Game-Theoretic Foundations for Probability and Finance
- 7h 30m
- Glenn Shafer, Vladimir Vovk
- John Wiley & Sons (US)
- 2019
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.
About the Authors
Glenn Shafer is University Professor at Rutgers University.
Vladimir Vovk is Professor in the Department of Computer Science at Royal Holloway, University of London.
Shafer and Vovk are the authors of Probability and Finance: It's Only a Game, published by Wiley and co-authors of Algorithmic Learning in a Random World. Shafer's other previous books include A Mathematical Theory of Evidence and The Art of Causal Conjecture.
In this Book
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Borel's Law of Large Numbers
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Bernoulli's and De Moivre's Theorems
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Some Basic Supermartingales
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Kolmogorov's Law of Large Numbers
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The Law of the Iterated Logarithm
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Betting on a Single Outcome
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Abstract Testing Protocols
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Zero-One Laws
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Relation to Measure-Theoretic Probability
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Using Testing Protocols in Science and Technology
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Calibrating Lookbacks and p-Values
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Defensive Forecasting
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Emergence of Randomness in Idealized Financial Markets
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A Game-Theoretic it Calculus
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Numeraires in Market Spaces
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Equity Premium and CAPM
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Game-Theoretic Portfolio Theory
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Terminology and Notation
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List of Symbols
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References
