description- – This note shows that Machina's (1982) assumption that preferences over lotteries are smooth has some economic implications. We show that FrÚchet 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 FrÚchet differentiability are equivalent.
subjectcollectiondatepublishercreatorformat subjectcollectiondatepublishercreatorformat description- – Rabin proved that a low level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. Rabin's arguments strongly depend on expected utility theory, but we show that similar arguments apply to almost all non-expected utility theories.
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