書名：GAME-THEORETIC FOUNDATIONS FOR PROBABILITY AND FINANCE 作者：SHAFER 出版年：2021 出版社：John Wiley ISBN：9780470903056 內容簡介： DESCRIPTION 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’s 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. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden. TABLE OF CONTENTS Preface xi Acknowledgments xv Part I Examples in Discrete Time 1 1 Borel’s Law of Large Numbers 5 2 Bernoulli’s and De Moivre’s Theorems 31 3 Some Basic Supermartingales 55 4 Kolmogorov’s Law of Large Numbers 69 5 The Law of the Iterated Logarithm 93 Part II Abstract Theory in Discrete Time 109 6 Betting on a Single Outcome 111 7 Abstract Testing Protocols 135 8 Zero-One Laws 157 9 Relation to Measure-Theoretic Probability 175 Part III Applications in Discrete Time 195 10 Using Testing Protocols in Science and Technology 197 11 Calibrating Lookbacks and p-Values 229 12 Defensive Forecasting 253 Part IV Game-Theoretic Finance 305 13 Emergence of Randomness in Idealized Financial Markets 309 14 A Game-Theoretic Itô Calculus 339 15 Numeraires in Market Spaces 371 16 Equity Premium and CAPM 385 17 Game-Theoretic Portfolio Theory 403 Terminology and Notation 419 List of Symbols 425 References 429 Index 455