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.
Chapter 11: Introduction to the Classic Pagers and Theories (431
Chapter 12: Competitive Optimality of Logarithmic Investment (588
Contents: "The Early Ideas and Contributions: "Introduction to the
Early Ideas and ContributionsExposition 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 Latane)"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 TheoriesCompetitive
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-Hoppe)"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 Alloca
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