On the Economic Meaning of Machina's Fréchet Differentiability Assumption

Zvi Safra and Uzi Segal
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Zvi Safra: Tel Aviv University

No 511, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: 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.

JEL-codes: D81 (search for similar items in EconPapers)
Date: 2001-10-01
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Journal Article: On the Economic Meaning of Machina's Frechet Differentiability Assumption (2002)
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