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

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 Proba...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Shafer, Glenn
Otros Autores: Vovk, Vladimir
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2019.
Edición:2nd ed.
Temas:
Finance > Statistical methods.
Finance > Mathematical models.
Game theory.
Finances > Méthodes statistiques.
Finances > Modèles mathématiques.
Théorie des jeux.
Finance > Mathematical models
Finance > Statistical methods
Game theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 Forecasting2.5 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 Bound5.2 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 Values7.4 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 Spaces9.4 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

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