Author:
Shafer, Glenn, 1946- author.
ImprintHoboken, NJ : John Wiley & Sons, Inc., 2019.
Descriptionxvi, 464 pages : illustrations ; 24 cm.
Note:Part I. Examples in Discrete Time -- Borel's Law of Large Numbers -- Bernoulli's and De Moivre's Theorems -- Some Basic Supermartingales -- Kolmogorov's Law of Large Numbers -- The Law of the Iterated Logarithm -- Part II. Abstract Theory in Discrete Time -- Betting on a Single Outcome -- Abstract Testing Protocols -- Zero-One Laws -- Relation to Measure-Theoretic Probability -- Part III. Applications in Discrete Time -- Using Testing Protocols in Science and Technology -- Calibrating Lookbacks and p-Values -- Defensive Forecasting -- Part IV. Game-Theoretic Finance -- Emergence of Randomness in Idealized Financial Markets -- A Game-Theoretic Itô Calculus -- Numeraires in Market Spaces -- Equity Premium and CAPM -- Game-Theoretic Portfolio Theory.
Bibliography Note:Includes bibliographical references (pages 429-454) and index.
Note:"Game-theoretic probability and finance come of age. Glenn Shafer and Vladimir Vovk's Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context." --Back cover.
