## The Kelly Capital Growth Investment Criterion: Theory and PracticeThis volume provides the definitive treatment of fortune's formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor's wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured. |

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### Contents

Part II Classic papers and theories | 141 |

Part III The relationship of Kelly to asset allocation | 299 |

Part IV Critics and assessing the good and bad properties of Kelly | 456 |

Part V Utility foundations | 573 |

Part VI Evidence of the use of Kelly type strategies by the great investors and others | 655 |

Bibliography | 833 |

839 | |

843 | |

### Common terms and phrases

analysis asset allocation asset prices assume assumption asymptotic asymptotic optimality benchmark Berkshire Hathaway Bernoulli Bernoulli trials bets blackjack Breiman capital growth concave consider constant consumption covariances decision deﬁned deﬁnition denote distribution dynamic Economics equation estimates example expected utility expected value Finance ﬁnancial ﬁnd ﬁnite ﬁrst ﬁxed fractional Kelly strategies funds gambling geometric Brownian motion geometric mean given growth rate Hakansson Hausch horse independent inﬁnite initial wealth investment strategy investor Journal Kelly criterion Lemma log-optimum logarithmic MacLean Markowitz maximizing maximum mean-variance measure Merton optimal investment optimal portfolio optimal strategy parameters payoff period Petersburg paradox portfolio selection positive probability problem properties proportions random variable rebalanced portfolio retum risk aversion risky assets Samuelson satisﬁes sequence Sharpe ratio small stocks speciﬁc Sports Betting stochastic Theorem theory Thorp utility function variance vector W. T. Ziemba wagers wealth goals zero