Crossing points of distributions and a theorem that relates them to second order stochastic dominance |
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Authors: | Edgar Elias Osuna |
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Institution: | Instituto de Estudios Superiores de Administración (IESA), Ave. IESA, San Bernardino, Caracas 1010, Venezuela |
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Abstract: | We state formal definitions for crossing points in pairs of distributions and give a detailed proof of a theorem that relates those points to the second order stochastic dominance (SSD). The theorem states that the fulfillment of the area balance conditions for SSD at the t values that correspond to crossing points, and at the limit t→∞, is a necessary and sufficient condition for its fulfillment at all t: {−∞<t<∞}, as required for the existence of SSD. We provide examples for the application of the theorem in the case of continuous distributions, including a continuous counter example to prove that the Mean-Variance criterion is not sufficient to state preferences under risk aversion. |
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Keywords: | primary 60E15 secondary 91B30 90B50 |
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