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Stochastic dominance in an ordinal world
Institution:1. Departamento de Matemáticas. Universidad de Castilla-La Mancha. Albacete, Spain;2. Departamento de Sistemas Informáticos. Universidad de Castilla-La Mancha. Albacete, Spain;3. Departamento de Matemáticas. Universidad de Castilla-La Mancha. Ciudad Real, Spain;1. Department of Medicine D, Rabin Medical Center, Beilinson hospital, Petach-Tikva, Israel;2. The Liver Institute, Rabin Medical Center, Beilinson hospital, Petach-Tikva, Israel;3. Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel;4. Coller School of Management, Tel Aviv University, Tel Aviv, Israel;5. Department of Cardiology, Rabin Medical Center, Petach-Tikva, Israel
Abstract:Existing stochastic dominance rules apply to variables such as income, wealth and rates of return, all of which are measured on cardinal scales. This study develops and applies stochastic dominance rules for ordinal data. It is shown that the new rules are consistent with the traditional von Neumann-Morgenstern expected utility approach, and that they are applicable and relevant in a wide variety of managerial decision making situations, where existing stochastic dominance rules fail to apply. We apply ordinal SD rules to the transformation of random variables.
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