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Risk apportionment and stochastic dominance

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This paper characterizes higher order risk effects, such as prudence and temperance, via preferences that partially order a set of simple 50-50 lotteries. In particular, consider the random variables , , and , and assume that dominates via ith-order stochastic dominance for i = M, N. We show that the 50-50 lottery [ + , + ] dominates the lottery [ + , + ] via (N+M)th-order stochastic dominance. A preference ranking over these lotteries is shown to characterize higher orders of risk preference. We apply our results in several examples of decision making under risk.

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