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

Author

Listed:
  • Uzi Segal

    (Department of Economics, University of Western Ontario, London, CANADA N6A 5C2)

  • Avia Spivak

    (Department of Economics, Ben Gurion University, Beer Sheva 84105, ISRAEL)

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]).

Suggested Citation

  • Uzi Segal & Avia Spivak, 1996. "First-order risk aversion and non-differentiability (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 179-183.
    • Handle: RePEc:spr:joecth:v:9:y:1996:i:1:p:179-183
    Note: Received: June 26, 1995; revised version November 20, 1995
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    Cited by:

    1. repec:kap:iaecre:v:17:y:2011:i:2:p:169-180 is not listed on IDEAS
    2. 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.
    3. Matthias Lang, 2017. "First-Order and Second-Order Ambiguity Aversion," Management Science, INFORMS, vol. 63(4), pages 1254-1269, April.
    4. 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.
    5. Zvi Safra & Uzi Segal, 2008. "Calibration Results for Non-Expected Utility Theories," Econometrica, Econometric Society, vol. 76(5), pages 1143-1166, September.
    6. Battauz, Anna & De Donno, Marzia & Ortu, Fulvio, 2011. "Intertemporal asset pricing and the marginal utility of wealth," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 227-244, March.

    More about this item

    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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