On the Economic Meaning of Machina's Fréchet 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.
|Date of creation:||01 Oct 2001|
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9519, University of Western Ontario, Department of Economics.
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- repec:cdl:ucsdec:qt7vn7d2hs is not listed on IDEAS
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- L. Epstein & S. Zin, 2010. "First order risk aversion and the equity premium puzzle," Levine's Working Paper Archive 1400, David K. Levine.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
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- 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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