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Ordering risks: expected utility theory versus Yaari’s dual theory of risk. (English) Zbl 0907.90102

Summary: We introduce a class of partial orderings of risks that are dual to stochastic dominance orderings. These arise as “distortion free” orderings in Yaari’s dual theory of risk. We show that these dual orderings are equivalent to inverse stochastic dominance orderings. We motivate third dual stochastic dominance via insurance economics while providing an alternative interpretation for second (dual) stochastic dominance. We apply dual stochastic dominance to actuarial science and show how the dual ordering of risks is related to ordering income distributions in the economics of income inequality.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B82 Statistical methods; economic indices and measures
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B16 Utility theory
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