This 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.Contents: The Early Ideas and Contributions: Introduction to the Early Ideas and Contributions Exposition of a New Theory on the Measurement of Risk (translated by Louise Sommer) (D Bernoulli) A New Interpretation of Information Rate (J R Kelly, Jr) Criteria for Choice among Risky Ventures (H A Latané) Optimal Gambling Systems for Favorable Games (L Breiman) Optimal Gambling Systems for Favorable Games (E O Thorp) Portfolio Choice and the Kelly Criterion (E O Thorp) Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions (N H Hakansson) On Optimal Myopic Portfolio Policies, with and without Serial Correlation of Yields (N H Hakansson) Evidence on the “Growth-Optimum-Model” (R Roll) Classic Papers and Theories: Introduction to the Classic Papers and Theories Competitive Optimality of Logarithmic Investment (R M Bell and T M Cover) A Bound on the Financial Value of Information (A R Barron and T M Cover) Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment (P H Algoet and T M Cover) Universal Portfolios (T M Cover) The Cost of Achieving the Best Portfolio in Hindsight (E Ordentlich and T M Cover) Optimal Strategies for Repeated Games (M Finkelstein and R Whitley) The Effect of Errors in Means, Variances and Co-Variances on Optimal Portfolio Choice (V K Chopra and W T Ziemba) Time to Wealth Goals in Capital Accumulation (L C MacLean, W T Ziemba, and Y Li) Survival and Evolutionary Stability of Rule the Kelly (I V Evstigneev, T Hens, and K R Schenk-Hoppé) Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes (Y Lv and B K Meister) The Relationship of Kelly Optimization to Asset Allocation: Introduction to the Relationship of Kelly Optimization to Asset Allocation Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time (S Browne) Growth versus Security in Dynamic Investment Analysis (L C MacLean, W T Ziemba, and G Blazenko) Capital Growth with Security (L C MacLean, R Sanegre, Y Zhao, and W T Ziemba) Risk-Constrained Dynamic Active Portfolio Management (S Browne) Fractional Kelly Strategies for Benchmark Asset Management (M Davis and S Lleo) A Benchmark Approach to Investing and Pricing (E Platen) Growing Wealth with Fixed-Mix Strategies (M A H Dempster, I V Evstigneev, and K R Schenk-Hoppé) Critics and Assessing the Good and Bad Properties of Kelly: Introduction to the Good and Bad Properties of Kelly Lifetime Portfolio Selection by Dynamic Stochastic Programming (P A Samuelson) Models of Optimal Capital Accumulation and Portfolio Selection and the Captial Growth Criterion (W T Ziemba and R G Vickson) The “Fallacy” of...