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Introduction to the Good and Bad Properties of Kelly

In: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE

Author

Listed:
  • Leonard C MacLean
  • Edward O Thorp
  • William T Ziemba

Abstract

Multiperiod lifetime investment-savings optimization dates at least to Ramsey (1928). Phelps (1962) extended the model to include uncertainty while maximizing expected utility of lifetime consumption by choosing between consumption and investment in a single risky asset using an additive utility function. He obtained explicit solutions for a constant member of the isolastic utility class. Samuelson (1969) and Merton (1969) in companion articles develop, following Ramsey (1928) and Phelps (1962), in both discrete-time and continuous time, lifetime portfolio selection models where the objective function is the discounted sum of concave functions of period by period consumption. Samuelson solves the case when there are interior maxima, and shows that for isoelastic period by period utility functions u′ (C) = Cδ−1, δ < 1, the optimal portfolio decisions are independent of current wealth at each stage and independent of all consumption-savings decisions with a stationary optimal policy to invest a fixed proportion of current wealth in each period. Ziemba and Vickson (2010) review this literature and point to some queries regarding the validity of the interior maxima as discussed in problems in Ziemba and Vickson (1975, 2006).

Suggested Citation

  • Leonard C MacLean & Edward O Thorp & William T Ziemba, 2011. "Introduction to the Good and Bad Properties of Kelly," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 30, pages 459-464, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814293501_0030
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