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On the Economic Meaning of Machina's Frechet Differentiability Assumption

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  • Safra, Zvi
  • Segal, Uzi

Abstract

This note shows that Machina's (1982) assumption that preferences over lotteries are smooth has some economic implications. We show that Frâ„chet differentiability implies that preferences represent second order risk aversion (as well as conditional second order risk aversion). This implies, among other things, that decision makers buy full insurance only at the absence of marginal loading. We also show that with constant absolute and relative risk aversion, expected value maximization, second order risk aversion, and Frâ„chet differentiability are equivalent.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 104 (2002)
Issue (Month): 2 (June)
Pages: 450-461

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Handle: RePEc:eee:jetheo:v:104:y:2002:i:2:p:450-461

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
  2. Epstein, Larry G. & Zin, Stanley E., 1990. "'First-order' risk aversion and the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 26(3), pages 387-407, December.
  3. Machina, Mark J, 2000. "Payoff Kinks in Preferences Over Lotteries," University of California at San Diego, Economics Working Paper Series qt7vn7d2hs, Department of Economics, UC San Diego.
  4. Loomes, Graham & Segal, Uzi, 1994. "Observing Different Orders of Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 239-56, December.
  5. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  7. Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
  8. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  9. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  10. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  11. Edi Karni, 1995. "Non-Expected Utility and The Robustness of the Classical Insurance Paradigm: Discussion," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 20(1), pages 51-56, June.
  12. 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.
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Cited by:
  1. Alon Harel & Zvi Safra & Uzi Segal, 2003. "Ex-Post Egalitarianism," Boston College Working Papers in Economics 563, Boston College Department of Economics.

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