economic Theory, Elsevier, vol. 104(2), pages 450-461, June.
4. Matthias Lang, 2015. "First-Order and Second-Order Ambiguity Aversion," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_13, Max Planck Institute for Research on Collective Goods.
5. Dionne, Georges & Li, Jingyuan, 2014. "When can expected utility handle first-order risk aversion?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 403-422.

### Keywords

DECISION MAKING;

### JEL classification:

• D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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