Book description
Gametheoretic probability and finance come of age
Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfectinformation games can be used to define mathematical probability. Based on fifteen years of further research, GameTheoretic 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 gametheoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory.
GameTheoretic 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 measuretheoretic. In this groundbreaking work, Shafer and Vovk give a gametheoretic foundation instead. While being just as rigorous, the gametheoretic approach allows for vast and useful generalizations of classical measuretheoretic 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
“Shafer and Vovk have thoroughly rewritten their 2001 book on the gametheoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the gametheoretic and pathwise approaches to stochastic analysis and in their applications to continuoustime finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University
Table of contents
 Cover
 WILEY SERIES IN PROBABILITY AND STATISTICS
 Preface
 Acknowledgments
 Part I: Examples in Discrete Time
 Part II: Abstract Theory in Discrete Time
 Part III: Applications in Discrete Time

Part IV: Game‐Theoretic Finance
 13 Emergence of Randomness in Idealized Financial Markets

14 A Game‐Theoretic It Calculus
 14.1 Martingale Spaces
 14.2 Conservatism of Continuous Martingales
 14.3 It Integration
 14.4 Covariation and Quadratic Variation
 14.5 It's Formula
 14.6 DOLÉANS EXPONENTIAL AND LOGARITHM
 14.7 GAME‐THEORETIC EXPECTATION AND PROBABILITY
 14.8 Game‐Theoretic Dubins–Schwarz Theorem
 14.9 Coherence
 14.10 Exercises
 14.11 Context
 15 Numeraires in Market Spaces
 16 Equity Premium and CAPM
 17 Game‐Theoretic Portfolio Theory
 Terminology and Notation
 List of Symbols
 References
 Index
 End User License Agreement
Product information
 Title: GameTheoretic Foundations for Probability and Finance
 Author(s):
 Release date: May 2019
 Publisher(s): Wiley
 ISBN: 9780470903056
You might also like
book
Introduction to Probability
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding …
book
Advances in Financial Machine Learning
Machine learning (ML) is changing virtually every aspect of our lives. Today ML algorithms accomplish tasks …
book
Probability, Random Variables, Statistics, and Random Processes
Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduatelevel textbook. With …
book
Probability and Statistics for Computer Scientists, 2nd Edition
StudentFriendly Coverage of Probability, Statistical Methods, Simulation, and Modeling ToolsIncorporating feedback from instructors and researchers who …