Apportioning of risks via stochastic dominance - Louis Eeckhoudt; Harris Schlesinger; Ilia Tsetlin (Center for Economic Studies and ifo Institute (CESifo), 2008)
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)th-order 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.
Keywords: D81; 330; Downside risk; precautionary effects; prudence; risk apportionment; risk aversion; stochastic dominance; temperance; Entscheidung bei Unsicherheit; Entscheidung bei Risiko; Stochastischer Prozess; Risikoaversion; Theorie