On the economic meaning of Machina's Fréchet differentiability assumption

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This note shows that M. J. Machina's (1982, Econometrica 50, 277-323) 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. Journal of Economic Literature Classification Number: D81.

Original languageEnglish
Pages (from-to)450-461
Number of pages12
JournalJournal of Economic Theory
Issue number2
StatePublished - 2002


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