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Rubinstein2005-page127 - 12:18 master Sheet number 125 Page...

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October 21, 2005 12:18 master Sheet number 125 Page number 109 Risk Aversion 109 Nevertheless, in the economic literature it is usually assumed that a decision maker’s preferences over wealth changes are induced from his preferences with regard to “final wealth levels.” Formally, when starting with wealth w , denote by w the decision maker’s prefer- ences over lotteries in which the prizes are interpreted as “changes” in wealth. By the doctrine of consequentialism all relations w are de- rived from the same preference relation, , defined over the “final wealth levels” by p w q iff w + p w + q (where w + p is the lottery that awards a prize w + x with probability p ( x ) ). If is represented by a vNM utility function u , this doctrine implies that for all w , the function v w ( x ) = u ( w + x ) is a vNM utility function representing the preferences w . Invariance to Wealth We say that the preference relation exhibits invariance to wealth (in the literature it is often called constant absolute risk aversion ) if
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