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Apportioning of risks via stochastic dominance

Author: Eeckhoudt, Louis ; Schlesinger, Harris ; Tsetlin, IliaINSEAD Area: Decision SciencesIn: Journal of Economic Theory, vol. 144, no. 3, May 2009 Language: EnglishDescription: p. 994-1003.Type of document: INSEAD ArticleNote: Please ask us for this itemAbstract: Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50–50 lottery [XN + YM,YN + XM] dominates the lottery [XN + XM,YN + YM] via (N + M)thorder stochastic dominance. The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two “bad” lotteries in the same state, where “bad” is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as precautionary effects and tempering effects
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Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50–50 lottery [XN + YM,YN + XM] dominates the lottery [XN + XM,YN + YM] via (N + M)thorder stochastic dominance. The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two “bad” lotteries in the same state, where “bad” is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as precautionary effects and tempering effects

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