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Stochastic Dominance with Specific Distributions

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

Abstract

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).

Keywords

Lognormal Distribution Risky Asset Strict Inequality Stochastic Dominance Specific Distribution 
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Notes

  1. 1.
    Markowitz, H.M., “Portfolio Selection,” Journal of Finance, 7, March 1952, pp. 77–91.Google Scholar
  2. Markowitz, H.M., Portfolio Selection, New York, Wiley 1959.Google Scholar
  3. Markowitz, H.M., Mean-Variance Analysis in Portfolio Choice and Capital Markets, Basil Blackwell, New York, 1987.Google Scholar
  4. 2.
    Sharpe, W.F., “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 19, September 1964, pp. 425–442.Google Scholar
  5. 5.
    For more details on the lognormal distribution, see Aitchison, J., and J.A.C. Brown, The Lognormal Distribution, Cambridge: Cambridge University Press, 1963.Google Scholar
  6. 7.
    Levy H., and Kroll, Y., “Stochastic Dominance with Riskless Assets,” Journal of Financial and Quantitative Analyses, 11, December 1976, pp. 743–773.CrossRefGoogle Scholar
  7. 8.
    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
  8. 9.
    For the density function and other properties of truncated normal distribution, see Johnson, N., and S. Kotz Continuous Univariate Distributions, Boston: Houghton Mifflin, 1970.Google Scholar
  9. 10.
    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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