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On the Economic Meaning of Machina's Frâ„chet Differentiability Assumption

  • Zvi Safra

    (Tel Aviv University)

  • Uzi Segal

    ()

    (Boston College)

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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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 511.

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Length: 14 pages
Date of creation: 01 Oct 2001
Date of revision:
Handle: RePEc:boc:bocoec:511
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  1. L. Epstein & S. Zin, 2010. "First order risk aversion and the equity premium puzzle," Levine's Working Paper Archive 1400, David K. Levine.
  2. Uzi Segal & Avia Spivak, 1988. "First Order Versus Second Order Risk Aversion," UCLA Economics Working Papers 540, UCLA Department of Economics.
  3. Loomes, Graham & Segal, Uzi, 1994. "Observing Different Orders of Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 239-56, December.
  4. Uzi Segal & Avia Spivak, 1996. "First-order risk aversion and non-differentiability (*)," Economic Theory, Springer, vol. 9(1), pages 179-183.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  6. 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.
  7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  8. 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.
  9. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  10. Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
  11. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  12. 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.
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