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.
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Length: 14 pages Date of creation: 01 Oct 2001 Date of revision: Handle: RePEc:boc:bocoec:511
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Find related papers by JEL classification: D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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