Stochastic Dominance with Specific Distributions

  • Haim Levy
Part of the Studies in Risk and Uncertainty book series (SIRU, volume 12)


In the derivation of the SD and SDR rules presented in the previous chapters (see Chapters 3 and 4), assumptions on preference, Ui are made but no assumptions are made on the shape of the distributions of rates of return. In that sense, stochastic dominance rules are distribution-free decision rules. However, assumptions on the shape of the distributions of rates of return can be added and, in some cases, parametric investment decision rules can be derived because the rules will be stated in terms of the distribution’s parameters (e.g., mean and variance).


Lognormal Distribution Risky Asset Strict Inequality Stochastic Dominance Specific Distribution 
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    The proof of this theorem is very long and cumbersome; hence, for the sake of brevity, it is not provided in the book. It appears in Kroll, Y., “Preferences Among Combinations of Risky Assets and a Riskless Asset: Criteria and Implication,” Ph.D. dissertation, Hebrew University, Israel, 1977.Google Scholar
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    See Baumol, W.J., “An Expected Gain Confidence Limit Criterion for Portfolio Selection,” Management Science, October, 10, 1963, pp. 174–182.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Haim Levy
    • 1
  1. 1.The Hebrew University of JerusalemIsrael

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