On the Economic Meaning of Machina's Frechet Differentiability Assumption
This note shows that Machina's (1982) assumption that preferences over lotteries are smooth has some economic implications. We show that Fréchet 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 Fréchet differentiability are equivalent.
(This abstract was borrowed from another version of this item.)
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- 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.
- L. Epstein & S. Zin, 2010. "First order risk aversion and the equity premium puzzle," Levine's Working Paper Archive 1400, David K. Levine.
- 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.
- Edi Karni, 1995. "Non-Expected Utility and The Robustness of the Classical Insurance Paradigm: Discussion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 51-56, June.
- Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
- Uzi Segal & Avia Spivak, 1988. "First Order Versus Second Order Risk Aversion," UCLA Economics Working Papers 540, UCLA Department of Economics.
- Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
- Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
- 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.
- 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.
- Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
- Loomes, Graham & Segal, Uzi, 1994. "Observing Different Orders of Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 239-256, December.
- Graham Loomes & Uzi Segal, "undated". "Observing Different Orders of Risk Aversion," Discussion Papers 92/5, Department of Economics, University of York.
- Wang Tan, 1993. "Lp-Frechet Differentiable Preference and Local Utility Analysis," Journal of Economic Theory, Elsevier, vol. 61(1), pages 139-159, October.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
- Machina, Mark J, 2001. "Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-260, November. Full references (including those not matched with items on IDEAS)