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Rubinstein2005-page123

Rubinstein2005-page123 - satisfying vNM assumptions(See Fg...

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October 21, 2005 12:18 master Sheet number 121 Page number 105 Risk Aversion 105 Figure 9.3 1 is more risk averse than 2. In case the preferences satisfy vNM assumptions, we have a third deFnition: 3. Let u 1 and u 2 be vNM utility functions representing % 1 and % 2 , respectively. The preference relation % 1 is more risk averse than % 2 if the function ϕ , deFned by u 1 ( t ) = ϕ( u 2 ( t )) , is concave. I Fnd deFnition (1) particularly attractive since it is meaningful in any space of prizes (not only those in which consequences are numerical) and for a general set of preferences (and not only those
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Unformatted text preview: satisfying vNM assumptions). (See Fg. 9.3.) Claim: If both % 1 and % 2 are preference relations on L ( Z ) represented by increasing and continuous vNM utility functions, then the three deFnitions are equivalent. Proof: • If (2), then (1). Assume (2). Then, if p % 1 [ c ] , it has to be that [ CE 1 ( p ) ] % 1 [ c ] and thus CE 1 ( p ) ≥ c , which implies also that CE 2 ( p ) ≥ c , that is, p % 2 [ c ] ....
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