TY  - BOOK
AU  - Shafer,Glenn
AU  - Vovk,Vladimir
TI  - Game-Theoretic Foundations for Probability and Finance
T2  - Wiley Series in Probability and Statistics Series
SN  - 9781118547939
AV  - HG176.5 .S534 2019 
PY  - 2019///
CY  - Newark
PB  - John Wiley & Sons, Incorporated
KW  - Game theory
KW  - Electronic books
N1  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5741206
ER  -