Growth–Security Models and Stochastic Dominance

  • Leonard C. MacLean
  • Yonggan Zhao
  • William T. Ziemba
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 150)


The accumulated wealth from investment in risky assets is a random variable. If investment strategies are to be ordered, so that one is preferred to another, then the ordering of random variables is required. In this paper the levels of stochastic dominance for random variables are used to define bi-criteria problems for determining an efficient investment strategy. The criteria are characterized as growth and security, respectively, and produce an ordering of strategies consistent with stochastic dominance. In the case where the dynamics of asset returns follow geometric Brownian motion in continuous time, the efficient strategies are shown to be proportional to the growth optimum or Kelly strategy. The analogous problem in discrete time requires solving a stochastic program. An example is provided which compares the continuous and discrete time solutions.


Asset Price Planning Horizon Investment Strategy Risky Asset Stochastic Dominance 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Leonard C. MacLean
    • 1
  • Yonggan Zhao
    • 2
  • William T. Ziemba
    • 3
    • 4
    • 5
  1. 1.Herbert Lamb Chair School of Business AdministrationDalhousie UniversityHalifaxCanada
  2. 2.Canada Research Chair (Tier II), School of Business AdministrationDalhousie UniversityHalifaxCanada
  3. 3.Sauder School of BusinessUniversity of British ColumbiaVancouverCanada
  4. 4.Mathematical InstituteUniversity of OxfordOxfordEngland
  5. 5.ICMA CenterUniversity of ReadingReadingUK

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