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Growth–Security Models and Stochastic Dominance

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Stochastic Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 150))

Abstract

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.

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Author information

Authors and Affiliations

  1. Herbert Lamb Chair School of Business Administration, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Leonard C. MacLean

  2. Canada Research Chair (Tier II), School of Business Administration, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Yonggan Zhao

  3. Sauder School of Business, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    William T. Ziemba

  4. Mathematical Institute, University of Oxford, Oxford, England

    William T. Ziemba

  5. ICMA Center, University of Reading, Reading, UK

    William T. Ziemba

Authors
  1. Leonard C. MacLean
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  2. Yonggan Zhao
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  3. William T. Ziemba
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Corresponding author

Correspondence to Leonard C. MacLean .

Editor information

Editors and Affiliations

  1. Dept. Management Science & Engineering, Stanford University, Stanford, 94305, California, USA

    Gerd Infanger

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MacLean, L.C., Zhao, Y., Ziemba, W.T. (2010). Growth–Security Models and Stochastic Dominance. In: Infanger, G. (eds) Stochastic Programming. International Series in Operations Research & Management Science, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1642-6_13

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