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Growth Versus Security in Dynamic Investment Analysis


  • L. C. MacLean

    (School of Business Administration, Dalhousie University, Halifax, Nova Scotia, Canada B3H 1Z5)

  • W. T. Ziemba

    (Faculty of Commerce, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2)

  • G. Blazenko

    (School of Business Administration, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6)


This paper concerns the problem of optimal dynamic choice in discrete time for an investor. In each period the investor is faced with one or more risky investments. The maximization of the expected logarithm of the period by period wealth, referred to as the Kelly criterion, is a very desirable investment procedure. It has many attractive properties, such as maximizing the asymptotic rate of growth of the investor's fortune. On the other hand, instead of focusing on maximal growth, one can develop strategies based on maximum security. For example, one can minimize the ruin probability subject to making a positive return or compute a confidence level of increasing the investor's initial fortune to a given final wealth goal. This paper is concerned with methods to combine these two approaches. We derive computational formulas for a variety of growth and security measures. Utilizing fractional Kelly strategies, we can develop a complete tradeoff of growth versus security. The theory is applicable to favorable investment situations such as blackjack, horseracing, lotto games, index and commodity futures and options trading. The results provide insight into how one should properly invest in these situations.

Suggested Citation

  • L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
  • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:11:p:1562-1585

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