Game-Theoretic Probability: Theory and Applications to Prediction, Science, and Finance

✍ Scribed by Glenn Shafer, Vladimir Vovk

• Publisher: Wiley
• Year: 2019
• Tongue: English
• Leaves: 483
• Series: Wiley Series in Probability and Statistics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Part I Examples in Discrete Time
1 Borel’s Law of Large Numbers
2 Bernoulli’s and De Moivre’s Theorems
3 Some Basic Supermartingales
4 Kolmogorov’s Law of Large Numbers
5 The Law of the Iterated Logarithm

Part II Abstract Theory in Discrete Time
6 Betting on a Single Outcome
7 Abstract Testing Protocols
8 Zero-One Laws
9 Relation to Measure-Theoretic Probability

Part III Applications in Discrete Time
10 Using Testing Protocols in Science and Technology
11 Calibrating Lookbacks and p-Values
12 Defensive Forecasting

Part IV Game-Theoretic Finance
13 Emergence of Randomness in Idealized Financial Markets
14 A Game-Theoretic Itô Calculus
15 Numeraires in Market Spaces
16 Equity Premium and CAPM
17 Game-Theoretic Portfolio Theory

Terminology and Notation
List of Symbols
References
Index

✦ Subjects

Probability; Game Theory; Finance; Mathematical Foundations of Probability