Efficiency Of Racetrack Betting Markets (2008 Edition)

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Publisher : World Scientific
ISBN 13 : 9814470643
Total Pages : 679 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Efficiency Of Racetrack Betting Markets (2008 Edition) by : Donald B Hausch

Download or read book Efficiency Of Racetrack Betting Markets (2008 Edition) written by Donald B Hausch and published by World Scientific. This book was released on 2008-06-20 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reprint of one of the classic volumes on racetrack efficiency, this book is the only one in its field that deals with the racetrack betting market in-depth, containing all the important historical papers on racetrack efficiency. As evidenced by the collection of articles, the understanding of racetrack betting is clearly drawn from, and has correspondingly returned something to, all the fields of psychology, economics, finance, statistics, mathematics and management science.

Preface to

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Preface to by : Donald B. Hausch

Download or read book Preface to written by Donald B. Hausch and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reprint of one of the classic volumes on racetrack efficiency, this book is the only one in its field that deals with the racetrack betting market in-depth, containing all the important historical papers on racetrack efficiency. As evidenced by the collection of articles, the understanding of racetrack betting is clearly drawn from, and has correspondingly returned something to, all the fields of psychology, economics, finance, statistics, mathematics and management science.

Handbook of Sports and Lottery Markets

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Publisher : Elsevier
ISBN 13 : 0080559956
Total Pages : 561 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Sports and Lottery Markets by : Donald B. Hausch

Download or read book Handbook of Sports and Lottery Markets written by Donald B. Hausch and published by Elsevier. This book was released on 2011-08-11 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Its basic empirical research and investigation of pure theories of investment in the sports and lottery markets make this volume a winner. These markets are simpler to study than traditional financial markets, and their expected values and outcomes are uncomplicated. By means of new overviews of scholarship on the industry side of racetrack and other betting markets to betting exchanges and market efficiencies, contributors consider a variety of sports in countries around the world. The result is not only superior information about market forecasting, but macro- and micro-analyses that are relevant to other markets. Easily studied sports markets reveal features relevant for more complex traditional financial markets Significant coverage of sports from racing to jai alai New studies of betting exchanges and Internet wagering markets

Efficiency of the Market for Racetrack Betting

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (848 download)

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Book Synopsis Efficiency of the Market for Racetrack Betting by : Donald B. Hausch

Download or read book Efficiency of the Market for Racetrack Betting written by Donald B. Hausch and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Information Efficiency in Financial and Betting Markets

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Publisher : Cambridge University Press
ISBN 13 : 1139445405
Total Pages : 412 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Information Efficiency in Financial and Betting Markets by : Leighton Vaughan Williams

Download or read book Information Efficiency in Financial and Betting Markets written by Leighton Vaughan Williams and published by Cambridge University Press. This book was released on 2005-09-29 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The degree to which markets incorporate information is one of the most important questions facing economists today. This book provides a fascinating study of the existence and extent of information efficiency in financial markets, with a special focus on betting markets. Betting markets are selected for study because they incorporate features highly appropriate to a study of information efficiency, in particular the fact that each bet has a well-defined end point at which its value becomes certain. Using international examples, this book reviews and analyses the issue of information efficiency in both financial and betting markets. Part I is an extensive survey of the existing literature, while Part II presents a range of readings by leading academics. Insights gained from the book will interest students of financial economics, financial market analysts, mathematicians and statisticians, and all those with a special interest in finance or gambling.

Stochastic Programming

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Publisher : World Scientific
ISBN 13 : 981440750X
Total Pages : 549 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Stochastic Programming by : Horand Gassmann

Download or read book Stochastic Programming written by Horand Gassmann and published by World Scientific. This book was released on 2013 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.

The Kelly Capital Growth Investment Criterion

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Publisher : World Scientific
ISBN 13 : 9814293490
Total Pages : 883 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis The Kelly Capital Growth Investment Criterion by : Leonard C. MacLean

Download or read book The Kelly Capital Growth Investment Criterion written by Leonard C. MacLean and published by World Scientific. This book was released on 2011 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exotic Betting At The Racetrack

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Publisher : World Scientific
ISBN 13 : 9813278803
Total Pages : 489 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Exotic Betting At The Racetrack by : William T Ziemba

Download or read book Exotic Betting At The Racetrack written by William T Ziemba and published by World Scientific. This book was released on 2018-12-21 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exotic Betting at the Racetrack is unique as it covers the efficient-inefficient strategy to price and find profitable racetrack bets, along with handicapping that provides actual bets made by the author on essentially all of the major wagers offered at US racetracks. The book starts with efficiency, accuracy of the win odds, arbitrage, and optimal betting strategies. Examples and actual bets are shown for various wagers including win, place and show, exacta, quinella, double, trifecta, superfecta, Pick 3, 4 and 6 and rainbow pick 5 and 6. There are discussions of major races including the Breeders' Cup, Pegasus, Dubai World Cup and the US Triple Crown from 2012-2018. Dosage analysis is also described and used. An additional feature concerns great horses such as the great mares Rachel Alexandra, Zenyatta, Goldikova, Treve, Beholder and Song Bird. There is a discussion of horse ownership and a tour through arguably the world's top trainer Frederico Tesio and his stables and horses in Italy.Related Link(s)

Racetrack Betting

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Publisher : Praeger
ISBN 13 : 0275941035
Total Pages : 0 pages
Book Rating : 4.2/5 (759 download)

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Book Synopsis Racetrack Betting by : Peter Asch

Download or read book Racetrack Betting written by Peter Asch and published by Praeger. This book was released on 1991-10-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A day at the races, with its colorful variety and fast-paced action, appeals to people from all walks of life. Not surprisingly, the idea of going home with a few more dollars than when one arrived is part of horseracing's charm. In this entertaining but substantive volume, two distinguished economists, who happen to be horseracing buffs, outline a tested strategy for placing bets that will increase the reader's chances of a happy outcome at the track. The authors are the first to point out that getting rich at the racetrack is unlikely. They do maintain, however, that with attention to their systematic approach, the racing fan can achieve the best possible chance at winning. In the process, the reader learns some of the most important measurement techniques in the social sciences, as well as the basic methods of market analysis.

A Test of Market Efficiency in "exotic" Racetrack Betting

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Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (39 download)

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Book Synopsis A Test of Market Efficiency in "exotic" Racetrack Betting by : Peter Asch

Download or read book A Test of Market Efficiency in "exotic" Racetrack Betting written by Peter Asch and published by . This book was released on 1986 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The World Scientific Handbook of Futures Markets

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Publisher : World Scientific
ISBN 13 : 9814566926
Total Pages : 844 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis The World Scientific Handbook of Futures Markets by : Anastasios G. E. T. Al MALLIARIS

Download or read book The World Scientific Handbook of Futures Markets written by Anastasios G. E. T. Al MALLIARIS and published by World Scientific. This book was released on 2015-08-06 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The World Scientific Handbook of Futures Markets serves as a definitive source for comprehensive and accessible information in futures markets. The emphasis is on the unique characteristics of futures markets that make them worthy of a special volume. In our judgment, futures markets are currently undergoing remarkable changes as trading is shifting from open outcry to electronic and as the traditional functions of hedging and speculation are extended to include futures as an alternative investment vehicle in traditional portfolios. The unique feature of this volume is the selection of five classic papers that lay the foundations of the futures markets and the invitation to the leading academics who do work in the area to write critical surveys in a dozen important topics."--$cProvided by publisher.

The Economics of Sports Betting

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Publisher : Edward Elgar Publishing
ISBN 13 : 1785364553
Total Pages : pages
Book Rating : 4.7/5 (853 download)

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Book Synopsis The Economics of Sports Betting by : Plácido Rodríguez

Download or read book The Economics of Sports Betting written by Plácido Rodríguez and published by Edward Elgar Publishing. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book delves into a number of intriguing issues and addresses several pertinent questions including, should gambling markets be privatized? Is the ‘hot hand’ hypothesis real or a myth? Are the ‘many’ smarter than the ‘few’ in estimating betting odds? How are prices set in fixed odds betting markets? The book also explores the informational efficiency of betting markets and the prevalence of corruption and illegal betting in sports.

Handbook Of The Fundamentals Of Financial Decision Making (In 2 Parts)

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Publisher : World Scientific
ISBN 13 : 981441736X
Total Pages : 941 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Handbook Of The Fundamentals Of Financial Decision Making (In 2 Parts) by : Leonard C Maclean

Download or read book Handbook Of The Fundamentals Of Financial Decision Making (In 2 Parts) written by Leonard C Maclean and published by World Scientific. This book was released on 2013-05-10 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook in two parts covers key topics of the theory of financial decision making. Some of the papers discuss real applications or case studies as well. There are a number of new papers that have never been published before especially in Part II.Part I is concerned with Decision Making Under Uncertainty. This includes subsections on Arbitrage, Utility Theory, Risk Aversion and Static Portfolio Theory, and Stochastic Dominance. Part II is concerned with Dynamic Modeling that is the transition for static decision making to multiperiod decision making. The analysis starts with Risk Measures and then discusses Dynamic Portfolio Theory, Tactical Asset Allocation and Asset-Liability Management Using Utility and Goal Based Consumption-Investment Decision Models.A comprehensive set of problems both computational and review and mind expanding with many unsolved problems are in an accompanying problems book. The handbook plus the book of problems form a very strong set of materials for PhD and Masters courses both as the main or as supplementary text in finance theory, financial decision making and portfolio theory. For researchers, it is a valuable resource being an up to date treatment of topics in the classic books on these topics by Johnathan Ingersoll in 1988, and William Ziemba and Raymond Vickson in 1975 (updated 2nd edition published in 2006).

Handbook Of The Economics Of Wine (In 2 Volumes)

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Publisher : World Scientific
ISBN 13 : 9813232730
Total Pages : 1048 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Handbook Of The Economics Of Wine (In 2 Volumes) by : Gergaud Olivier

Download or read book Handbook Of The Economics Of Wine (In 2 Volumes) written by Gergaud Olivier and published by World Scientific. This book was released on 2018-03-21 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last three decades, wine economics has emerged as a growing field within agricultural economics, but also in other fields such as finance, trade, growth, environmental economics and industrial organization. Wine has a few characteristics that differentiate it from other agricultural commodities, rendering it an interesting topic for economists in general. Fine wine can regularly fetch bottle prices that exceed several thousand dollars. It can be stored a long time and may increase in value with age. Fine wine quality and prices are extraordinarily sensitive to fluctuations in the weather of the year in which the grapes were grown. And wine is an experience good, i.e., its quality cannot be ascertained before consumption. As a result, consumers often rely on 'expert opinion' regarding quality and maturation prospects.This handbook takes a broad approach and familiarizes the reader with the main research strands in wine economics.After a general introduction to wine economics by Karl Storchmann, Volume 1 focuses on the core areas of wine economics. The first papers shed light on the relevance of the vineyard's natural environment for wine quality and prices. 'Predicting the Quality and Prices of Bordeaux Wine' by Orley Ashenfelter is a classic paper and may be the first wine economics publication ever. Ashenfelter shows how weather influences the quality and the price of Bordeaux Grands Crus wine. Since the weather condition of the year when the grapes were grown is known, an econometric analysis may be constructed. It turns out this model outperforms expert opinion, i.e., critical vintage scores. At best, expert opinion reflects public information. The subsequent papers, by Ashenfelter and Storchmann, Gergaud and Ginsburgh, and Cross, Plantinga and Stavins, tackle the terroir question. That is, they examine the relevance of a vineyard's physical characteristics for wine quality and prices, but from various dimensions and with different results. Next, Alston et al. analyze a question of great concern in the California wine industry: the causes and consequences of the rising alcohol content in California wine. Is climate change the culprit?The next chapter presents three papers that apply hedonic price analyses to fine wine. Combris, Lecocq and Visser show that Bordeaux wine market prices are essentially determined by the wines' objective characteristics. Costanigro, McCluskey and Mittelhammer differentiate their hedonic analysis for various market segments. Ali and Nauges incorporate reputational variables into their pricing model and distinguish between short- and long-run price effects.The next section of this volume deals with one of the unique characteristics of wine — its long storage life, which makes it potentially an investment asset. Studying wine's increasing role as an alternative asset class, Sanning et al., Burton and Jacobsen, Masset and Weisskopf, Masset and Henderson, and Fogarty all examine the rate of return to holding wine as well as the related risks. Since these papers analyze different wines and different time periods there is no 'one message.' However, all point out that, while wine may diversify an investor's portfolio, wine's returns do not beat common stock in the long run.The last two chapters examine the role of wine experts. First, Ashenfelter and Quandt revisit the 1976 'Judgment of Paris' and show that aggregating the assessments of several judges should go beyond 'adding points.' Depending on the method employed, the results may vary, and some measure of statistical precision is essential for interpreting the reliability of the results. In two different papers, Cicchetti and Quandt respond to the necessity to provide statistical tools for the assessment of wine tastings.In a seminal paper, Hodgson reports a remarkable field experiment in which similar wines were placed before judges at a major competition. The results have the shocking implication that how medals are awarded at a major California wine fair is not far from being random. Ashton analyzes the performance of professional wine judges and finds little support for the idea that experienced wine judges should be regarded as experts.Do experts scores influence the price of wine? The answer to this question is less obvious then commonly thought since expert opinion oftentimes only repeats public information such as wine quality that results from the weather that produced the wine grapes. Hadj Ali, Lecocq, and Visser as well as Dubois and Nauges find that high critical scores exert only small effects on wine prices. However, Roberts and Reagans show that a high critical exposure reduces the price-quality dispersion of wineries.Lecocq and Visser analyze wine prices and find that 'characteristics that are directly revealed to the consumer upon inspection of the bottle and its label explain the major part of price differences.' Expert opinion and sensory variables appear to play only a minor role. In an experimental setting using two Vickrey auctions, Combris, Lange and Issanchou confirm the leading role of public information, i.e., the label remains a key determinant for champagne prices. In a provocative and widely discussed study drawing on blind tasting results of some 5,000 wines, Goldstein and collaborators find that most consumers prefer less expensive over expensive wine.Finally, Weil examines the value of expert wine descriptions and lets several hundred subjects match the wines and their descriptors. His results suggest that the ability to assign a certain description to the matching wine is more or less random.Volume 2 covers the topics reputation, regulation, auctions, and market organizational. Landon and Smith, Anderson and Schamel, and Schamel analyze the impact of current quality and reputation (i.e., past quality) on wine prices from different regions. Their results suggest that prices are more influenced by reputation than by current quality. Costanigro, McCluskey and Goemans develop a nested framework for jointly examining the effects of product, firm and collective reputation on market prices.The following four papers deal with regulatory issues in the US as well as in Europe. While Riekoff and Sykuta shed light on the politics and economics of the three-tier system of alcohol distribution and the prohibition of direct wine shipments in the US, Deconinck and Swinnen analyze the European planting rights system. The political economy of European wine regulation is then covered by Melonie and Swinnen, before Anderson and Jensen shed light on Europe's complex system of wine industry subsidies.The next chapter is devoted to wine auctions. In three different papers, Fevrier, Roos and Visser, Ashenfelter, and Ginsburgh analyze the effects of specific auction designs on the resulting hammer prices. The papers focus on multi-unit ascending auctions, absentee bidders, and declining price anomalies.The last chapter, supply and organization, is devoted to a wide range of issues. First, Heien illuminates the price formation process in the California winegrape industry. Then, Frick analyzes if and how the separation of ownership and control affects the performance of German wineries.Vink, Kleynhans and Willem Hoffmann introduce us to various models of wine barrel financing, particularly to the Vincorp model employed in South Africa. Galbreath analyzes the role of women in the wine industry. He finds that (1) women are underrepresented and (2) that the presence of a female CEO increases the likelihood of women in winemaker, viticulturist, and marketing roles in that firm. Gokcekus, Hewstone, and Cakal draw on crowdsourced wine evaluations, i.e., Wine Tracker data, and show that private wine assessments are largely influenced by peer scores lending support to the assumption of the presence of a strong herding effect.Mahenc refers to the classic model of information asymmetries and develops a theoretical model highlighting the role of informed buyers in markets that are susceptible to the lemons problem. Lastly, in their paper 'Love or Money?' Scott, Morton and Podolny analyze how the presence of hobby winemakers may distort market outcomes. Hobby winemakers produce higher quality wines, charge higher prices, and enjoy lower financial returns than professional for-profit winemakers. As a result, profit-oriented winemakers are discouraged from locating at the high-quality end of the market.

Investing at the Racetrack

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Author :
Publisher : Simon & Schuster
ISBN 13 : 9780671630171
Total Pages : 292 pages
Book Rating : 4.6/5 (31 download)

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Book Synopsis Investing at the Racetrack by : William L. Scott

Download or read book Investing at the Racetrack written by William L. Scott and published by Simon & Schuster. This book was released on 1986-07 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Adventures Of A Modern Renaissance Academic In Investing And Gambling

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Author :
Publisher : World Scientific
ISBN 13 : 9813148535
Total Pages : 484 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis The Adventures Of A Modern Renaissance Academic In Investing And Gambling by : Ziemba William T

Download or read book The Adventures Of A Modern Renaissance Academic In Investing And Gambling written by Ziemba William T and published by World Scientific. This book was released on 2017-08-23 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Kelly Capital Growth Investment Criterion, The: Theory And Practice

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Author :
Publisher : World Scientific
ISBN 13 : 981446581X
Total Pages : 883 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Kelly Capital Growth Investment Criterion, The: Theory And Practice by : Leonard C Maclean

Download or read book Kelly Capital Growth Investment Criterion, The: Theory And Practice written by Leonard C Maclean and published by World Scientific. This book was released on 2011-02-10 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 Latan‚)"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-Hopp‚)"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 AllocationSurvival 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)"