Game-theoretic foundations for probability and finance

Game-theoretic foundations for probability 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 Probabilit...

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Detalles Bibliográficos
Otros Autores: Shafer, Glenn, 1946- author (author), Vovk, Vladimir, 1960- author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, NJ : Wiley 2019.
Edición:1st edition
Colección:Wiley series in probability and statistics.
Materias:
Finance > Statistical methods.
Finance > Mathematical models.
Game theory.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009631597306719
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 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.
  • 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.
  • 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.

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