Rubinstein2005-page120

Rubinstein2005-page120 - L ( Z ) , For what pairs p , q L (...

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October 21, 2005 12:18 master Sheet number 118 Page number 102 102 Lecture Nine Figure 9.1 p frst-order stochastically dominates q . Now, iF G ( p , x k ) G ( q , x k ) For all k , then For all increasing u , Eu ( p ) = u ( x 0 ) + X k 1 G ( p , x k )( u ( x k ) u ( x k 1 )) u ( x 0 ) + X k 1 G ( q , x k )( u ( x k ) u ( x k 1 )) = Eu ( q ). Conversely, iF there exists k For which G ( p , x k )< G ( q , x k ) , then we can fnd an increasing Function u so that Eu ( p )< Eu ( q ) , by setting u ( x k ) u ( x k 1 ) to be very large and the other increments to be very small. We have just discussed the simplest example oF questions oF the type: “Given a set oF preFerence relations on
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Unformatted text preview: L ( Z ) , For what pairs p , q L ( Z ) is p % q For all % in the set? In the problem set you will discuss another example oF this kind oF question. Risk Aversion We say that % is risk averse iF For any lottery p , [ Ep ] % p . We will see now that For a decision maker with preFerences % obey-ing the vNM axioms, risk aversion is closely related to the concavity oF the vNM utility Function representing % ....
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