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.
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- 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.
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92/5, Department of Economics, University of York.
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7650, David K. Levine.
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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.
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540, UCLA Department of Economics.
- 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.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- 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.
- Wang Tan, 1993. "Lp-Frechet Differentiable Preference and Local Utility Analysis," Journal of Economic Theory, Elsevier, vol. 61(1), pages 139-159, October.
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