Game-theoretic foundations for probability and finance
Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk 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 a...
| Main Authors: | , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, NJ
John Wiley & Sons, Inc.
2019
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | |
| Collection: | O'Reilly - Collection details see MPG.ReNa |
Table of Contents:
- 13.5 Getting Rich Quick with the Axiom of Choice
- 13.6 Exercises
- 13.7 Context
- Chapter 14 A Game-Theoretic Ito Calculus
- 14.1 Martingale Spaces
- 14.2 Conservatism of Continuous Martingales
- 14.3 Ito Integration
- 14.4 Covariation and Quadratic Variation
- 14.5 Ito'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
- Chapter 15 Numeraires in Market Spaces
- 15.1 Market Spaces
- 15.2 Martingale Theory in Market Spaces
- 15.3 Girsanov's Theorem
- 15.4 Exercises
- 15.5 Context
- Chapter 16 Equity Premium and CAPM
- 16.1 Three Fundamental Continuous I-Martingales
- 16.2 Equity Premium
- 16.3 Capital Asset Pricing Model
- 16.4 Theoretical Performance Deficit
- 16.5 Sharpe Ratio
- 16.6 Exercises
- 16.7 Context
- Chapter 17 Game-Theoretic Portfolio Theory
- 17.1 Stroock-Varadhan Martingales
- 17.2 Boosting Stroock-Varadhan Martingales
- 17.3 Outperforming the Market with Dubins-Schwarz
- 17.4 Jeffreys's Law in Finance
- 17.5 Exercises
- 17.6 Context
- Terminology and Notation
- List of Symbols
- References
- Index
- EULA.
- 7.4 Lindeberg's Central Limit Theorem for Martingales
- 7.5 General Abstract Testing Protocols
- 7.6 Making the Results of Part I Abstract
- 7.7 Exercises
- 7.8 Context
- Chapter 8 Zero-One Laws
- 8.1 LÉvy's Zero-One Law
- 8.2 Global Upper Expectation
- 8.3 Global Upper and Lower Probabilities
- 8.4 Global Expected Values and Probabilities
- 8.5 Other Zero-One Laws
- 8.6 Exercises
- 8.7 Context
- Chapter 9 Relation to Measure-Theoretic Probability
- 9.1 VILLE'S THEOREM
- 9.2 Measure-Theoretic Representation of Upper Expectations
- 9.3 Embedding Game-Theoretic Martingales in Probability Spaces
- 9.4 Exercises
- 9.5 Context
- Part III Applications in Discrete Time
- Chapter 10 Using Testing Protocols in Science and Technology
- 10.1 Signals in Open Protocols
- 10.2 Cournot's Principle
- 10.3 Daltonism
- 10.4 Least Squares
- 10.5 Parametric Statistics with Signals
- 10.6 Quantum Mechanics
- 10.7 Jeffreys's Law
- 10.8 Exercises
- 10.9 Context
- Chapter 11 Calibrating Lookbacks and p-Values
- 11.1 Lookback Calibrators
- 11.2 Lookback Protocols
- 11.3 Lookback Compromises
- 11.4 Lookbacks in Financial Markets
- 11.5 Calibrating p-values
- 11.6 Exercises
- 11.7 Context
- Chapter 12 Defensive Forecasting
- 12.1 Defeating Strategies for Skeptic
- 12.2 Calibrated Forecasts
- 12.3 Proving the Calibration Theorems
- 12.4 Using Calibrated Forecasts for Decision Making
- 12.5 Proving the Decision Theorems
- 12.6 From Theory to Algorithm
- 12.7 Discontinuous Strategies for Skeptic
- 12.8 Exercises
- 12.9 Context
- Part IV Game-Theoretic Finance
- Chapter 13 Emergence of Randomness in Idealized Financial Markets
- 13.1 Capital Processes and Instant Enforcement
- 13.2 Emergence of Brownian Randomness
- 13.3 Emergence of Brownian Expectation
- 13.4 Applications of Dubins-Schwarz
- Cover
- Title Page
- Copyright
- Contents
- Preface
- Acknowledgments
- Part I Examples in Discrete Time
- Chapter 1 Borel's Law of Large Numbers
- 1.1 A Protocol for Testing Forecasts
- 1.2 A Game-Theoretic Generalization of Borel's Theorem
- 1.3 Binary Outcomes
- 1.4 Slackenings and Supermartingales
- 1.5 Calibration
- 1.6 The Computation of Strategies
- 1.7 Exercises
- 1.8 Context
- Chapter 2 Bernoulli's and De Moivre's Theorems
- 2.1 Game-Theoretic Expected value and Probability
- 2.2 Bernoulli's Theorem for Bounded Forecasting
- 2.3 A Central Limit Theorem
- 2.4 Global Upper Expected Values for Bounded Forecasting
- 2.5 Exercises
- 2.6 Context
- Chapter 3 Some Basic Supermartingales
- 3.1 Kolmogorov's Martingale
- 3.2 Doléans's Supermartingale
- 3.3 Hoeffding's Supermartingale
- 3.4 Bernstein's Supermartingale
- 3.5 Exercises
- 3.6 Context
- Chapter 4 Kolmogorov's Law of Large Numbers
- 4.1 Stating Kolmogorov's Law
- 4.2 Supermartingale Convergence Theorem
- 4.3 How Skeptic Forces Convergence
- 4.4 How Reality Forces Divergence
- 4.5 Forcing Games
- 4.6 Exercises
- 4.7 Context
- Chapter 5 The Law of the Iterated Logarithm
- 5.1 Validity of the Iterated-Logarithm Bound
- 5.2 Sharpness of the Iterated-Logarithm Bound
- 5.3 Additional Recent Game-Theoretic Results
- 5.4 Connections with Large Deviation Inequalities
- 5.5 Exercises
- 5.6 Context
- Part II Abstract Theory in Discrete Time
- Chapter 6 Betting on a Single Outcome
- 6.1 Upper and Lower Expectations
- 6.2 Upper and Lower Probabilities
- 6.3 Upper Expectations with Smaller Domains
- 6.4 Offers
- 6.5 Dropping the Continuity Axiom
- 6.6 Exercises
- 6.7 Context
- Chapter 7 Abstract Testing Protocols
- 7.1 Terminology and Notation
- 7.2 Supermartingales
- 7.3 Global Upper Expected Values
- Includes bibliographical references and index