We show that the only coherent distortion risk measure that is consistent with respect to 3-convex order and hence with stochastic dominance of order 3 is the expected value, thus generalizing previous results of Hurlimann and solving a problem posed by Yamai and Yoshiba
Bellini, F., Caperdoni, C. (2007). Coherent distortion risk measures and higher order stochastic dominances. NORTH AMERICAN ACTUARIAL JOURNAL, 2007(April), 35-42.
Coherent distortion risk measures and higher order stochastic dominances
BELLINI, FABIO;
2007
Abstract
We show that the only coherent distortion risk measure that is consistent with respect to 3-convex order and hence with stochastic dominance of order 3 is the expected value, thus generalizing previous results of Hurlimann and solving a problem posed by Yamai and Yoshiba
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