Abstract
This chapter focuses on Kelly's capital growth criterion for long-term portfolio growth. The Kelly (–Breiman–Bernoulli–Latané or capital growth) criterion is to maximize the expected value E log X of the logarithm of the random variable X, representing wealth. The chapter presents a treatment of the Kelly criterion and Breiman's results. Breiman's results can be extended to cover many if not most of the more complicated situations which arise in real-world portfolios Specifically, the number and distribution of investments can vary with the time period, the random variables need not be finite or even discrete, and a certain amount of dependence can be introduced between the investment universes for different time periods. The chapter also discusses a few relationships between the max expected log approach and Markowitz's mean-variance approach. It highlights a few misconceptions concerning the Kelly criterion, the most notable being the fact that decisions that maximize the expected log of wealth do not necessarily maximize expected utility of terminal wealth for arbitrarily large time horizons.
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