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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- Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
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UCLA Economics Working Papers
540, UCLA Department of Economics.
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9519, University of Western Ontario, Department of Economics.
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"Observing Different Orders of Risk Aversion,"
92/5, Department of Economics, University of York.
- 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.
- Mark J Machina, 1982.
""Expected Utility" Analysis without the Independence Axiom,"
Levine's Working Paper Archive
7650, David K. Levine.
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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.
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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.
- 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.
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